Daily Papers

Voice activity detection (VAD) is an important pre-processing step for speech technology applications. The task consists of deriving segment boundaries of audio signals which contain voicing information. In recent years, it has been shown that voice source and vocal tract system information can be extracted using zero-frequency filtering (ZFF) without making any explicit model assumptions about the speech signal. This paper investigates the potential of zero-frequency filtering for jointly modeling voice source and vocal tract system information, and proposes two approaches for VAD. The first approach demarcates voiced regions using a composite signal composed of different zero-frequency filtered signals. The second approach feeds the composite signal as input to the rVAD algorithm. These approaches are compared with other supervised and unsupervised VAD methods in the literature, and are evaluated on the Aurora-2 database, across a range of SNRs (20 to -5 dB). Our studies show that the proposed ZFF-based methods perform comparable to state-of-art VAD methods and are more invariant to added degradation and different channel characteristics.

Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep understanding, improvement, and parallel execution. This paper develops a simple, generalized AD algorithm calculated from a simple, natural specification. The general algorithm is then specialized by varying the representation of derivatives. In particular, applying well-known constructions to a naive representation yields two RAD algorithms that are far simpler than previously known. In contrast to commonly used RAD implementations, the algorithms defined here involve no graphs, tapes, variables, partial derivatives, or mutation. They are inherently parallel-friendly, correct by construction, and usable directly from an existing programming language with no need for new data types or programming style, thanks to use of an AD-agnostic compiler plugin.

We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance tau. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision Processes (MDPs) setting. To extend CVaR RL to settings where state space is large, function approximation must be deployed. We study CVaR RL in low-rank MDPs with nonlinear function approximation. Low-rank MDPs assume the underlying transition kernel admits a low-rank decomposition, but unlike prior linear models, low-rank MDPs do not assume the feature or state-action representation is known. We propose a novel Upper Confidence Bound (UCB) bonus-driven algorithm to carefully balance the interplay between exploration, exploitation, and representation learning in CVaR RL. We prove that our algorithm achieves a sample complexity of Oleft(H^7 A^2 d^4{tau^2 epsilon^2}right) to yield an epsilon-optimal CVaR, where H is the length of each episode, A is the capacity of action space, and d is the dimension of representations. Computational-wise, we design a novel discretized Least-Squares Value Iteration (LSVI) algorithm for the CVaR objective as the planning oracle and show that we can find the near-optimal policy in a polynomial running time with a Maximum Likelihood Estimation oracle. To our knowledge, this is the first provably efficient CVaR RL algorithm in low-rank MDPs.

We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and leverages its underlying structure making the gradients sequentially predictable. By exploiting the predictability and ideas from optimistic online learning, the proposed algorithm can accelerate the convergence and increase sample efficiency. After establishing a tighter upper bound under some convexity conditions on the regret, we offer a complimentary view of our algorithm which generalizes the offline and stochastic version of nonconvex optimization. In the nonconvex case, we establish a non-asymptotic convergence bound independently of the initialization. We illustrate the practical speedup on several deep learning models via numerical experiments.

High-dimensional vector embeddings are widely used in retrieval systems, yet dimensionality reduction (DR) is seldom applied due to its tendency to distort nearest-neighbor (NN) structure critical for search. Existing DR techniques such as PCA and UMAP optimize global or manifold-preserving criteria, rather than retrieval-specific objectives. We present MPAD: Maximum Pairwise Absolute Difference, an unsupervised DR method that explicitly preserves approximate NN relations by maximizing the margin between k-NNs and non-k-NNs under a soft orthogonality constraint. This design enables MPAD to retain ANN-relevant geometry without supervision or changes to the original embedding model. Experiments across multiple domains show that MPAD consistently outperforms standard DR methods in preserving neighborhood structure, enabling more accurate search in reduced dimensions.

Remote sensing object detection (RSOD) faces formidable challenges in complex visual environments. Aerial and satellite images inherently suffer from limitations such as low spatial resolution, sensor noise, blurred objects, low-light degradation, and partial occlusions. These degradation factors collectively compromise the feature discriminability in detection models, resulting in three key issues: (1) reduced contrast that hampers foreground-background separation, (2) structural discontinuities in edge representations, and (3) ambiguous feature responses caused by variations in illumination. These collectively weaken model robustness and deployment feasibility. To address these challenges, we propose LEGNet, a lightweight network that incorporates a novel edge-Gaussian aggregation (EGA) module specifically designed for low-quality remote sensing images. Our key innovation lies in the synergistic integration of Scharr operator-based edge priors with uncertainty-aware Gaussian modeling: (a) The orientation-aware Scharr filters preserve high-frequency edge details with rotational invariance; (b) The uncertainty-aware Gaussian layers probabilistically refine low-confidence features through variance estimation. This design enables precision enhancement while maintaining architectural simplicity. Comprehensive evaluations across four RSOD benchmarks (DOTA-v1.0, v1.5, DIOR-R, FAIR1M-v1.0) and a UAV-view dataset (VisDrone2019) demonstrate significant improvements. LEGNet achieves state-of-the-art performance across five benchmark datasets while ensuring computational efficiency, making it well-suited for deployment on resource-constrained edge devices in real-world remote sensing applications. The code is available at https://github.com/lwCVer/LEGNet.

This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly defined as the locus of points which are weighted means of k+1 reference points. As this definition relies on points and not on tangent vectors, it can also be extended to geodesic spaces which are not Riemannian. For instance, in stratified spaces, it naturally allows principal subspaces that span several strata, which is impossible in previous generalizations of PCA. We show that barycentric subspaces locally define a submanifold of dimension k which generalizes geodesic subspaces.Second, we rephrase PCA in Euclidean spaces as an optimization on flags of linear subspaces (a hierarchy of properly embedded linear subspaces of increasing dimension). We show that the Euclidean PCA minimizes the Accumulated Unexplained Variances by all the subspaces of the flag (AUV). Barycentric subspaces are naturally nested, allowing the construction of hierarchically nested subspaces. Optimizing the AUV criterion to optimally approximate data points with flags of affine spans in Riemannian manifolds lead to a particularly appealing generalization of PCA on manifolds called Barycentric Subspaces Analysis (BSA).

Modern ML applications increasingly rely on complex deep learning models and large datasets. There has been an exponential growth in the amount of computation needed to train the largest models. Therefore, to scale computation and data, these models are inevitably trained in a distributed manner in clusters of nodes, and their updates are aggregated before being applied to the model. However, a distributed setup is prone to Byzantine failures of individual nodes, components, and software. With data augmentation added to these settings, there is a critical need for robust and efficient aggregation systems. We define the quality of workers as reconstruction ratios in (0,1], and formulate aggregation as a Maximum Likelihood Estimation procedure using Beta densities. We show that the Regularized form of log-likelihood wrt subspace can be approximately solved using iterative least squares solver, and provide convergence guarantees using recent Convex Optimization landscape results. Our empirical findings demonstrate that our approach significantly enhances the robustness of state-of-the-art Byzantine resilient aggregators. We evaluate our method in a distributed setup with a parameter server, and show simultaneous improvements in communication efficiency and accuracy across various tasks. The code is publicly available at https://github.com/hamidralmasi/FlagAggregator

Few-shot learning is valuable in many real-world applications, but learning a generalizable model without overfitting to the few labeled datapoints is challenging. In this work, we focus on Few-shot Learning with Auxiliary Data (FLAD), a training paradigm that assumes access to auxiliary data during few-shot learning in hopes of improving generalization. Previous works have proposed automated methods for mixing auxiliary and target data, but these methods typically scale linearly (or worse) with the number of auxiliary datasets, limiting their practicality. In this work we relate FLAD to the explore-exploit dilemma that is central to the multi-armed bandit setting and derive algorithms whose computational complexity is independent of the number of auxiliary datasets, allowing us to scale to 100x more auxiliary datasets than prior methods. We propose two algorithms -- EXP3-FLAD and UCB1-FLAD -- and compare them with prior FLAD methods that either explore or exploit, finding that the combination of exploration and exploitation is crucial. Through extensive experimentation we find that our methods outperform all pre-existing FLAD methods by 4% and lead to the first 3 billion parameter language models that outperform the 175 billion parameter GPT-3. Overall, our work suggests that the discovery of better, more efficient mixing strategies for FLAD may provide a viable path towards substantially improving generalization in few-shot learning.

Several first order stochastic optimization methods commonly used in the Euclidean domain such as stochastic gradient descent (SGD), accelerated gradient descent or variance reduced methods have already been adapted to certain Riemannian settings. However, some of the most popular of these optimization tools - namely Adam , Adagrad and the more recent Amsgrad - remain to be generalized to Riemannian manifolds. We discuss the difficulty of generalizing such adaptive schemes to the most agnostic Riemannian setting, and then provide algorithms and convergence proofs for geodesically convex objectives in the particular case of a product of Riemannian manifolds, in which adaptivity is implemented across manifolds in the cartesian product. Our generalization is tight in the sense that choosing the Euclidean space as Riemannian manifold yields the same algorithms and regret bounds as those that were already known for the standard algorithms. Experimentally, we show faster convergence and to a lower train loss value for Riemannian adaptive methods over their corresponding baselines on the realistic task of embedding the WordNet taxonomy in the Poincare ball.

Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared with SGD or even fail to converge due to unstable and extreme learning rates. Recent work has put forward some algorithms such as AMSGrad to tackle this issue but they failed to achieve considerable improvement over existing methods. In our paper, we demonstrate that extreme learning rates can lead to poor performance. We provide new variants of Adam and AMSGrad, called AdaBound and AMSBound respectively, which employ dynamic bounds on learning rates to achieve a gradual and smooth transition from adaptive methods to SGD and give a theoretical proof of convergence. We further conduct experiments on various popular tasks and models, which is often insufficient in previous work. Experimental results show that new variants can eliminate the generalization gap between adaptive methods and SGD and maintain higher learning speed early in training at the same time. Moreover, they can bring significant improvement over their prototypes, especially on complex deep networks. The implementation of the algorithm can be found at https://github.com/Luolc/AdaBound .

Out-of-distribution (OOD) detection is critical to building reliable machine learning systems in the open world. Researchers have proposed various strategies to reduce model overconfidence on OOD data. Among them, ReAct is a typical and effective technique to deal with model overconfidence, which truncates high activations to increase the gap between in-distribution and OOD. Despite its promising results, is this technique the best choice for widening the gap? To answer this question, we leverage the variational method to find the optimal operation and verify the necessity of suppressing abnormally low and high activations and amplifying intermediate activations in OOD detection, rather than focusing only on high activations like ReAct. This motivates us to propose a novel technique called ``Variational Rectified Activation (VRA)'', which simulates these suppression and amplification operations using piecewise functions. Experimental results on multiple benchmark datasets demonstrate that our method outperforms existing post-hoc strategies. Meanwhile, VRA is compatible with different scoring functions and network architectures. \textcolor[rgb]{0.93,0.0,0.47}{Our code can be found in Supplementary Material}.

Nesterov's accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence issues may arise when it is applied to nonconvex penalties, such as SCAD. A recent proposal generalizes Nesterov's AG method to the nonconvex setting. The proposed algorithm requires specification of several hyperparameters for its practical application. Aside from some general conditions, there is no explicit rule for selecting the hyperparameters, and how different selection can affect convergence of the algorithm. In this article, we propose a hyperparameter setting based on the complexity upper bound to accelerate convergence, and consider the application of this nonconvex AG algorithm to high-dimensional linear and logistic sparse learning problems. We further establish the rate of convergence and present a simple and useful bound to characterize our proposed optimal damping sequence. Simulation studies show that convergence can be made, on average, considerably faster than that of the conventional proximal gradient algorithm. Our experiments also show that the proposed method generally outperforms the current state-of-the-art methods in terms of signal recovery.

A novel algorithm to detect road lanes in videos, called recursive video lane detector (RVLD), is proposed in this paper, which propagates the state of a current frame recursively to the next frame. RVLD consists of an intra-frame lane detector (ILD) and a predictive lane detector (PLD). First, we design ILD to localize lanes in a still frame. Second, we develop PLD to exploit the information of the previous frame for lane detection in a current frame. To this end, we estimate a motion field and warp the previous output to the current frame. Using the warped information, we refine the feature map of the current frame to detect lanes more reliably. Experimental results show that RVLD outperforms existing detectors on video lane datasets. Our codes are available at https://github.com/dongkwonjin/RVLD.

Autonomous driving requires a comprehensive understanding of the surrounding environment for reliable trajectory planning. Previous works rely on dense rasterized scene representation (e.g., agent occupancy and semantic map) to perform planning, which is computationally intensive and misses the instance-level structure information. In this paper, we propose VAD, an end-to-end vectorized paradigm for autonomous driving, which models the driving scene as a fully vectorized representation. The proposed vectorized paradigm has two significant advantages. On one hand, VAD exploits the vectorized agent motion and map elements as explicit instance-level planning constraints which effectively improves planning safety. On the other hand, VAD runs much faster than previous end-to-end planning methods by getting rid of computation-intensive rasterized representation and hand-designed post-processing steps. VAD achieves state-of-the-art end-to-end planning performance on the nuScenes dataset, outperforming the previous best method by a large margin. Our base model, VAD-Base, greatly reduces the average collision rate by 29.0% and runs 2.5x faster. Besides, a lightweight variant, VAD-Tiny, greatly improves the inference speed (up to 9.3x) while achieving comparable planning performance. We believe the excellent performance and the high efficiency of VAD are critical for the real-world deployment of an autonomous driving system. Code and models are available at https://github.com/hustvl/VAD for facilitating future research.

In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance tau. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is Omega(tau^{-1AK}), where A is the number of actions and K is the number of episodes, and that it is achieved by an Upper Confidence Bound algorithm with a novel Bernstein bonus. For online RL in tabular Markov Decision Processes (MDPs), we show a minimax regret lower bound of Omega(tau^{-1SAK}) (with normalized cumulative rewards), where S is the number of states, and we propose a novel bonus-driven Value Iteration procedure. We show that our algorithm achieves the optimal regret of widetilde O(tau^{-1SAK}) under a continuity assumption and in general attains a near-optimal regret of widetilde O(tau^{-1}SAK), which is minimax-optimal for constant tau. This improves on the best available bounds. By discretizing rewards appropriately, our algorithms are computationally efficient.

Vector Symbolic Architectures (VSAs) have emerged as a novel framework for enabling interpretable machine learning algorithms equipped with the ability to reason and explain their decision processes. The basic idea is to represent discrete information through high dimensional random vectors. Complex data structures can be built up with operations over vectors such as the "binding" operation involving element-wise vector multiplication, which associates data together. The reverse task of decomposing the associated elements is a combinatorially hard task, with an exponentially large search space. The main algorithm for performing this search is the resonator network, inspired by Hopfield network-based memory search operations. In this work, we introduce a new variant of the resonator network, based on self-attention based update rules in the iterative search problem. This update rule, based on the Hopfield network with log-sum-exp energy function and norm-bounded states, is shown to substantially improve the performance and rate of convergence. As a result, our algorithm enables a larger capacity for associative memory, enabling applications in many tasks like perception based pattern recognition, scene decomposition, and object reasoning. We substantiate our algorithm with a thorough evaluation and comparisons to baselines.

Efficiently approximating local curvature information of the loss function is a key tool for optimization and compression of deep neural networks. Yet, most existing methods to approximate second-order information have high computational or storage costs, which can limit their practicality. In this work, we investigate matrix-free, linear-time approaches for estimating Inverse-Hessian Vector Products (IHVPs) for the case when the Hessian can be approximated as a sum of rank-one matrices, as in the classic approximation of the Hessian by the empirical Fisher matrix. We propose two new algorithms as part of a framework called M-FAC: the first algorithm is tailored towards network compression and can compute the IHVP for dimension d, if the Hessian is given as a sum of m rank-one matrices, using O(dm^2) precomputation, O(dm) cost for computing the IHVP, and query cost O(m) for any single element of the inverse Hessian. The second algorithm targets an optimization setting, where we wish to compute the product between the inverse Hessian, estimated over a sliding window of optimization steps, and a given gradient direction, as required for preconditioned SGD. We give an algorithm with cost O(dm + m^2) for computing the IHVP and O(dm + m^3) for adding or removing any gradient from the sliding window. These two algorithms yield state-of-the-art results for network pruning and optimization with lower computational overhead relative to existing second-order methods. Implementations are available at [9] and [17].

We introduce the Discrete Min-Max Violation (DMMV) as a general optimization problem which seeks an assignment of discrete values to variables that minimizes the largest constraint violation. This context-free mathematical formulation is applicable to a wide range of use cases that have worst-case performance requirements. After defining the DMMV problem mathematically, we explore its properties to establish a foundational understanding. To tackle DMMV instance sizes of practical relevance, we develop a GPU-accelerated heuristic that takes advantage of the mathematical properties of DMMV for speeding up the solution process. We demonstrate the versatile applicability of our heuristic by solving three optimization problems as use cases: (1) post-training quantization of language models, (2) discrete tomography, and (3) Finite Impulse Response (FIR) filter design. In quantization without outlier separation, our heuristic achieves 14% improvement on average over existing methods. In discrete tomography, it reduces reconstruction error by 16% under uniform noise and accelerates computations by a factor of 6 on GPU. For FIR filter design, it nearly achieves 50% ripple reduction compared to using the commercial integer optimization solver, Gurobi. Our comparative results point to the benefits of studying DMMV as a context-free optimization problem and the advantages that our proposed heuristic offers on three distinct problems. Our GPU-accelerated heuristic will be made open-source to further stimulate research on DMMV and its other applications. The code is available at https://anonymous.4open.science/r/AMVM-5F3E/

Minimizing the difference of two submodular (DS) functions is a problem that naturally occurs in various machine learning problems. Although it is well known that a DS problem can be equivalently formulated as the minimization of the difference of two convex (DC) functions, existing algorithms do not fully exploit this connection. A classical algorithm for DC problems is called the DC algorithm (DCA). We introduce variants of DCA and its complete form (CDCA) that we apply to the DC program corresponding to DS minimization. We extend existing convergence properties of DCA, and connect them to convergence properties on the DS problem. Our results on DCA match the theoretical guarantees satisfied by existing DS algorithms, while providing a more complete characterization of convergence properties. In the case of CDCA, we obtain a stronger local minimality guarantee. Our numerical results show that our proposed algorithms outperform existing baselines on two applications: speech corpus selection and feature selection.

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a). We apply new analysis techniques to demonstrate that this algorithm enjoys variance-dependent bounds with respect to the norms we propose. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

Exploiting partial first-order information in a cyclic way is arguably the most natural strategy to obtain scalable first-order methods. However, despite their wide use in practice, cyclic schemes are far less understood from a theoretical perspective than their randomized counterparts. Motivated by a recent success in analyzing an extrapolated cyclic scheme for generalized variational inequalities, we propose an Accelerated Cyclic Coordinate Dual Averaging with Extrapolation (A-CODER) method for composite convex optimization, where the objective function can be expressed as the sum of a smooth convex function accessible via a gradient oracle and a convex, possibly nonsmooth, function accessible via a proximal oracle. We show that A-CODER attains the optimal convergence rate with improved dependence on the number of blocks compared to prior work. Furthermore, for the setting where the smooth component of the objective function is expressible in a finite sum form, we introduce a variance-reduced variant of A-CODER, VR-A-CODER, with state-of-the-art complexity guarantees. Finally, we demonstrate the effectiveness of our algorithms through numerical experiments.

Policy gradient is a widely utilized and foundational algorithm in the field of reinforcement learning (RL). Renowned for its convergence guarantees and stability compared to other RL algorithms, its practical application is often hindered by sensitivity to hyper-parameters, particularly the step-size. In this paper, we introduce the integration of the Polyak step-size in RL, which automatically adjusts the step-size without prior knowledge. To adapt this method to RL settings, we address several issues, including unknown f* in the Polyak step-size. Additionally, we showcase the performance of the Polyak step-size in RL through experiments, demonstrating faster convergence and the attainment of more stable policies.

Given a matrix Min R^{mtimes n}, the low rank matrix completion problem asks us to find a rank-k approximation of M as UV^top for Uin R^{mtimes k} and Vin R^{ntimes k} by only observing a few entries specified by a set of entries Omegasubseteq [m]times [n]. In particular, we examine an approach that is widely used in practice -- the alternating minimization framework. Jain, Netrapalli and Sanghavi~jns13 showed that if M has incoherent rows and columns, then alternating minimization provably recovers the matrix M by observing a nearly linear in n number of entries. While the sample complexity has been subsequently improved~glz17, alternating minimization steps are required to be computed exactly. This hinders the development of more efficient algorithms and fails to depict the practical implementation of alternating minimization, where the updates are usually performed approximately in favor of efficiency. In this paper, we take a major step towards a more efficient and error-robust alternating minimization framework. To this end, we develop an analytical framework for alternating minimization that can tolerate moderate amount of errors caused by approximate updates. Moreover, our algorithm runs in time widetilde O(|Omega| k), which is nearly linear in the time to verify the solution while preserving the sample complexity. This improves upon all prior known alternating minimization approaches which require widetilde O(|Omega| k^2) time.

Radio maps (RMs) serve as a critical foundation for enabling environment-aware wireless communication, as they provide the spatial distribution of wireless channel characteristics. Despite recent progress in RM construction using data-driven approaches, most existing methods focus solely on pathloss prediction in a fixed 2D plane, neglecting key parameters such as direction of arrival (DoA), time of arrival (ToA), and vertical spatial variations. Such a limitation is primarily due to the reliance on static learning paradigms, which hinder generalization beyond the training data distribution. To address these challenges, we propose UrbanRadio3D, a large-scale, high-resolution 3D RM dataset constructed via ray tracing in realistic urban environments. UrbanRadio3D is over 37times3 larger than previous datasets across a 3D space with 3 metrics as pathloss, DoA, and ToA, forming a novel 3Dtimes33D dataset with 7times3 more height layers than prior state-of-the-art (SOTA) dataset. To benchmark 3D RM construction, a UNet with 3D convolutional operators is proposed. Moreover, we further introduce RadioDiff-3D, a diffusion-model-based generative framework utilizing the 3D convolutional architecture. RadioDiff-3D supports both radiation-aware scenarios with known transmitter locations and radiation-unaware settings based on sparse spatial observations. Extensive evaluations on UrbanRadio3D validate that RadioDiff-3D achieves superior performance in constructing rich, high-dimensional radio maps under diverse environmental dynamics. This work provides a foundational dataset and benchmark for future research in 3D environment-aware communication. The dataset is available at https://github.com/UNIC-Lab/UrbanRadio3D.

We study contextual combinatorial bandits with probabilistically triggered arms (C^2MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C^2-UCB-T algorithm and propose a novel analysis that achieves an O(dKT) regret bound, removing a potentially exponentially large factor O(1/p_{min}), where d is the dimension of contexts, p_{min} is the minimum positive probability that any arm can be triggered, and batch-size K is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC^2-UCB and derive a regret bound O(dT), which is independent of the batch-size K. As a valuable by-product, our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C^2MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets.

This paper provides the first tight convergence analyses for RMSProp and Adam in non-convex optimization under the most relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. We first analyze RMSProp, which is a special case of Adam with adaptive learning rates but without first-order momentum. Specifically, to solve the challenges due to dependence among adaptive update, unbounded gradient estimate and Lipschitz constant, we demonstrate that the first-order term in the descent lemma converges and its denominator is upper bounded by a function of gradient norm. Based on this result, we show that RMSProp with proper hyperparameters converges to an epsilon-stationary point with an iteration complexity of mathcal O(epsilon^{-4}). We then generalize our analysis to Adam, where the additional challenge is due to a mismatch between the gradient and first-order momentum. We develop a new upper bound on the first-order term in the descent lemma, which is also a function of the gradient norm. We show that Adam with proper hyperparameters converges to an epsilon-stationary point with an iteration complexity of mathcal O(epsilon^{-4}). Our complexity results for both RMSProp and Adam match with the complexity lower bound established in arjevani2023lower.

We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that is a standard component of recent consumer devices, e.g., smartphones. We provide an exhaustive analysis of minimal line configurations and derive two new 2-line solvers, one of which does not suffer from singularities affecting existing solvers. Additionally, we design a new non-minimal method, running on an arbitrary number of lines, to boost the performance in local optimization. Combining all solvers in a hybrid robust estimator, our method achieves increased accuracy even with a rough prior. Experiments on synthetic and real-world datasets demonstrate the superior accuracy of our method compared to the state of the art, while having comparable runtimes. We further demonstrate the applicability of our solvers for relative rotation estimation. The code is available at https://github.com/cvg/VP-Estimation-with-Prior-Gravity.

Diffusion models have demonstrated remarkable generation quality but at the cost of numerous function evaluations. Recently, advanced ODE-based solvers have been developed to mitigate the substantial computational demands of reverse-diffusion solving under limited sampling steps. However, these solvers, heavily inspired by Adams-like multistep methods, rely solely on t-related Lagrange interpolation. We show that t-related Lagrange interpolation is suboptimal for diffusion model and reveal a compact search space comprised of time steps and solver coefficients. Building on our analysis, we propose a novel differentiable solver search algorithm to identify more optimal solver. Equipped with the searched solver, rectified-flow models, e.g., SiT-XL/2 and FlowDCN-XL/2, achieve FID scores of 2.40 and 2.35, respectively, on ImageNet256 with only 10 steps. Meanwhile, DDPM model, DiT-XL/2, reaches a FID score of 2.33 with only 10 steps. Notably, our searched solver outperforms traditional solvers by a significant margin. Moreover, our searched solver demonstrates generality across various model architectures, resolutions, and model sizes.

SLEDGE is the first generative simulator for vehicle motion planning trained on real-world driving logs. Its core component is a learned model that is able to generate agent bounding boxes and lane graphs. The model's outputs serve as an initial state for traffic simulation. The unique properties of the entities to be generated for SLEDGE, such as their connectivity and variable count per scene, render the naive application of most modern generative models to this task non-trivial. Therefore, together with a systematic study of existing lane graph representations, we introduce a novel raster-to-vector autoencoder (RVAE). It encodes agents and the lane graph into distinct channels in a rasterized latent map. This facilitates both lane-conditioned agent generation and combined generation of lanes and agents with a Diffusion Transformer. Using generated entities in SLEDGE enables greater control over the simulation, e.g. upsampling turns or increasing traffic density. Further, SLEDGE can support 500m long routes, a capability not found in existing data-driven simulators like nuPlan. It presents new challenges for planning algorithms, evidenced by failure rates of over 40% for PDM, the winner of the 2023 nuPlan challenge, when tested on hard routes and dense traffic generated by our model. Compared to nuPlan, SLEDGE requires 500times less storage to set up (<4GB), making it a more accessible option and helping with democratizing future research in this field.

This paper introduces RouteFinder, a comprehensive foundation model framework to tackle different Vehicle Routing Problem (VRP) variants. Our core idea is that a foundation model for VRPs should be able to represent variants by treating each as a subset of a generalized problem equipped with different attributes. We propose a unified VRP environment capable of efficiently handling any attribute combination. The RouteFinder model leverages a modern transformer-based encoder and global attribute embeddings to improve task representation. Additionally, we introduce two reinforcement learning techniques to enhance multi-task performance: mixed batch training, which enables training on different variants at once, and multi-variant reward normalization to balance different reward scales. Finally, we propose efficient adapter layers that enable fine-tuning for new variants with unseen attributes. Extensive experiments on 48 VRP variants show RouteFinder outperforms recent state-of-the-art learning methods. Code: https://github.com/ai4co/routefinder.

3D shape generation has greatly flourished through the development of so-called "native" 3D diffusion, particularly through the Vecset Diffusion Model (VDM). While recent advancements have shown promising results in generating high-resolution 3D shapes, VDM still struggles with high-speed generation. Challenges exist because of difficulties not only in accelerating diffusion sampling but also VAE decoding in VDM, areas under-explored in previous works. To address these challenges, we present FlashVDM, a systematic framework for accelerating both VAE and DiT in VDM. For DiT, FlashVDM enables flexible diffusion sampling with as few as 5 inference steps and comparable quality, which is made possible by stabilizing consistency distillation with our newly introduced Progressive Flow Distillation. For VAE, we introduce a lightning vecset decoder equipped with Adaptive KV Selection, Hierarchical Volume Decoding, and Efficient Network Design. By exploiting the locality of the vecset and the sparsity of shape surface in the volume, our decoder drastically lowers FLOPs, minimizing the overall decoding overhead. We apply FlashVDM to Hunyuan3D-2 to obtain Hunyuan3D-2 Turbo. Through systematic evaluation, we show that our model significantly outperforms existing fast 3D generation methods, achieving comparable performance to the state-of-the-art while reducing inference time by over 45x for reconstruction and 32x for generation. Code and models are available at https://github.com/Tencent/FlashVDM.

Mirror descent value iteration (MDVI), an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL), has served as the basis for recent high-performing practical RL algorithms. However, despite the use of function approximation in practice, the theoretical understanding of MDVI has been limited to tabular Markov decision processes (MDPs). We study MDVI with linear function approximation through its sample complexity required to identify an varepsilon-optimal policy with probability 1-delta under the settings of an infinite-horizon linear MDP, generative model, and G-optimal design. We demonstrate that least-squares regression weighted by the variance of an estimated optimal value function of the next state is crucial to achieving minimax optimality. Based on this observation, we present Variance-Weighted Least-Squares MDVI (VWLS-MDVI), the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs. Furthermore, we propose a practical VWLS algorithm for value-based deep RL, Deep Variance Weighting (DVW). Our experiments demonstrate that DVW improves the performance of popular value-based deep RL algorithms on a set of MinAtar benchmarks.

Learning decompositions of expensive-to-evaluate black-box functions promises to scale Bayesian optimisation (BO) to high-dimensional problems. However, the success of these techniques depends on finding proper decompositions that accurately represent the black-box. While previous works learn those decompositions based on data, we investigate data-independent decomposition sampling rules in this paper. We find that data-driven learners of decompositions can be easily misled towards local decompositions that do not hold globally across the search space. Then, we formally show that a random tree-based decomposition sampler exhibits favourable theoretical guarantees that effectively trade off maximal information gain and functional mismatch between the actual black-box and its surrogate as provided by the decomposition. Those results motivate the development of the random decomposition upper-confidence bound algorithm (RDUCB) that is straightforward to implement - (almost) plug-and-play - and, surprisingly, yields significant empirical gains compared to the previous state-of-the-art on a comprehensive set of benchmarks. We also confirm the plug-and-play nature of our modelling component by integrating our method with HEBO, showing improved practical gains in the highest dimensional tasks from Bayesmark.

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over K episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al., 2021) is of order mathcal O(K^{2/3}) (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to mathcal O(sqrt K) in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves mathcal O(K^{8/9}) regret and greatly improves over the best existing bound mathcal O(K^{14/15}). This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

We consider the block coordinate descent methods of Gauss-Seidel type with proximal regularization (BCD-PR), which is a classical method of minimizing general nonconvex objectives under constraints that has a wide range of practical applications. We theoretically establish the worst-case complexity bound for this algorithm. Namely, we show that for general nonconvex smooth objectives with block-wise constraints, the classical BCD-PR algorithm converges to an epsilon-stationary point within O(1/epsilon) iterations. Under a mild condition, this result still holds even if the algorithm is executed inexactly in each step. As an application, we propose a provable and efficient algorithm for `Wasserstein CP-dictionary learning', which seeks a set of elementary probability distributions that can well-approximate a given set of d-dimensional joint probability distributions. Our algorithm is a version of BCD-PR that operates in the dual space, where the primal problem is regularized both entropically and proximally.

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

We give a new algorithm for best arm identification in linearly parameterised bandits in the fixed confidence setting. The algorithm generalises the well-known LUCB algorithm of Kalyanakrishnan et al. (2012) by playing an arm which minimises a suitable notion of geometric overlap of the statistical confidence set for the unknown parameter, and is fully adaptive and computationally efficient as compared to several state-of-the methods. We theoretically analyse the sample complexity of the algorithm for problems with two and three arms, showing optimality in many cases. Numerical results indicate favourable performance over other algorithms with which we compare.

Distributed optimization problems usually face inexact communication issues induced by communication quantization, differential privacy protection, or channels noise. Most existing algorithms need two-timescale setting of the stepsize of gradient descent and the parameter of noise suppression to ensure the convergence to the optimal solution. In this paper, we propose two single-timescale algorithms, VRA-DGT and VRA--DSGT, for distributed deterministic and stochastic optimization problems with inexact communication respectively. VRA-DGT integrates the Variance-Reduced Aggregation (VRA) mechanism with the distributed gradient tracking framework, which achieves a convergence rate of Oleft(k^{-1}right) in the mean-square sense when the objective function is strongly convex and smooth. For distributed stochastic optimization problem,VRA-DSGT, where a hybrid variance reduction technique has been introduced in VRA-DGT, VRA-DGT,, maintains the convergence rate of Oleft(k^{-1}right) for strongly convex and smooth objective function. Simulated experiments on logistic regression problem with real-world data verify the effectiveness of the proposed algorithms.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

This paper introduces EXAdam (EXtended Adam), a novel optimization algorithm that builds upon the widely-used Adam optimizer. EXAdam incorporates three key enhancements: (1) new debiasing terms for improved moment estimation, (2) a gradient-based acceleration mechanism for increased responsiveness to the current loss landscape, and (3) a dynamic step size formula that allows for continuous growth of the learning rate throughout training. These innovations work synergistically to address limitations of the original Adam algorithm, potentially offering improved convergence properties, enhanced ability to escape saddle points, and greater robustness to hyperparameter choices. I provide a theoretical analysis of EXAdam's components and their interactions, highlighting the algorithm's potential advantages in navigating complex optimization landscapes. Empirical evaluations demonstrate EXAdam's superiority over Adam, achieving 48.07% faster convergence and yielding improvements of 4.6%, 4.13%, and 2.39% in training, validation, and testing accuracies, respectively, when applied to a CNN trained on the CIFAR-10 dataset. While these results are promising, further empirical validation across diverse tasks is essential to fully gauge EXAdam's efficacy. Nevertheless, EXAdam represents a significant advancement in adaptive optimization techniques, with promising implications for a wide range of machine learning applications. This work aims to contribute to the ongoing development of more efficient, adaptive, and universally applicable optimization methods in the field of machine learning and artificial intelligence.

Vehicle Routing Problems (VRPs) are a class of NP-hard problems ubiquitous in several real-world logistics scenarios that pose significant challenges for optimization. Neural Combinatorial Optimization (NCO) has emerged as a promising alternative to classical approaches, as it can learn fast heuristics to solve VRPs. However, most research works in NCO for VRPs focus on simplified settings, which do not account for asymmetric distances and travel durations that cannot be derived by simple Euclidean distances and unrealistic data distributions, hindering real-world deployment. This work introduces RRNCO (Real Routing NCO) to bridge the gap of NCO between synthetic and real-world VRPs in the critical aspects of both data and modeling. First, we introduce a new, openly available dataset with real-world data containing a diverse dataset of locations, distances, and duration matrices from 100 cities, considering realistic settings with actual routing distances and durations obtained from Open Source Routing Machine (OSRM). Second, we propose a novel approach that efficiently processes both node and edge features through contextual gating, enabling the construction of more informed node embedding, and we finally incorporate an Adaptation Attention Free Module (AAFM) with neural adaptive bias mechanisms that effectively integrates not only distance matrices but also angular relationships between nodes, allowing our model to capture rich structural information. RRNCO achieves state-of-the-art results in real-world VRPs among NCO methods. We make our dataset and code publicly available at https://github.com/ai4co/real-routing-nco.

We prove new convergence rates for a generalized version of stochastic Nesterov acceleration under interpolation conditions. Unlike previous analyses, our approach accelerates any stochastic gradient method which makes sufficient progress in expectation. The proof, which proceeds using the estimating sequences framework, applies to both convex and strongly convex functions and is easily specialized to accelerated SGD under the strong growth condition. In this special case, our analysis reduces the dependence on the strong growth constant from rho to rho as compared to prior work. This improvement is comparable to a square-root of the condition number in the worst case and address criticism that guarantees for stochastic acceleration could be worse than those for SGD.

Hyperbolic geometry is gaining traction in machine learning for its effectiveness at capturing hierarchical structures in real-world data. Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial advantages and consistently deliver state-of-the-art results across diverse applications. However, hyperbolic classifiers often grapple with computational challenges. Methods reliant on Riemannian optimization frequently exhibit sluggishness, stemming from the increased computational demands of operations on Riemannian manifolds. In response to these challenges, we present hyperDT, a novel extension of decision tree algorithms into hyperbolic space. Crucially, hyperDT eliminates the need for computationally intensive Riemannian optimization, numerically unstable exponential and logarithmic maps, or pairwise comparisons between points by leveraging inner products to adapt Euclidean decision tree algorithms to hyperbolic space. Our approach is conceptually straightforward and maintains constant-time decision complexity while mitigating the scalability issues inherent in high-dimensional Euclidean spaces. Building upon hyperDT we introduce hyperRF, a hyperbolic random forest model. Extensive benchmarking across diverse datasets underscores the superior performance of these models, providing a swift, precise, accurate, and user-friendly toolkit for hyperbolic data analysis.

A basic algorithmic task in automated video surveillance is to separate background and foreground objects. Camera tampering, noisy videos, low frame rate, etc., pose difficulties in solving the problem. A general approach that classifies the tampered frames, and performs subsequent analysis on the remaining frames after discarding the tampered ones, results in loss of information. Several robust methods based on robust principal component analysis (PCA) have been introduced to solve this problem. To date, considerable effort has been expended to develop robust PCA via Principal Component Pursuit (PCP) methods with reduced computational cost and visually appealing foreground detection. However, the convex optimizations used in these algorithms do not scale well to real-world large datasets due to large matrix inversion steps. Also, an integral component of these foreground detection algorithms is singular value decomposition which is nonrobust. In this paper, we present a new video surveillance background modelling algorithm based on a new robust singular value decomposition technique rSVDdpd which takes care of both these issues. We also demonstrate the superiority of our proposed algorithm on a benchmark dataset and a new real-life video surveillance dataset in the presence of camera tampering. Software codes and additional illustrations are made available at the accompanying website rSVDdpd Homepage (https://subroy13.github.io/rsvddpd-home/)

Geolocating images of a ground-level scene entails estimating the location on Earth where the picture was taken, in absence of GPS or other location metadata. Typically, methods are evaluated by measuring the Great Circle Distance (GCD) between a predicted location and ground truth. However, this measurement is limited because it only evaluates a single point, not estimates of regions or score heatmaps. This is especially important in applications to rural, wilderness and under-sampled areas, where finding the exact location may not be possible, and when used in aggregate systems that progressively narrow down locations. In this paper, we introduce a novel metric, Recall vs Area (RvA), which measures the accuracy of estimated distributions of locations. RvA treats image geolocation results similarly to document retrieval, measuring recall as a function of area: For a ranked list of (possibly non-contiguous) predicted regions, we measure the accumulated area required for the region to contain the ground truth coordinate. This produces a curve similar to a precision-recall curve, where "precision" is replaced by square kilometers area, allowing evaluation of performance for different downstream search area budgets. Following directly from this view of the problem, we then examine a simple ensembling approach to global-scale image geolocation, which incorporates information from multiple sources to help address domain shift, and can readily incorporate multiple models, attribute predictors, and data sources. We study its effectiveness by combining the geolocation models GeoEstimation and the current SOTA GeoCLIP, with attribute predictors based on ORNL LandScan and ESA-CCI Land Cover. We find significant improvements in image geolocation for areas that are under-represented in the training set, particularly non-urban areas, on both Im2GPS3k and Street View images.

A practical approach to learning robot skills, often termed sim2real, is to train control policies in simulation and then deploy them on a real robot. Popular techniques to improve the sim2real transfer build on domain randomization (DR) -- training the policy on a diverse set of randomly generated domains with the hope of better generalization to the real world. Due to the large number of hyper-parameters in both the policy learning and DR algorithms, one often ends up with a large number of trained policies, where choosing the best policy among them demands costly evaluation on the real robot. In this work we ask - can we rank the policies without running them in the real world? Our main idea is that a predefined set of real world data can be used to evaluate all policies, using out-of-distribution detection (OOD) techniques. In a sense, this approach can be seen as a `unit test' to evaluate policies before any real world execution. However, we find that by itself, the OOD score can be inaccurate and very sensitive to the particular OOD method. Our main contribution is a simple-yet-effective policy score that combines OOD with an evaluation in simulation. We show that our score - VSDR - can significantly improve the accuracy of policy ranking without requiring additional real world data. We evaluate the effectiveness of VSDR on sim2real transfer in a robotic grasping task with image inputs. We extensively evaluate different DR parameters and OOD methods, and show that VSDR improves policy selection across the board. More importantly, our method achieves significantly better ranking, and uses significantly less data compared to baselines. Project website is available at https://sites.google.com/view/vsdr/home.

The trade-off between regret and computational cost is a fundamental problem for online kernel regression, and previous algorithms worked on the trade-off can not keep optimal regret bounds at a sublinear computational complexity. In this paper, we propose two new algorithms, AOGD-ALD and NONS-ALD, which can keep nearly optimal regret bounds at a sublinear computational complexity, and give sufficient conditions under which our algorithms work. Both algorithms dynamically maintain a group of nearly orthogonal basis used to approximate the kernel mapping, and keep nearly optimal regret bounds by controlling the approximate error. The number of basis depends on the approximate error and the decay rate of eigenvalues of the kernel matrix. If the eigenvalues decay exponentially, then AOGD-ALD and NONS-ALD separately achieves a regret of O(L(f)) and O(d_{eff}(mu)T) at a computational complexity in O(ln^2{T}). If the eigenvalues decay polynomially with degree pgeq 1, then our algorithms keep the same regret bounds at a computational complexity in o(T) in the case of p>4 and pgeq 10, respectively. L(f) is the cumulative losses of f and d_{eff}(mu) is the effective dimension of the problem. The two regret bounds are nearly optimal and are not comparable.

We study a family of distributed stochastic optimization algorithms where gradients are sampled by a token traversing a network of agents in random-walk fashion. Typically, these random-walks are chosen to be Markov chains that asymptotically sample from a desired target distribution, and play a critical role in the convergence of the optimization iterates. In this paper, we take a novel approach by replacing the standard linear Markovian token by one which follows a nonlinear Markov chain - namely the Self-Repellent Radom Walk (SRRW). Defined for any given 'base' Markov chain, the SRRW, parameterized by a positive scalar {\alpha}, is less likely to transition to states that were highly visited in the past, thus the name. In the context of MCMC sampling on a graph, a recent breakthrough in Doshi et al. (2023) shows that the SRRW achieves O(1/{\alpha}) decrease in the asymptotic variance for sampling. We propose the use of a 'generalized' version of the SRRW to drive token algorithms for distributed stochastic optimization in the form of stochastic approximation, termed SA-SRRW. We prove that the optimization iterate errors of the resulting SA-SRRW converge to zero almost surely and prove a central limit theorem, deriving the explicit form of the resulting asymptotic covariance matrix corresponding to iterate errors. This asymptotic covariance is always smaller than that of an algorithm driven by the base Markov chain and decreases at rate O(1/{\alpha}^2) - the performance benefit of using SRRW thereby amplified in the stochastic optimization context. Empirical results support our theoretical findings.

The profiled vehicle routing problem (PVRP) is a generalization of the heterogeneous capacitated vehicle routing problem (HCVRP) in which the objective is to optimize the routes of vehicles to serve client demands subject to different vehicle profiles, with each having a preference or constraint on a per-client basis. While existing learning methods have shown promise for solving the HCVRP in real-time, no learning method exists to solve the more practical and challenging PVRP. In this paper, we propose a Collaborative Attention Model with Profiles (CAMP), a novel approach that learns efficient solvers for PVRP using multi-agent reinforcement learning. CAMP employs a specialized attention-based encoder architecture to embed profiled client embeddings in parallel for each vehicle profile. We design a communication layer between agents for collaborative decision-making across profiled embeddings at each decoding step and a batched pointer mechanism to attend to the profiled embeddings to evaluate the likelihood of the next actions. We evaluate CAMP on two variants of PVRPs: PVRP with preferences, which explicitly influence the reward function, and PVRP with zone constraints with different numbers of agents and clients, demonstrating that our learned solvers achieve competitive results compared to both classical state-of-the-art neural multi-agent models in terms of solution quality and computational efficiency. We make our code openly available at https://github.com/ai4co/camp.

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution (of nodes), and hence suffer from limited generalization performance. This paper studies a challenging yet realistic setting, which considers generalization across both size and distribution in VRPs. We propose a generic meta-learning framework, which enables effective training of an initialized model with the capability of fast adaptation to new tasks during inference. We further develop a simple yet efficient approximation method to reduce the training overhead. Extensive experiments on both synthetic and benchmark instances of the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) demonstrate the effectiveness of our method. The code is available at: https://github.com/RoyalSkye/Omni-VRP.

We propose an adaptive step size with an energy approach for a suitable class of preconditioned gradient descent methods. We focus on settings where the preconditioning is applied to address the constraints in optimization problems, such as the Hessian-Riemannian and natural gradient descent methods. More specifically, we incorporate these preconditioned gradient descent algorithms in the recently introduced Adaptive Energy Gradient Descent (AEGD) framework. In particular, we discuss theoretical results on the unconditional energy-stability and convergence rates across three classes of objective functions. Furthermore, our numerical results demonstrate excellent performance of the proposed method on several test bed optimization problems.

Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and a lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms other optimizers. Also, we show that diffGrad performs uniformly well for training CNN using different activation functions. The source code is made publicly available at https://github.com/shivram1987/diffGrad.

We consider the reinforcement learning (RL) problem with general utilities which consists in maximizing a function of the state-action occupancy measure. Beyond the standard cumulative reward RL setting, this problem includes as particular cases constrained RL, pure exploration and learning from demonstrations among others. For this problem, we propose a simpler single-loop parameter-free normalized policy gradient algorithm. Implementing a recursive momentum variance reduction mechanism, our algorithm achieves mathcal{O}(epsilon^{-3}) and mathcal{O}(epsilon^{-2}) sample complexities for epsilon-first-order stationarity and epsilon-global optimality respectively, under adequate assumptions. We further address the setting of large finite state action spaces via linear function approximation of the occupancy measure and show a mathcal{O}(epsilon^{-4}) sample complexity for a simple policy gradient method with a linear regression subroutine.

We propose a new variant of the Adam optimizer [Kingma and Ba, 2014] called MICROADAM that specifically minimizes memory overheads, while maintaining theoretical convergence guarantees. We achieve this by compressing the gradient information before it is fed into the optimizer state, thereby reducing its memory footprint significantly. We control the resulting compression error via a novel instance of the classical error feedback mechanism from distributed optimization [Seide et al., 2014, Alistarh et al., 2018, Karimireddy et al., 2019] in which the error correction information is itself compressed to allow for practical memory gains. We prove that the resulting approach maintains theoretical convergence guarantees competitive to those of AMSGrad, while providing good practical performance. Specifically, we show that MICROADAM can be implemented efficiently on GPUs: on both million-scale (BERT) and billion-scale (LLaMA) models, MicroAdam provides practical convergence competitive to that of the uncompressed Adam baseline, with lower memory usage and similar running time. Our code is available at https://github.com/IST-DASLab/MicroAdam.

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce RVGP, a generalisation of GPs for learning vector signals over latent Riemannian manifolds. Our method uses positional encoding with eigenfunctions of the connection Laplacian, associated with the tangent bundle, readily derived from common graph-based approximation of data. We demonstrate that RVGP possesses global regularity over the manifold, which allows it to super-resolve and inpaint vector fields while preserving singularities. Furthermore, we use RVGP to reconstruct high-density neural dynamics derived from low-density EEG recordings in healthy individuals and Alzheimer's patients. We show that vector field singularities are important disease markers and that their reconstruction leads to a comparable classification accuracy of disease states to high-density recordings. Thus, our method overcomes a significant practical limitation in experimental and clinical applications.

Recent advances show that Neural Architectural Search (NAS) method is able to find state-of-the-art image classification deep architectures. In this paper, we consider the one-shot NAS problem for resource constrained applications. This problem is of great interest because it is critical to choose different architectures according to task complexity when the resource is constrained. Previous techniques are either too slow for one-shot learning or does not take the resource constraint into consideration. In this paper, we propose the resource constrained differentiable architecture search (RC-DARTS) method to learn architectures that are significantly smaller and faster while achieving comparable accuracy. Specifically, we propose to formulate the RC-DARTS task as a constrained optimization problem by adding the resource constraint. An iterative projection method is proposed to solve the given constrained optimization problem. We also propose a multi-level search strategy to enable layers at different depths to adaptively learn different types of neural architectures. Through extensive experiments on the Cifar10 and ImageNet datasets, we show that the RC-DARTS method learns lightweight neural architectures which have smaller model size and lower computational complexity while achieving comparable or better performances than the state-of-the-art methods.

As models for nature language processing (NLP), computer vision (CV) and recommendation systems (RS) require surging computation, a large number of GPUs/TPUs are paralleled as a large batch (LB) to improve training throughput. However, training such LB tasks often meets large generalization gap and downgrades final precision, which limits enlarging the batch size. In this work, we develop the variance reduced gradient descent technique (VRGD) based on the gradient signal to noise ratio (GSNR) and apply it onto popular optimizers such as SGD/Adam/LARS/LAMB. We carry out a theoretical analysis of convergence rate to explain its fast training dynamics, and a generalization analysis to demonstrate its smaller generalization gap on LB training. Comprehensive experiments demonstrate that VRGD can accelerate training (1sim 2 times), narrow generalization gap and improve final accuracy. We push the batch size limit of BERT pretraining up to 128k/64k and DLRM to 512k without noticeable accuracy loss. We improve ImageNet Top-1 accuracy at 96k by 0.52pp than LARS. The generalization gap of BERT and ImageNet training is significantly reduce by over 65%.

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In this paper, we introduce a fundamentally different strategy: We formulate the structure learning problem as a purely continuous optimization problem over real matrices that avoids this combinatorial constraint entirely. This is achieved by a novel characterization of acyclicity that is not only smooth but also exact. The resulting problem can be efficiently solved by standard numerical algorithms, which also makes implementation effortless. The proposed method outperforms existing ones, without imposing any structural assumptions on the graph such as bounded treewidth or in-degree. Code implementing the proposed algorithm is open-source and publicly available at https://github.com/xunzheng/notears.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size. The search direction contains gradient information preconditioned by a well-scaled diagonal preconditioning matrix that captures the local curvature information. Our methodology does not require the tedious task of learning rate tuning, as the learning rate is updated automatically without adding an extra hyperparameter. We provide convergence guarantees on a comprehensive collection of optimization problems, including convex, strongly convex, and nonconvex problems, in both deterministic and stochastic regimes. We also conduct an extensive empirical evaluation on standard machine learning problems, justifying our algorithm's versatility and demonstrating its strong performance compared to other start-of-the-art first-order and second-order methods.

Covariance matrices have proven highly effective across many scientific fields. Since these matrices lie within the Symmetric Positive Definite (SPD) manifold - a Riemannian space with intrinsic non-Euclidean geometry, the primary challenge in representation learning is to respect this underlying geometric structure. Drawing inspiration from the success of Euclidean deep learning, researchers have developed neural networks on the SPD manifolds for more faithful covariance embedding learning. A notable advancement in this area is the implementation of Riemannian batch normalization (RBN), which has been shown to improve the performance of SPD network models. Nonetheless, the Riemannian metric beneath the existing RBN might fail to effectively deal with the ill-conditioned SPD matrices (ICSM), undermining the effectiveness of RBN. In contrast, the Bures-Wasserstein metric (BWM) demonstrates superior performance for ill-conditioning. In addition, the recently introduced Generalized BWM (GBWM) parameterizes the vanilla BWM via an SPD matrix, allowing for a more nuanced representation of vibrant geometries of the SPD manifold. Therefore, we propose a novel RBN algorithm based on the GBW geometry, incorporating a learnable metric parameter. Moreover, the deformation of GBWM by matrix power is also introduced to further enhance the representational capacity of GBWM-based RBN. Experimental results on different datasets validate the effectiveness of our proposed method.

We present AI-SARAH, a practical variant of SARAH. As a variant of SARAH, this algorithm employs the stochastic recursive gradient yet adjusts step-size based on local geometry. AI-SARAH implicitly computes step-size and efficiently estimates local Lipschitz smoothness of stochastic functions. It is fully adaptive, tune-free, straightforward to implement, and computationally efficient. We provide technical insight and intuitive illustrations on its design and convergence. We conduct extensive empirical analysis and demonstrate its strong performance compared with its classical counterparts and other state-of-the-art first-order methods in solving convex machine learning problems.

We revisit the structure learning problem for dynamic Bayesian networks and propose a method that simultaneously estimates contemporaneous (intra-slice) and time-lagged (inter-slice) relationships between variables in a time-series. Our approach is score-based, and revolves around minimizing a penalized loss subject to an acyclicity constraint. To solve this problem, we leverage a recent algebraic result characterizing the acyclicity constraint as a smooth equality constraint. The resulting algorithm, which we call DYNOTEARS, outperforms other methods on simulated data, especially in high-dimensions as the number of variables increases. We also apply this algorithm on real datasets from two different domains, finance and molecular biology, and analyze the resulting output. Compared to state-of-the-art methods for learning dynamic Bayesian networks, our method is both scalable and accurate on real data. The simple formulation and competitive performance of our method make it suitable for a variety of problems where one seeks to learn connections between variables across time.

The manifold hypothesis posits that high-dimensional data often lies on a lower-dimensional manifold and that utilizing this manifold as the target space yields more efficient representations. While numerous traditional manifold-based techniques exist for dimensionality reduction, their application in self-supervised learning has witnessed slow progress. The recent MSimCLR method combines manifold encoding with SimCLR but requires extremely low target encoding dimensions to outperform SimCLR, limiting its applicability. This paper introduces a novel learning paradigm using an unbalanced atlas (UA), capable of surpassing state-of-the-art self-supervised learning approaches. We investigated and engineered the DeepInfomax with an unbalanced atlas (DIM-UA) method by adapting the Spatiotemporal DeepInfomax (ST-DIM) framework to align with our proposed UA paradigm. The efficacy of DIM-UA is demonstrated through training and evaluation on the Atari Annotated RAM Interface (AtariARI) benchmark, a modified version of the Atari 2600 framework that produces annotated image samples for representation learning. The UA paradigm improves existing algorithms significantly as the number of target encoding dimensions grows. For instance, the mean F1 score averaged over categories of DIM-UA is ~75% compared to ~70% of ST-DIM when using 16384 hidden units.

Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood training in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which improves computational efficiency significantly and works for all normalizing flow architectures of practical relevance. We then show that this estimator can also be applied to maximum likelihood training for which it has a regularizing effect as it can take the form of a given target energy function into account. We empirically establish its superior performance and reduced variance for several natural sciences applications.

Recent sparse detectors with multiple, e.g. six, decoder layers achieve promising performance but much inference time due to complex heads. Previous works have explored using dense priors as initialization and built one-decoder-layer detectors. Although they gain remarkable acceleration, their performance still lags behind their six-decoder-layer counterparts by a large margin. In this work, we aim to bridge this performance gap while retaining fast speed. We find that the architecture discrepancy between dense and sparse detectors leads to feature conflict, hampering the performance of one-decoder-layer detectors. Thus we propose Adaptive Sparse Anchor Generator (ASAG) which predicts dynamic anchors on patches rather than grids in a sparse way so that it alleviates the feature conflict problem. For each image, ASAG dynamically selects which feature maps and which locations to predict, forming a fully adaptive way to generate image-specific anchors. Further, a simple and effective Query Weighting method eases the training instability from adaptiveness. Extensive experiments show that our method outperforms dense-initialized ones and achieves a better speed-accuracy trade-off. The code is available at https://github.com/iSEE-Laboratory/ASAG.

Visual Autoregressive (VAR) modeling has gained popularity for its shift towards next-scale prediction. However, existing VAR paradigms process the entire token map at each scale step, leading to the complexity and runtime scaling dramatically with image resolution. To address this challenge, we propose FastVAR, a post-training acceleration method for efficient resolution scaling with VARs. Our key finding is that the majority of latency arises from the large-scale step where most tokens have already converged. Leveraging this observation, we develop the cached token pruning strategy that only forwards pivotal tokens for scale-specific modeling while using cached tokens from previous scale steps to restore the pruned slots. This significantly reduces the number of forwarded tokens and improves the efficiency at larger resolutions. Experiments show the proposed FastVAR can further speedup FlashAttention-accelerated VAR by 2.7times with negligible performance drop of <1%. We further extend FastVAR to zero-shot generation of higher resolution images. In particular, FastVAR can generate one 2K image with 15GB memory footprints in 1.5s on a single NVIDIA 3090 GPU. Code is available at https://github.com/csguoh/FastVAR.

The past decade has seen vast progress in deep reinforcement learning (RL) on the back of algorithms manually designed by human researchers. Recently, it has been shown that it is possible to meta-learn update rules, with the hope of discovering algorithms that can perform well on a wide range of RL tasks. Despite impressive initial results from algorithms such as Learned Policy Gradient (LPG), there remains a generalization gap when these algorithms are applied to unseen environments. In this work, we examine how characteristics of the meta-training distribution impact the generalization performance of these algorithms. Motivated by this analysis and building on ideas from Unsupervised Environment Design (UED), we propose a novel approach for automatically generating curricula to maximize the regret of a meta-learned optimizer, in addition to a novel approximation of regret, which we name algorithmic regret (AR). The result is our method, General RL Optimizers Obtained Via Environment Design (GROOVE). In a series of experiments, we show that GROOVE achieves superior generalization to LPG, and evaluate AR against baseline metrics from UED, identifying it as a critical component of environment design in this setting. We believe this approach is a step towards the discovery of truly general RL algorithms, capable of solving a wide range of real-world environments.

The paper proposes a novel machine learning-based approach to the pathfinding problem on extremely large graphs. This method leverages diffusion distance estimation via a neural network and uses beam search for pathfinding. We demonstrate its efficiency by finding solutions for 4x4x4 and 5x5x5 Rubik's cubes with unprecedentedly short solution lengths, outperforming all available solvers and introducing the first machine learning solver beyond the 3x3x3 case. In particular, it surpasses every single case of the combined best results in the Kaggle Santa 2023 challenge, which involved over 1,000 teams. For the 3x3x3 Rubik's cube, our approach achieves an optimality rate exceeding 98%, matching the performance of task-specific solvers and significantly outperforming prior solutions such as DeepCubeA (60.3%) and EfficientCube (69.6%). Additionally, our solution is more than 26 times faster in solving 3x3x3 Rubik's cubes while requiring up to 18.5 times less model training time than the most efficient state-of-the-art competitor.

Hyperdimensional computing (HD), also known as vector symbolic architectures (VSA), is a framework for computing with distributed representations by exploiting properties of random high-dimensional vector spaces. The commitment of the scientific community to aggregate and disseminate research in this particularly multidisciplinary area has been fundamental for its advancement. Joining these efforts, we present Torchhd, a high-performance open source Python library for HD/VSA. Torchhd seeks to make HD/VSA more accessible and serves as an efficient foundation for further research and application development. The easy-to-use library builds on top of PyTorch and features state-of-the-art HD/VSA functionality, clear documentation, and implementation examples from well-known publications. Comparing publicly available code with their corresponding Torchhd implementation shows that experiments can run up to 100x faster. Torchhd is available at: https://github.com/hyperdimensional-computing/torchhd.

We present a novel approach to accelerate stochastic gradient descent (SGD) by utilizing curvature information obtained from Hessian-vector products or finite differences of parameters and gradients, similar to the BFGS algorithm. Our approach involves two preconditioners: a matrix-free preconditioner and a low-rank approximation preconditioner. We update both preconditioners online using a criterion that is robust to stochastic gradient noise and does not require line search or damping. To preserve the corresponding symmetry or invariance, our preconditioners are constrained to certain connected Lie groups. The Lie group's equivariance property simplifies the preconditioner fitting process, while its invariance property eliminates the need for damping, which is commonly required in second-order optimizers. As a result, the learning rate for parameter updating and the step size for preconditioner fitting are naturally normalized, and their default values work well in most scenarios. Our proposed approach offers a promising direction for improving the convergence of SGD with low computational overhead. We demonstrate that Preconditioned SGD (PSGD) outperforms SoTA on Vision, NLP, and RL tasks across multiple modern deep-learning architectures. We have provided code for reproducing toy and large scale experiments in this paper.

This paper makes a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian eigendecomposition and singular value decomposition. The other consists of Gaussian elimination and the Gram-Schmidt procedure with various pivoting rules for computing the Cholesky decomposition and QR decomposition respectively. Both families are cast as special cases of a more general class of factorization algorithms. We provide a randomized pivoting rule that applies to this general class (which differs substantially from the usual pivoting rules for Gaussian elimination / Gram-Schmidt) which results in the same linear rate of convergence for each algorithm, irrespective of which factorization it computes. A second important consequence of this randomized pivoting rule is a provable, effective bound on the numerical stability of the Jacobi eigenvalue algorithm, which addresses a longstanding open problem of Demmel and Veseli\'c `92.

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

In Autonomous Driving (AD) transparency and safety are paramount, as mistakes are costly. However, neural networks used in AD systems are generally considered black boxes. As a countermeasure, we have methods of explainable AI (XAI), such as feature relevance estimation and dimensionality reduction. Coarse graining techniques can also help reduce dimensionality and find interpretable global patterns. A specific coarse graining method is Renormalization Groups from statistical physics. It has previously been applied to Restricted Boltzmann Machines (RBMs) to interpret unsupervised learning. We refine this technique by building a transparent backbone model for convolutional variational autoencoders (VAE) that allows mapping latent values to input features and has performance comparable to trained black box VAEs. Moreover, we propose a custom feature map visualization technique to analyze the internal convolutional layers in the VAE to explain internal causes of poor reconstruction that may lead to dangerous traffic scenarios in AD applications. In a second key contribution, we propose explanation and evaluation techniques for the internal dynamics and feature relevance of prediction networks. We test a long short-term memory (LSTM) network in the computer vision domain to evaluate the predictability and in future applications potentially safety of prediction models. We showcase our methods by analyzing a VAE-LSTM world model that predicts pedestrian perception in an urban traffic situation.

When the environment is partially observable (PO), a deep reinforcement learning (RL) agent must learn a suitable temporal representation of the entire history in addition to a strategy to control. This problem is not novel, and there have been model-free and model-based algorithms proposed for this problem. However, inspired by recent success in model-free image-based RL, we noticed the absence of a model-free baseline for history-based RL that (1) uses full history and (2) incorporates recent advances in off-policy continuous control. Therefore, we implement recurrent versions of DDPG, TD3, and SAC (RDPG, RTD3, and RSAC) in this work, evaluate them on short-term and long-term PO domains, and investigate key design choices. Our experiments show that RDPG and RTD3 can surprisingly fail on some domains and that RSAC is the most reliable, reaching near-optimal performance on nearly all domains. However, one task that requires systematic exploration still proved to be difficult, even for RSAC. These results show that model-free RL can learn good temporal representation using only reward signals; the primary difficulty seems to be computational cost and exploration. To facilitate future research, we have made our PyTorch implementation publicly available at https://github.com/zhihanyang2022/off-policy-continuous-control.

Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter beta is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying beta. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.

Predicting the future motion of dynamic agents is of paramount importance to ensuring safety and assessing risks in motion planning for autonomous robots. In this study, we propose a two-stage motion prediction method, called R-Pred, designed to effectively utilize both scene and interaction context using a cascade of the initial trajectory proposal and trajectory refinement networks. The initial trajectory proposal network produces M trajectory proposals corresponding to the M modes of the future trajectory distribution. The trajectory refinement network enhances each of the M proposals using 1) tube-query scene attention (TQSA) and 2) proposal-level interaction attention (PIA) mechanisms. TQSA uses tube-queries to aggregate local scene context features pooled from proximity around trajectory proposals of interest. PIA further enhances the trajectory proposals by modeling inter-agent interactions using a group of trajectory proposals selected by their distances from neighboring agents. Our experiments conducted on Argoverse and nuScenes datasets demonstrate that the proposed refinement network provides significant performance improvements compared to the single-stage baseline and that R-Pred achieves state-of-the-art performance in some categories of the benchmarks.

In machine learning applications, it is well known that carefully designed learning rate (step size) schedules can significantly improve the convergence of commonly used first-order optimization algorithms. Therefore how to set step size adaptively becomes an important research question. A popular and effective method is the Polyak step size, which sets step size adaptively for gradient descent or stochastic gradient descent without the need to estimate the smoothness parameter of the objective function. However, there has not been a principled way to generalize the Polyak step size for algorithms with momentum accelerations. This paper presents a general framework to set the learning rate adaptively for first-order optimization methods with momentum, motivated by the derivation of Polyak step size. It is shown that the resulting methods are much less sensitive to the choice of momentum parameter and may avoid the oscillation of the heavy-ball method on ill-conditioned problems. These adaptive step sizes are further extended to the stochastic settings, which are attractive choices for stochastic gradient descent with momentum. Our methods are demonstrated to be more effective for stochastic gradient methods than prior adaptive step size algorithms in large-scale machine learning tasks.

This work proposes a simple yet effective sampling framework for combinatorial optimization (CO). Our method builds on discrete Langevin dynamics (LD), an efficient gradient-guided generative paradigm. However, we observe that directly applying LD often leads to limited exploration. To overcome this limitation, we propose the Regularized Langevin Dynamics (RLD), which enforces an expected distance between the sampled and current solutions, effectively avoiding local minima. We develop two CO solvers on top of RLD, one based on simulated annealing (SA), and the other one based on neural network (NN). Empirical results on three classic CO problems demonstrate that both of our methods can achieve comparable or better performance against the previous state-of-the-art (SOTA) SA- and NN-based solvers. In particular, our SA algorithm reduces the runtime of the previous SOTA SA method by up to 80\%, while achieving equal or superior performance. In summary, RLD offers a promising framework for enhancing both traditional heuristics and NN models to solve CO problems. Our code is available at https://github.com/Shengyu-Feng/RLD4CO.

The fastrerandomize R package provides hardware-accelerated tools for performing rerandomization and randomization testing in experimental research. Using a JAX backend, the package enables exact rerandomization inference even for large experiments with hundreds of billions of possible randomizations. Key functionalities include generating pools of acceptable rerandomizations based on covariate balance, conducting exact randomization tests, and performing pre-analysis evaluations to determine optimal rerandomization acceptance thresholds. Through batched processing and GPU acceleration, fastrerandomize achieves substantial performance gains compared to existing implementations, making previously intractable designs computationally feasible. The package therefore extends the randomization-based inference toolkit in R, allowing researchers to efficiently implement more stringent rerandomization designs and conduct valid inference even with large sample sizes or in high-dimensional settings.

As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect infeasible or misspecified problem instances, but the computational complexity of first-order methods for doing so has yet to be formally studied. In this work, we characterize the optimal accelerated rate of infeasibility detection. We show that the standard fixed-point iteration achieves a O(1/k^2) and O(1/k) rates, respectively, on the normalized iterates and the fixed-point residual converging to the infimal displacement vector, while the accelerated fixed-point iteration achieves O(1/k^2) and mathcal{O}(1/k^2) rates. We then provide a matching complexity lower bound to establish that Theta(1/k^2) is indeed the optimal accelerated rate.

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights provides an advantageous ground for gradient descent (GD) optimizers: the effective step sizes are automatically reduced over time, stabilizing the overall training procedure. It is often overlooked, however, that the additional introduction of momentum in GD optimizers results in a far more rapid reduction in effective step sizes for scale-invariant weights, a phenomenon that has not yet been studied and may have caused unwanted side effects in the current practice. This is a crucial issue because arguably the vast majority of modern deep neural networks consist of (1) momentum-based GD (e.g. SGD or Adam) and (2) scale-invariant parameters. In this paper, we verify that the widely-adopted combination of the two ingredients lead to the premature decay of effective step sizes and sub-optimal model performances. We propose a simple and effective remedy, SGDP and AdamP: get rid of the radial component, or the norm-increasing direction, at each optimizer step. Because of the scale invariance, this modification only alters the effective step sizes without changing the effective update directions, thus enjoying the original convergence properties of GD optimizers. Given the ubiquity of momentum GD and scale invariance in machine learning, we have evaluated our methods against the baselines on 13 benchmarks. They range from vision tasks like classification (e.g. ImageNet), retrieval (e.g. CUB and SOP), and detection (e.g. COCO) to language modelling (e.g. WikiText) and audio classification (e.g. DCASE) tasks. We verify that our solution brings about uniform gains in those benchmarks. Source code is available at https://github.com/clovaai/AdamP.

Lattice-based planning techniques simplify the motion planning problem for autonomous vehicles by limiting available motions to a pre-computed set of primitives. These primitives are then combined online to generate more complex maneuvers. A set of motion primitives t-span a lattice if, given a real number t at least 1, any configuration in the lattice can be reached via a sequence of motion primitives whose cost is no more than a factor of t from optimal. Computing a minimal t-spanning set balances a trade-off between computed motion quality and motion planning performance. In this work, we formulate this problem for an arbitrary lattice as a mixed integer linear program. We also propose an A*-based algorithm to solve the motion planning problem using these primitives. Finally, we present an algorithm that removes the excessive oscillations from planned motions -- a common problem in lattice-based planning. Our method is validated for autonomous driving in both parking lot and highway scenarios.

Molecular docking is an important tool for structure-based drug design, accelerating the efficiency of drug development. Complex and dynamic binding processes between proteins and small molecules require searching and sampling over a wide spatial range. Traditional docking by searching for possible binding sites and conformations is computationally complex and results poorly under blind docking. Quantum-inspired algorithms combining quantum properties and annealing show great advantages in solving combinatorial optimization problems. Inspired by this, we achieve an improved in blind docking by using quantum-inspired combined with gradients learned by deep learning in the encoded molecular space. Numerical simulation shows that our method outperforms traditional docking algorithms and deep learning-based algorithms over 10\%. Compared to the current state-of-the-art deep learning-based docking algorithm DiffDock, the success rate of Top-1 (RMSD<2) achieves an improvement from 33\% to 35\% in our same setup. In particular, a 6\% improvement is realized in the high-precision region(RMSD<1) on molecules data unseen in DiffDock, which demonstrates the well-generalized of our method.

3D detection technology is widely used in the field of autonomous driving, with its application scenarios gradually expanding from enclosed highways to open conventional roads. For rare anomaly categories that appear on the road, 3D detection models trained on closed sets often misdetect or fail to detect anomaly objects. To address this risk, it is necessary to enhance the generalization ability of 3D detection models for targets of arbitrary shapes and to possess the capability to filter out anomalies. The generalization of 3D detection is limited by two factors: the coupled training of 2D and 3D, and the insufficient diversity in the scale distribution of training samples. This paper proposes a Stereo-based 3D Anomaly object Detection (S3AD) algorithm, which decouples the training strategy of 3D and 2D to release the generalization ability for arbitrary 3D foreground detection, and proposes an anomaly scoring algorithm based on foreground confidence prediction, achieving target-level anomaly scoring. In order to further verify and enhance the generalization of anomaly detection, we use a 3D rendering method to synthesize two augmented reality binocular stereo 3D detection datasets which named KITTI-AR. KITTI-AR extends upon KITTI by adding 97 new categories, totaling 6k pairs of stereo images. The KITTI-AR-ExD subset includes 39 common categories as extra training data to address the sparse sample distribution issue. Additionally, 58 rare categories form the KITTI-AR-OoD subset, which are not used in training to simulate zero-shot scenarios in real-world settings, solely for evaluating 3D anomaly detection. Finally, the performance of the algorithm and the dataset is verified in the experiments. (Code and dataset can be obtained at https://github.com/shiyi-mu/S3AD-Code).

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels K(x,y) = - |x-y|^r, r in (0,2) have exceptional properties which allow their efficient computation. We prove that the MMD of Riesz kernels, which is also known as energy distance, coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for r=1, a simple sorting algorithm can be applied to reduce the complexity from O(MN+N^2) to O((M+N)log(M+N)) for two measures with M and N support points. As another interesting follow-up result, the MMD of compactly supported measures can be estimated from above and below by the Wasserstein-1 distance. For the implementations we approximate the gradient of the sliced MMD by using only a finite number P of slices. We show that the resulting error has complexity O(d/P), where d is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for image applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10.

High network communication cost for synchronizing gradients and parameters is the well-known bottleneck of distributed training. In this work, we propose TernGrad that uses ternary gradients to accelerate distributed deep learning in data parallelism. Our approach requires only three numerical levels {-1,0,1}, which can aggressively reduce the communication time. We mathematically prove the convergence of TernGrad under the assumption of a bound on gradients. Guided by the bound, we propose layer-wise ternarizing and gradient clipping to improve its convergence. Our experiments show that applying TernGrad on AlexNet does not incur any accuracy loss and can even improve accuracy. The accuracy loss of GoogLeNet induced by TernGrad is less than 2% on average. Finally, a performance model is proposed to study the scalability of TernGrad. Experiments show significant speed gains for various deep neural networks. Our source code is available.

This study explores the recently proposed challenging multi-view Anomaly Detection (AD) task. Single-view tasks would encounter blind spots from other perspectives, resulting in inaccuracies in sample-level prediction. Therefore, we introduce the Multi-View Anomaly Detection (MVAD) framework, which learns and integrates features from multi-views. Specifically, we proposed a Multi-View Adaptive Selection (MVAS) algorithm for feature learning and fusion across multiple views. The feature maps are divided into neighbourhood attention windows to calculate a semantic correlation matrix between single-view windows and all other views, which is a conducted attention mechanism for each single-view window and the top-K most correlated multi-view windows. Adjusting the window sizes and top-K can minimise the computational complexity to linear. Extensive experiments on the Real-IAD dataset for cross-setting (multi/single-class) validate the effectiveness of our approach, achieving state-of-the-art performance among sample 4.1\%uparrow/ image 5.6\%uparrow/pixel 6.7\%uparrow levels with a total of ten metrics with only 18M parameters and fewer GPU memory and training time.

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the ABC condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.

In location estimation, we are given n samples from a known distribution f shifted by an unknown translation lambda, and want to estimate lambda as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error mathcal N(0, 1{nmathcal I}), where mathcal I is the Fisher information of f. However, the n required for convergence depends on f, and may be arbitrarily large. We build on the theory using smoothed estimators to bound the error for finite n in terms of mathcal I_r, the Fisher information of the r-smoothed distribution. As n to infty, r to 0 at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional f to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

Methods for carefully selecting or generating a small set of training data to learn from, i.e., data pruning, coreset selection, and data distillation, have been shown to be effective in reducing the ever-increasing cost of training neural networks. Behind this success are rigorously designed strategies for identifying informative training examples out of large datasets. However, these strategies come with additional computational costs associated with subset selection or data distillation before training begins, and furthermore, many are shown to even under-perform random sampling in high data compression regimes. As such, many data pruning, coreset selection, or distillation methods may not reduce 'time-to-accuracy', which has become a critical efficiency measure of training deep neural networks over large datasets. In this work, we revisit a powerful yet overlooked random sampling strategy to address these challenges and introduce an approach called Repeated Sampling of Random Subsets (RSRS or RS2), where we randomly sample the subset of training data for each epoch of model training. We test RS2 against thirty state-of-the-art data pruning and data distillation methods across four datasets including ImageNet. Our results demonstrate that RS2 significantly reduces time-to-accuracy compared to existing techniques. For example, when training on ImageNet in the high-compression regime (using less than 10% of the dataset each epoch), RS2 yields accuracy improvements up to 29% compared to competing pruning methods while offering a runtime reduction of 7x. Beyond the above meta-study, we provide a convergence analysis for RS2 and discuss its generalization capability. The primary goal of our work is to establish RS2 as a competitive baseline for future data selection or distillation techniques aimed at efficient training.

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) show that even if a learner is given linear features in R^d that approximate the rewards in a bandit or RL with a uniform error of varepsilon, searching for an O(varepsilon)-optimal action requires pulling at least Omega(exp(d)) queries. Furthermore, Lattimore et al. (2020) show that a degraded O(varepsilond)-optimal solution can be learned within poly(d/varepsilon) queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break the varepsilond barrier. In this paper, we address this question by showing that algorithms can obtain O(varepsilon)-optimal actions by querying O(varepsilon^{-s}d^s) actions, where s is the sparsity parameter, removing the exp(d)-dependence. We then establish information-theoretical lower bounds, i.e., Omega(exp(s)), to show that our upper bound on sample complexity is nearly tight if one demands an error O(s^{delta}varepsilon) for 0<delta<1. For deltageq 1, we further show that poly(s/varepsilon) queries are possible when the linear features are "good" and even in general settings. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are "useful" for bandit and reinforcement learning with misspecification.

While classifier-free guidance (CFG) is essential for conditional diffusion models, it doubles the number of neural function evaluations (NFEs) per inference step. To mitigate this inefficiency, we introduce adapter guidance distillation (AGD), a novel approach that simulates CFG in a single forward pass. AGD leverages lightweight adapters to approximate CFG, effectively doubling the sampling speed while maintaining or even improving sample quality. Unlike prior guidance distillation methods that tune the entire model, AGD keeps the base model frozen and only trains minimal additional parameters (sim2%) to significantly reduce the resource requirement of the distillation phase. Additionally, this approach preserves the original model weights and enables the adapters to be seamlessly combined with other checkpoints derived from the same base model. We also address a key mismatch between training and inference in existing guidance distillation methods by training on CFG-guided trajectories instead of standard diffusion trajectories. Through extensive experiments, we show that AGD achieves comparable or superior FID to CFG across multiple architectures with only half the NFEs. Notably, our method enables the distillation of large models (sim2.6B parameters) on a single consumer GPU with 24 GB of VRAM, making it more accessible than previous approaches that require multiple high-end GPUs. We will publicly release the implementation of our method.

Real-world object detection systems, such as those in autonomous driving and surveillance, must continuously learn new object categories and simultaneously adapt to changing environmental conditions. Existing approaches, Class Incremental Object Detection (CIOD) and Domain Incremental Object Detection (DIOD) only address one aspect of this challenge. CIOD struggles in unseen domains, while DIOD suffers from catastrophic forgetting when learning new classes, limiting their real-world applicability. To overcome these limitations, we introduce Dual Incremental Object Detection (DuIOD), a more practical setting that simultaneously handles class and domain shifts in an exemplar-free manner. We propose DuET, a Task Arithmetic-based model merging framework that enables stable incremental learning while mitigating sign conflicts through a novel Directional Consistency Loss. Unlike prior methods, DuET is detector-agnostic, allowing models like YOLO11 and RT-DETR to function as real-time incremental object detectors. To comprehensively evaluate both retention and adaptation, we introduce the Retention-Adaptability Index (RAI), which combines the Average Retention Index (Avg RI) for catastrophic forgetting and the Average Generalization Index for domain adaptability into a common ground. Extensive experiments on the Pascal Series and Diverse Weather Series demonstrate DuET's effectiveness, achieving a +13.12% RAI improvement while preserving 89.3% Avg RI on the Pascal Series (4 tasks), as well as a +11.39% RAI improvement with 88.57% Avg RI on the Diverse Weather Series (3 tasks), outperforming existing methods.

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes its target vector field in closed-form. The key ingredient behind RFM is the construction of a relatively simple premetric for defining target vector fields, which encompasses the existing Euclidean case. To extend to general geometries, we rely on the use of spectral decompositions to efficiently compute premetrics on the fly. Our method achieves state-of-the-art performance on many real-world non-Euclidean datasets, and we demonstrate tractable training on general geometries, including triangular meshes with highly non-trivial curvature and boundaries.

The Vehicle Routing Problem (VRP) is a widely studied combinatorial optimization problem and has been applied to various practical problems. While the explainability for VRP is significant for improving the reliability and interactivity in practical VRP applications, it remains unexplored. In this paper, we propose RouteExplainer, a post-hoc explanation framework that explains the influence of each edge in a generated route. Our framework realizes this by rethinking a route as the sequence of actions and extending counterfactual explanations based on the action influence model to VRP. To enhance the explanation, we additionally propose an edge classifier that infers the intentions of each edge, a loss function to train the edge classifier, and explanation-text generation by Large Language Models (LLMs). We quantitatively evaluate our edge classifier on four different VRPs. The results demonstrate its rapid computation while maintaining reasonable accuracy, thereby highlighting its potential for deployment in practical applications. Moreover, on the subject of a tourist route, we qualitatively evaluate explanations generated by our framework. This evaluation not only validates our framework but also shows the synergy between explanation frameworks and LLMs. See https://ntt-dkiku.github.io/xai-vrp for our code, datasets, models, and demo.

Sampling-based algorithms, which eliminate ''unimportant'' computations during forward and/or back propagation (BP), offer potential solutions to accelerate neural network training. However, since sampling introduces approximations to training, such algorithms may not consistently maintain accuracy across various tasks. In this work, we introduce a variance-controlled adaptive sampling (VCAS) method designed to accelerate BP. VCAS computes an unbiased stochastic gradient with fine-grained layerwise importance sampling in data dimension for activation gradient calculation and leverage score sampling in token dimension for weight gradient calculation. To preserve accuracy, we control the additional variance by learning the sample ratio jointly with model parameters during training. We assessed VCAS on multiple fine-tuning and pre-training tasks in both vision and natural language domains. On all the tasks, VCAS can preserve the original training loss trajectory and validation accuracy with an up to 73.87% FLOPs reduction of BP and 49.58% FLOPs reduction of the whole training process. The implementation is available at https://github.com/thu-ml/VCAS .

Reinforcement Learning algorithms that learn from human feedback (RLHF) need to be efficient in terms of statistical complexity, computational complexity, and query complexity. In this work, we consider the RLHF setting where the feedback is given in the format of preferences over pairs of trajectories. In the linear MDP model, using randomization in algorithm design, we present an algorithm that is sample efficient (i.e., has near-optimal worst-case regret bounds) and has polynomial running time (i.e., computational complexity is polynomial with respect to relevant parameters). Our algorithm further minimizes the query complexity through a novel randomized active learning procedure. In particular, our algorithm demonstrates a near-optimal tradeoff between the regret bound and the query complexity. To extend the results to more general nonlinear function approximation, we design a model-based randomized algorithm inspired by the idea of Thompson sampling. Our algorithm minimizes Bayesian regret bound and query complexity, again achieving a near-optimal tradeoff between these two quantities. Computation-wise, similar to the prior Thompson sampling algorithms under the regular RL setting, the main computation primitives of our algorithm are Bayesian supervised learning oracles which have been heavily investigated on the empirical side when applying Thompson sampling algorithms to RL benchmark problems.

We introduce Random Feature Representation Boosting (RFRBoost), a novel method for constructing deep residual random feature neural networks (RFNNs) using boosting theory. RFRBoost uses random features at each layer to learn the functional gradient of the network representation, enhancing performance while preserving the convex optimization benefits of RFNNs. In the case of MSE loss, we obtain closed-form solutions to greedy layer-wise boosting with random features. For general loss functions, we show that fitting random feature residual blocks reduces to solving a quadratically constrained least squares problem. We demonstrate, through numerical experiments on 91 tabular datasets for regression and classification, that RFRBoost significantly outperforms traditional RFNNs and end-to-end trained MLP ResNets, while offering substantial computational advantages and theoretical guarantees stemming from boosting theory.

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

A modified LAB algorithm is introduced in this paper. It builds upon the original LAB algorithm (Reddy et al. 2023), which is a socio-inspired algorithm that models competitive and learning behaviours within a group, establishing hierarchical roles. The proposed algorithm incorporates the roulette wheel approach and a reduction factor introducing inter-group competition and iteratively narrowing down the sample space. The algorithm is validated by solving the benchmark test problems from CEC 2005 and CEC 2017. The solutions are validated using standard statistical tests such as two-sided and pairwise signed rank Wilcoxon test and Friedman rank test. The algorithm exhibited improved and superior robustness as well as search space exploration capabilities. Furthermore, a Clustering-Based Search Space Reduction (C-SSR) method is proposed, making the algorithm capable to solve constrained problems. The C-SSR method enables the algorithm to identify clusters of feasible regions, satisfying the constraints and contributing to achieve the optimal solution. This method demonstrates its effectiveness as a potential alternative to traditional constraint handling techniques. The results obtained using the Modified LAB algorithm are then compared with those achieved by other recent metaheuristic algorithms.

We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies have observed that LR+GD can find a solution with arbitrarily large step sizes, defying conventional optimization theory. Our work investigates this phenomenon and makes three interconnected key observations about LR+GD with large step sizes. First, we find a remarkably simple explanation of why LR+GD with large step sizes solves the classification problem: LR+GD reduces to a batch version of the celebrated perceptron algorithm when the step size gamma to infty. Second, we observe that larger step sizes lead LR+GD to higher logistic losses when it tends to the perceptron algorithm, but larger step sizes also lead to faster convergence to a solution for the classification problem, meaning that logistic loss is an unreliable metric of the proximity to a solution. Surprisingly, high loss values can actually indicate faster convergence. Third, since the convergence rate in terms of loss function values of LR+GD is unreliable, we examine the iteration complexity required by LR+GD with large step sizes to solve the classification problem and prove that this complexity is suboptimal. To address this, we propose a new method, Normalized LR+GD - based on the connection between LR+GD and the perceptron algorithm - with much better theoretical guarantees.

Responding to the challenge of detecting unusual radar targets in a well identified environment, innovative anomaly and novelty detection methods keep emerging in the literature. This work aims at presenting a benchmark gathering common and recently introduced unsupervised anomaly detection (AD) methods, the results being generated using high-resolution range profiles. A semi-supervised AD (SAD) is considered to demonstrate the added value of having a few labeled anomalies to improve performances. Experiments were conducted with and without pollution of the training set with anomalous samples in order to be as close as possible to real operational contexts. The common AD methods composing our baseline will be One-Class Support Vector Machines (OC-SVM), Isolation Forest (IF), Local Outlier Factor (LOF) and a Convolutional Autoencoder (CAE). The more innovative AD methods put forward by this work are Deep Support Vector Data Description (Deep SVDD) and Random Projection Depth (RPD), belonging respectively to deep and shallow AD. The semi-supervised adaptation of Deep SVDD constitutes our SAD method. HRRP data was generated by a coastal surveillance radar, our results thus suggest that AD can contribute to enhance maritime and coastal situation awareness.

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced updates becomes increasingly important. Existing methods for updating truncated SVDs employ Rayleigh-Ritz projection procedures, where projection matrices are augmented based on original singular vectors. However, these methods suffer from inefficiency due to the densification of the update matrix and the application of the projection to all singular vectors. To address these limitations, we introduce a novel method for dynamically approximating the truncated SVD of a sparse and temporally evolving matrix. Our approach leverages sparsity in the orthogonalization process of augmented matrices and utilizes an extended decomposition to independently store projections in the column space of singular vectors. Numerical experiments demonstrate a remarkable efficiency improvement of an order of magnitude compared to previous methods. Remarkably, this improvement is achieved while maintaining a comparable precision to existing approaches.

In this work, we re-formulate the model compression problem into the customized compensation problem: Given a compressed model, we aim to introduce residual low-rank paths to compensate for compression errors under customized requirements from users (e.g., tasks, compression ratios), resulting in greater flexibility in adjusting overall capacity without being constrained by specific compression formats. However, naively applying SVD to derive residual paths causes suboptimal utilization of the low-rank representation capacity. Instead, we propose Training-free Eigenspace Low-Rank Approximation (EoRA), a method that directly minimizes compression-induced errors without requiring gradient-based training, achieving fast optimization in minutes using a small amount of calibration data. EoRA projects compression errors into the eigenspace of input activations, leveraging eigenvalues to effectively prioritize the reconstruction of high-importance error components. Moreover, EoRA can be seamlessly integrated with fine-tuning and quantization to further improve effectiveness and efficiency. EoRA consistently outperforms previous methods in compensating errors for compressed LLaMA2/3 models on various tasks, such as language generation, commonsense reasoning, and math reasoning tasks (e.g., 31.31%/12.88% and 9.69% improvements on ARC-Easy/ARC-Challenge and MathQA when compensating LLaMA3-8B that is quantized to 4-bit and pruned to 2:4 sparsity). EoRA offers a scalable, training-free solution to compensate for compression errors, making it a powerful tool to deploy LLMs in various capacity and efficiency requirements.

Robust estimation is a crucial and still challenging task, which involves estimating model parameters in noisy environments. Although conventional sampling consensus-based algorithms sample several times to achieve robustness, these algorithms cannot use data features and historical information effectively. In this paper, we propose RLSAC, a novel Reinforcement Learning enhanced SAmple Consensus framework for end-to-end robust estimation. RLSAC employs a graph neural network to utilize both data and memory features to guide exploring directions for sampling the next minimum set. The feedback of downstream tasks serves as the reward for unsupervised training. Therefore, RLSAC can avoid differentiating to learn the features and the feedback of downstream tasks for end-to-end robust estimation. In addition, RLSAC integrates a state transition module that encodes both data and memory features. Our experimental results demonstrate that RLSAC can learn from features to gradually explore a better hypothesis. Through analysis, it is apparent that RLSAC can be easily transferred to other sampling consensus-based robust estimation tasks. To the best of our knowledge, RLSAC is also the first method that uses reinforcement learning to sample consensus for end-to-end robust estimation. We release our codes at https://github.com/IRMVLab/RLSAC.

Radio frequency (RF) signal mapping, which is the process of analyzing and predicting the RF signal strength and distribution across specific areas, is crucial for cellular network planning and deployment. Traditional approaches to RF signal mapping rely on statistical models constructed based on measurement data, which offer low complexity but often lack accuracy, or ray tracing tools, which provide enhanced precision for the target area but suffer from increased computational complexity. Recently, machine learning (ML) has emerged as a data-driven method for modeling RF signal propagation, which leverages models trained on synthetic datasets to perform RF signal mapping in "unseen" areas. In this paper, we present Geo2SigMap, an ML-based framework for efficient and high-fidelity RF signal mapping using geographic databases. First, we develop an automated framework that seamlessly integrates three open-source tools: OpenStreetMap (geographic databases), Blender (computer graphics), and Sionna (ray tracing), enabling the efficient generation of large-scale 3D building maps and ray tracing models. Second, we propose a cascaded U-Net model, which is pre-trained on synthetic datasets and employed to generate detailed RF signal maps, leveraging environmental information and sparse measurement data. Finally, we evaluate the performance of Geo2SigMap via a real-world measurement campaign, where three types of user equipment (UE) collect over 45,000 data points related to cellular information from six LTE cells operating in the citizens broadband radio service (CBRS) band. Our results show that Geo2SigMap achieves an average root-mean-square-error (RMSE) of 6.04 dB for predicting the reference signal received power (RSRP) at the UE, representing an average RMSE improvement of 3.59 dB compared to existing methods.

In online algorithm selection (OAS), instances of an algorithmic problem class are presented to an agent one after another, and the agent has to quickly select a presumably best algorithm from a fixed set of candidate algorithms. For decision problems such as satisfiability (SAT), quality typically refers to the algorithm's runtime. As the latter is known to exhibit a heavy-tail distribution, an algorithm is normally stopped when exceeding a predefined upper time limit. As a consequence, machine learning methods used to optimize an algorithm selection strategy in a data-driven manner need to deal with right-censored samples, a problem that has received little attention in the literature so far. In this work, we revisit multi-armed bandit algorithms for OAS and discuss their capability of dealing with the problem. Moreover, we adapt them towards runtime-oriented losses, allowing for partially censored data while keeping a space- and time-complexity independent of the time horizon. In an extensive experimental evaluation on an adapted version of the ASlib benchmark, we demonstrate that theoretically well-founded methods based on Thompson sampling perform specifically strong and improve in comparison to existing methods.

Dimensionality reduction in vector databases is pivotal for streamlining AI data management, enabling efficient storage, faster computation, and improved model performance. This paper explores the benefits of reducing vector database dimensions, with a focus on computational efficiency and overcoming the curse of dimensionality. We introduce a novel application of Fast Fourier Transform (FFT) to dimensionality reduction, a method previously underexploited in this context. By demonstrating its utility across various AI domains, including Retrieval-Augmented Generation (RAG) models and image processing, this FFT-based approach promises to improve data retrieval processes and enhance the efficiency and scalability of AI solutions. The incorporation of FFT may not only optimize operations in real-time processing and recommendation systems but also extend to advanced image processing techniques, where dimensionality reduction can significantly improve performance and analysis efficiency. This paper advocates for the broader adoption of FFT in vector database management, marking a significant stride towards addressing the challenges of data volume and complexity in AI research and applications. Unlike many existing approaches, we directly handle the embedding vectors produced by the model after processing a test input.

As a telecom provider, our company has a critical mission to maintain telecom services even during power outages. To accomplish the mission, it is essential to maintain the power of the telecom base stations. Here we consider a solution where electric vehicles (EVs) directly supply power to base stations by traveling to their locations. The goal is to find EV routes that minimize both the total travel distance of all EVs and the number of downed base stations. In this paper, we formulate this routing problem as a new variant of the Electric Vehicle Routing Problem (EVRP) and propose a solver that combines a rule-based vehicle selector and a reinforcement learning (RL)-based node selector. The rule of the vehicle selector ensures the exact environmental states when the selected EV starts to move. In addition, the node selection by the RL model enables fast route generation, which is critical in emergencies. We evaluate our solver on both synthetic datasets and real datasets. The results show that our solver outperforms baselines in terms of the objective value and computation time. Moreover, we analyze the generalization and scalability of our solver, demonstrating the capability toward unseen settings and large-scale problems. Check also our project page: https://ntt-dkiku.github.io/rl-evrpeps.

Many optimization problems are inherently multi-objective. To address them, we formalize Jacobian descent (JD), a direct generalization of gradient descent for vector-valued functions. Each step of this algorithm relies on a Jacobian matrix consisting of one gradient per objective. The aggregator, responsible for reducing this matrix into an update vector, characterizes JD. While the multi-task learning literature already contains a variety of aggregators, they often lack some natural properties. In particular, the update should not conflict with any objective and should scale proportionally to the norm of each gradient. We propose a new aggregator specifically designed to satisfy this. Emphasizing conflict between objectives, we then highlight direct applications for our methods. Most notably, we introduce instance-wise risk minimization (IWRM), a learning paradigm in which the loss of each training example is considered a separate objective. On simple image classification tasks, IWRM exhibits promising results compared to the direct minimization of the average loss. The performance of our aggregator in those experiments also corroborates our theoretical findings. Lastly, as speed is the main limitation of JD, we provide a path towards a more efficient implementation.

We propose ScaledGD(\lambda), a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor representations, ScaledGD(\lambda) starts from a small random initialization, and proceeds by gradient descent with a specific form of damped preconditioning to combat bad curvatures induced by overparameterization and ill-conditioning. At the expense of light computational overhead incurred by preconditioners, ScaledGD(\lambda) is remarkably robust to ill-conditioning compared to vanilla gradient descent (GD) even with overprameterization. Specifically, we show that, under the Gaussian design, ScaledGD(\lambda) converges to the true low-rank matrix at a constant linear rate after a small number of iterations that scales only logarithmically with respect to the condition number and the problem dimension. This significantly improves over the convergence rate of vanilla GD which suffers from a polynomial dependency on the condition number. Our work provides evidence on the power of preconditioning in accelerating the convergence without hurting generalization in overparameterized learning.

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term K-RCPS, which allows to (i) provide entrywise calibrated intervals for future samples of any diffusion model, and (ii) control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

Robust Markov decision processes (MDPs) address the challenge of model uncertainty by optimizing the worst-case performance over an uncertainty set of MDPs. In this paper, we focus on the robust average-reward MDPs under the model-free setting. We first theoretically characterize the structure of solutions to the robust average-reward Bellman equation, which is essential for our later convergence analysis. We then design two model-free algorithms, robust relative value iteration (RVI) TD and robust RVI Q-learning, and theoretically prove their convergence to the optimal solution. We provide several widely used uncertainty sets as examples, including those defined by the contamination model, total variation, Chi-squared divergence, Kullback-Leibler (KL) divergence and Wasserstein distance.

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

We study the algorithm configuration (AC) problem, in which one seeks to find an optimal parameter configuration of a given target algorithm in an automated way. Recently, there has been significant progress in designing AC approaches that satisfy strong theoretical guarantees. However, a significant gap still remains between the practical performance of these approaches and state-of-the-art heuristic methods. To this end, we introduce AC-Band, a general approach for the AC problem based on multi-armed bandits that provides theoretical guarantees while exhibiting strong practical performance. We show that AC-Band requires significantly less computation time than other AC approaches providing theoretical guarantees while still yielding high-quality configurations.

We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal algorithm with a closed-form projection and proximal operator scheme, thereby affording a more scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry, compared to previous regularizers.

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their efficiency and scalability, the existing feature grids with linear indexing for continuous-space points can only provide degenerate linear latent space representations, and such representations cannot be adequately compensated to represent complex nonlinear signals by the following compact decoder. To address this problem while keeping the simplicity of a regular grid structure, our approach builds upon the standard grid-based paradigm by constructing multiple elementary metric grids as high-order terms to approximate complex nonlinearities, following the Taylor expansion principle. Furthermore, we enhance model compactness with hash encoding based on different sparsities of the grids to prevent detrimental hash collisions, and a high-order extrapolation decoder to reduce explicit grid storage requirements. experimental results on both 2D and 3D reconstructions demonstrate the superior fitting and rendering accuracy of the proposed method across diverse signal types, validating its robustness and generalizability. Code is available at https://github.com/wangshu31/MetricGrids}{https://github.com/wangshu31/MetricGrids.

This paper establishes a mathematical foundation for the Adam optimizer, elucidating its connection to natural gradient descent through Riemannian and information geometry. We rigorously analyze the diagonal empirical Fisher information matrix (FIM) in Adam, clarifying all detailed approximations and advocating for the use of log probability functions as loss, which should be based on discrete distributions, due to the limitations of empirical FIM. Our analysis uncovers flaws in the original Adam algorithm, leading to proposed corrections such as enhanced momentum calculations, adjusted bias corrections, and gradient clipping. We refine the weight decay term based on our theoretical framework. Our modified algorithm, Fisher Adam (FAdam), demonstrates superior performance across diverse domains including LLM, ASR, and VQ-VAE, achieving state-of-the-art results in ASR.

This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds. The class of FMa has reached a significant popularity in bigdata stream learning, and the attention of the literature has mainly been based on algorithmic aspects, basically complexity optimality, while the statistical analysis of these class of algorithms has been often faced heuristically. The analysis provided here shows deep connections with mathematical special functions and with extreme value theory. The latter connection may help in explaining heuristic considerations, while the first opens many numerical issues, faced at the end of the present paper. Finally, the algorithms are tested on an anonymized real data stream and MonteCarlo simulations are provided to support our analytical choice in this context.

Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix scaling and guarantees an approximated solution with near-linear runtime. Despite the success of the Sinkhorn algorithm, its runtime may still be slow due to the potentially large number of iterations needed for convergence. To achieve possibly super-exponential convergence, we present Sinkhorn-Newton-Sparse (SNS), an extension to the Sinkhorn algorithm, by introducing early stopping for the matrix scaling steps and a second stage featuring a Newton-type subroutine. Adopting the variational viewpoint that the Sinkhorn algorithm maximizes a concave Lyapunov potential, we offer the insight that the Hessian matrix of the potential function is approximately sparse. Sparsification of the Hessian results in a fast O(n^2) per-iteration complexity, the same as the Sinkhorn algorithm. In terms of total iteration count, we observe that the SNS algorithm converges orders of magnitude faster across a wide range of practical cases, including optimal transportation between empirical distributions and calculating the Wasserstein W_1, W_2 distance of discretized densities. The empirical performance is corroborated by a rigorous bound on the approximate sparsity of the Hessian matrix.

Many problems, such as online ad display, can be formulated as online bipartite matching. The crucial challenge lies in the nature of sequentially-revealed online item information, based on which we make irreversible matching decisions at each step. While numerous expert online algorithms have been proposed with bounded worst-case competitive ratios, they may not offer satisfactory performance in average cases. On the other hand, reinforcement learning (RL) has been applied to improve the average performance, but it lacks robustness and can perform arbitrarily poorly. In this paper, we propose a novel RL-based approach to edge-weighted online bipartite matching with robustness guarantees (LOMAR), achieving both good average-case and worst-case performance. The key novelty of LOMAR is a new online switching operation which, based on a judicious condition to hedge against future uncertainties, decides whether to follow the expert's decision or the RL decision for each online item. We prove that for any rhoin[0,1], LOMAR is rho-competitive against any given expert online algorithm. To improve the average performance, we train the RL policy by explicitly considering the online switching operation. Finally, we run empirical experiments to demonstrate the advantages of LOMAR compared to existing baselines. Our code is available at: https://github.com/Ren-Research/LOMAR

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat\'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

Vector Quantization (VQ) is an appealing model compression method to obtain a tiny model with less accuracy loss. While methods to obtain better codebooks and codes under fixed clustering dimensionality have been extensively studied, optimizations of the vectors in favour of clustering performance are not carefully considered, especially via the reduction of vector dimensionality. This paper reports our recent progress on the combination of dimensionality compression and vector quantization, proposing a Low-Rank Representation Vector Quantization (LR^2VQ) method that outperforms previous VQ algorithms in various tasks and architectures. LR^2VQ joins low-rank representation with subvector clustering to construct a new kind of building block that is directly optimized through end-to-end training over the task loss. Our proposed design pattern introduces three hyper-parameters, the number of clusters k, the size of subvectors m and the clustering dimensionality d. In our method, the compression ratio could be directly controlled by m, and the final accuracy is solely determined by d. We recognize d as a trade-off between low-rank approximation error and clustering error and carry out both theoretical analysis and experimental observations that empower the estimation of the proper d before fine-tunning. With a proper d, we evaluate LR^2VQ with ResNet-18/ResNet-50 on ImageNet classification datasets, achieving 2.8\%/1.0\% top-1 accuracy improvements over the current state-of-the-art VQ-based compression algorithms with 43times/31times compression factor.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

We present a new regular grid search algorithm for quick fixed-radius nearest-neighbor lookup developed in Python. This module indexes a set of k-dimensional points in a regular grid, with optional periodic conditions, providing a fast approach for nearest neighbors queries. In this first installment we provide three types of queries: bubble, shell and the nth-nearest; as well as three different metrics of interest in astronomy: the euclidean and two distance functions in spherical coordinates of varying precision, haversine and Vincenty; and the possibility of providing a custom distance function. This package results particularly useful for large datasets where a brute-force search turns impractical.

RANSAC-based algorithms are the standard techniques for robust estimation in computer vision. These algorithms are iterative and computationally expensive; they alternate between random sampling of data, computing hypotheses, and running inlier counting. Many authors tried different approaches to improve efficiency. One of the major improvements is having a guided sampling, letting the RANSAC cycle stop sooner. This paper presents a new adaptive sampling process for RANSAC. Previous methods either assume no prior information about the inlier/outlier classification of data points or use some previously computed scores in the sampling. In this paper, we derive a dynamic Bayesian network that updates individual data points' inlier scores while iterating RANSAC. At each iteration, we apply weighted sampling using the updated scores. Our method works with or without prior data point scorings. In addition, we use the updated inlier/outlier scoring for deriving a new stopping criterion for the RANSAC loop. We test our method in multiple real-world datasets for several applications and obtain state-of-the-art results. Our method outperforms the baselines in accuracy while needing less computational time.

Motivation: Ab initio protein docking represents a major challenge for optimizing a noisy and costly "black box"-like function in a high-dimensional space. Despite progress in this field, there is no docking method available for rigorous uncertainty quantification (UQ) of its solution quality (e.g. interface RMSD or iRMSD). Results: We introduce a novel algorithm, Bayesian Active Learning (BAL), for optimization and UQ of such black-box functions and flexible protein docking. BAL directly models the posterior distribution of the global optimum (or native structures for protein docking) with active sampling and posterior estimation iteratively feeding each other. Furthermore, we use complex normal modes to represent a homogeneous Euclidean conformation space suitable for high-dimension optimization and construct funnel-like energy models for encounter complexes. Over a protein docking benchmark set and a CAPRI set including homology docking, we establish that BAL significantly improve against both starting points by rigid docking and refinements by particle swarm optimization, providing for one third targets a top-3 near-native prediction. BAL also generates tight confidence intervals with half range around 25% of iRMSD and confidence level at 85%. Its estimated probability of a prediction being native or not achieves binary classification AUROC at 0.93 and AUPRC over 0.60 (compared to 0.14 by chance); and also found to help ranking predictions. To the best of our knowledge, this study represents the first uncertainty quantification solution for protein docking, with theoretical rigor and comprehensive assessment. Source codes are available at https://github.com/Shen-Lab/BAL.

Robust Markov decision processes (RMDPs) provide a promising framework for computing reliable policies in the face of model errors. Many successful reinforcement learning algorithms build on variations of policy-gradient methods, but adapting these methods to RMDPs has been challenging. As a result, the applicability of RMDPs to large, practical domains remains limited. This paper proposes a new Double-Loop Robust Policy Gradient (DRPG), the first generic policy gradient method for RMDPs. In contrast with prior robust policy gradient algorithms, DRPG monotonically reduces approximation errors to guarantee convergence to a globally optimal policy in tabular RMDPs. We introduce a novel parametric transition kernel and solve the inner loop robust policy via a gradient-based method. Finally, our numerical results demonstrate the utility of our new algorithm and confirm its global convergence properties.

This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear measurements. First, we consider the symmetric setting with the symmetric parameterization where M^* in R^{n times n} is a positive semi-definite unknown matrix of rank r ll n, and one uses a symmetric parameterization XX^top to learn M^*. Here X in R^{n times k} with k > r is the factor matrix. We give a novel Omega (1/T^2) lower bound of randomly initialized GD for the over-parameterized case (k >r) where T is the number of iterations. This is in stark contrast to the exact-parameterization scenario (k=r) where the convergence rate is exp (-Omega (T)). Next, we study asymmetric setting where M^* in R^{n_1 times n_2} is the unknown matrix of rank r ll min{n_1,n_2}, and one uses an asymmetric parameterization FG^top to learn M^* where F in R^{n_1 times k} and G in R^{n_2 times k}. Building on prior work, we give a global exact convergence result of randomly initialized GD for the exact-parameterization case (k=r) with an exp (-Omega(T)) rate. Furthermore, we give the first global exact convergence result for the over-parameterization case (k>r) with an exp(-Omega(alpha^2 T)) rate where alpha is the initialization scale. This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from Omega (1/T^2) to linear convergence. On the other hand, we propose a novel method that only modifies one step of GD and obtains a convergence rate independent of alpha, recovering the rate in the exact-parameterization case.

Enabling On-Device Learning (ODL) for Ultra-Low-Power Micro-Controller Units (MCUs) is a key step for post-deployment adaptation and fine-tuning of Deep Neural Network (DNN) models in future TinyML applications. This paper tackles this challenge by introducing a novel reduced precision optimization technique for ODL primitives on MCU-class devices, leveraging the State-of-Art advancements in RISC-V RV32 architectures with support for vectorized 16-bit floating-point (FP16) Single-Instruction Multiple-Data (SIMD) operations. Our approach for the Forward and Backward steps of the Back-Propagation training algorithm is composed of specialized shape transform operators and Matrix Multiplication (MM) kernels, accelerated with parallelization and loop unrolling. When evaluated on a single training step of a 2D Convolution layer, the SIMD-optimized FP16 primitives result up to 1.72times faster than the FP32 baseline on a RISC-V-based 8+1-core MCU. An average computing efficiency of 3.11 Multiply and Accumulate operations per clock cycle (MAC/clk) and 0.81 MAC/clk is measured for the end-to-end training tasks of a ResNet8 and a DS-CNN for Image Classification and Keyword Spotting, respectively -- requiring 17.1 ms and 6.4 ms on the target platform to compute a training step on a single sample. Overall, our approach results more than two orders of magnitude faster than existing ODL software frameworks for single-core MCUs and outperforms by 1.6 times previous FP32 parallel implementations on a Continual Learning setup.

We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover a network that can be expressed using a certain number of nonzero terms. Specifically, if there is a set of weights that uses at most s terms that can re-create the layer outputs from the layer inputs, we can find these weights from O(slog N/s) samples, where N is the input size. These theoretical results are similar to those for sparse regression using the Lasso, and our analysis uses some of the same recently-developed tools (namely recent results on the concentration of measure and convex analysis). Finally, we propose an algorithmic framework based on the alternating direction method of multipliers (ADMM), which allows a fast and simple implementation of Net-Trim for network pruning and compression.

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. We show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.

In this empirical article, we introduce INNAprop, an optimization algorithm that combines the INNA method with the RMSprop adaptive gradient scaling. It leverages second-order information and rescaling while keeping the memory requirements of standard DL methods as AdamW or SGD with momentum.After having recalled our geometrical motivations, we provide quite extensive experiments. On image classification (CIFAR-10, ImageNet) and language modeling (GPT-2), INNAprop consistently matches or outperforms AdamW both in training speed and accuracy, with minimal hyperparameter tuning in large-scale settings. Our code is publicly available at https://github.com/innaprop/innaprop.

Crop row detection is essential for enabling autonomous navigation in GPS-denied environments, such as under-canopy agricultural settings. Traditional methods often struggle with occlusions, variable lighting conditions, and the structural variability of crop rows. To address these challenges, RowDetr, a novel end-to-end neural network architecture, is introduced for robust and efficient row detection. A new dataset of approximately 6,900 images is curated, capturing a diverse range of real-world agricultural conditions, including occluded rows, uneven terrain, and varying crop densities. Unlike previous approaches, RowDetr leverages smooth polynomial functions to precisely delineate crop boundaries in the image space, ensuring a more structured and interpretable representation of row geometry. A key innovation of this approach is PolyOptLoss, a novel energy-based loss function designed to enhance learning robustness, even in the presence of noisy or imperfect labels. This loss function significantly improves model stability and generalization by optimizing polynomial curve fitting directly in image space. Extensive experiments demonstrate that RowDetr significantly outperforms existing frameworks, including Agronav and RowColAttention, across key performance metrics. Additionally, RowDetr achieves a sixfold speedup over Agronav, making it highly suitable for real-time deployment on resource-constrained edge devices. To facilitate better comparisons across future studies, lane detection metrics from autonomous driving research are adapted, providing a more standardized and meaningful evaluation framework for crop row detection. This work establishes a new benchmark in under-canopy

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

This work presents a fast and scalable algorithm for incremental learning of Gaussian mixture models. By performing rank-one updates on its precision matrices and determinants, its asymptotic time complexity is of NKD^2 for N data points, K Gaussian components and D dimensions. The resulting algorithm can be applied to high dimensional tasks, and this is confirmed by applying it to the classification datasets MNIST and CIFAR-10. Additionally, in order to show the algorithm's applicability to function approximation and control tasks, it is applied to three reinforcement learning tasks and its data-efficiency is evaluated.

Autoregressive (AR) models have achieved state-of-the-art performance in text and image generation but suffer from slow generation due to the token-by-token process. We ask an ambitious question: can a pre-trained AR model be adapted to generate outputs in just one or two steps? If successful, this would significantly advance the development and deployment of AR models. We notice that existing works that try to speed up AR generation by generating multiple tokens at once fundamentally cannot capture the output distribution due to the conditional dependencies between tokens, limiting their effectiveness for few-step generation. To address this, we propose Distilled Decoding (DD), which uses flow matching to create a deterministic mapping from Gaussian distribution to the output distribution of the pre-trained AR model. We then train a network to distill this mapping, enabling few-step generation. DD doesn't need the training data of the original AR model, making it more practical.We evaluate DD on state-of-the-art image AR models and present promising results on ImageNet-256. For VAR, which requires 10-step generation, DD enables one-step generation (6.3times speed-up), with an acceptable increase in FID from 4.19 to 9.96. For LlamaGen, DD reduces generation from 256 steps to 1, achieving an 217.8times speed-up with a comparable FID increase from 4.11 to 11.35. In both cases, baseline methods completely fail with FID>100. DD also excels on text-to-image generation, reducing the generation from 256 steps to 2 for LlamaGen with minimal FID increase from 25.70 to 28.95. As the first work to demonstrate the possibility of one-step generation for image AR models, DD challenges the prevailing notion that AR models are inherently slow, and opens up new opportunities for efficient AR generation. The project website is at https://imagination-research.github.io/distilled-decoding.

This work investigates the integration of spatially aligned aerial imagery into perception tasks for automated vehicles (AVs). As a central contribution, we present AID4AD, a publicly available dataset that augments the nuScenes dataset with high-resolution aerial imagery precisely aligned to its local coordinate system. The alignment is performed using SLAM-based point cloud maps provided by nuScenes, establishing a direct link between aerial data and nuScenes local coordinate system. To ensure spatial fidelity, we propose an alignment workflow that corrects for localization and projection distortions. A manual quality control process further refines the dataset by identifying a set of high-quality alignments, which we publish as ground truth to support future research on automated registration. We demonstrate the practical value of AID4AD in two representative tasks: in online map construction, aerial imagery serves as a complementary input that improves the mapping process; in motion prediction, it functions as a structured environmental representation that replaces high-definition maps. Experiments show that aerial imagery leads to a 15-23% improvement in map construction accuracy and a 2% gain in trajectory prediction performance. These results highlight the potential of aerial imagery as a scalable and adaptable source of environmental context in automated vehicle systems, particularly in scenarios where high-definition maps are unavailable, outdated, or costly to maintain. AID4AD, along with evaluation code and pretrained models, is publicly released to foster further research in this direction: https://github.com/DriverlessMobility/AID4AD.

We propose to study and promote the robustness of a model as per its performance through the interpolation of training data distributions. Specifically, (1) we augment the data by finding the worst-case Wasserstein barycenter on the geodesic connecting subpopulation distributions of different categories. (2) We regularize the model for smoother performance on the continuous geodesic path connecting subpopulation distributions. (3) Additionally, we provide a theoretical guarantee of robustness improvement and investigate how the geodesic location and the sample size contribute, respectively. Experimental validations of the proposed strategy on four datasets, including CIFAR-100 and ImageNet, establish the efficacy of our method, e.g., our method improves the baselines' certifiable robustness on CIFAR10 up to 7.7%, with 16.8% on empirical robustness on CIFAR-100. Our work provides a new perspective of model robustness through the lens of Wasserstein geodesic-based interpolation with a practical off-the-shelf strategy that can be combined with existing robust training methods.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

The Distributionally Robust Markov Decision Process (DRMDP) is a popular framework for addressing dynamics shift in reinforcement learning by learning policies robust to the worst-case transition dynamics within a constrained set. However, solving its dual optimization oracle poses significant challenges, limiting theoretical analysis and computational efficiency. The recently proposed Robust Regularized Markov Decision Process (RRMDP) replaces the uncertainty set constraint with a regularization term on the value function, offering improved scalability and theoretical insights. Yet, existing RRMDP methods rely on unstructured regularization, often leading to overly conservative policies by considering transitions that are unrealistic. To address these issues, we propose a novel framework, the d-rectangular linear robust regularized Markov decision process (d-RRMDP), which introduces a linear latent structure into both transition kernels and regularization. For the offline RL setting, where an agent learns robust policies from a pre-collected dataset in the nominal environment, we develop a family of algorithms, Robust Regularized Pessimistic Value Iteration (R2PVI), employing linear function approximation and f-divergence based regularization terms on transition kernels. We provide instance-dependent upper bounds on the suboptimality gap of R2PVI policies, showing these bounds depend on how well the dataset covers state-action spaces visited by the optimal robust policy under robustly admissible transitions. This term is further shown to be fundamental to d-RRMDPs via information-theoretic lower bounds. Finally, numerical experiments validate that R2PVI learns robust policies and is computationally more efficient than methods for constrained DRMDPs.

Machine learning is a prevalent approach to tame the complexity of design space exploration for domain-specific architectures. Using ML for design space exploration poses challenges. First, it's not straightforward to identify the suitable algorithm from an increasing pool of ML methods. Second, assessing the trade-offs between performance and sample efficiency across these methods is inconclusive. Finally, lack of a holistic framework for fair, reproducible, and objective comparison across these methods hinders progress of adopting ML-aided architecture design space exploration and impedes creating repeatable artifacts. To mitigate these challenges, we introduce ArchGym, an open-source gym and easy-to-extend framework that connects diverse search algorithms to architecture simulators. To demonstrate utility, we evaluate ArchGym across multiple vanilla and domain-specific search algorithms in designing custom memory controller, deep neural network accelerators, and custom SoC for AR/VR workloads, encompassing over 21K experiments. Results suggest that with unlimited samples, ML algorithms are equally favorable to meet user-defined target specification if hyperparameters are tuned; no solution is necessarily better than another (e.g., reinforcement learning vs. Bayesian methods). We coin the term hyperparameter lottery to describe the chance for a search algorithm to find an optimal design provided meticulously selected hyperparameters. The ease of data collection and aggregation in ArchGym facilitates research in ML-aided architecture design space exploration. As a case study, we show this advantage by developing a proxy cost model with an RMSE of 0.61% that offers a 2,000-fold reduction in simulation time. Code and data for ArchGym is available at https://bit.ly/ArchGym.

Model evolution and constant availability of data are two common phenomena in large-scale real-world machine learning applications, e.g. ads and recommendation systems. To adapt, the real-world system typically retrain with all available data and online learn with recently available data to update the models periodically with the goal of better serving performance. In this paper, we propose a novel framework, named Confidence Ranking, which designs the optimization objective as a ranking function with two different models. Our confidence ranking loss allows direct optimization of the logits output for different convex surrogate functions of metrics, e.g. AUC and Accuracy depending on the target task and dataset. Armed with our proposed methods, our experiments show that the introduction of confidence ranking loss can outperform all baselines on the CTR prediction tasks of public and industrial datasets. This framework has been deployed in the advertisement system of JD.com to serve the main traffic in the fine-rank stage.

Variance reduction (VR) techniques have contributed significantly to accelerating learning with massive datasets in the smooth and strongly convex setting (Schmidt et al., 2017; Johnson & Zhang, 2013; Roux et al., 2012). However, such techniques have not yet met the same success in the realm of large-scale deep learning due to various factors such as the use of data augmentation or regularization methods like dropout (Defazio & Bottou, 2019). This challenge has recently motivated the design of novel variance reduction techniques tailored explicitly for deep learning (Arnold et al., 2019; Ma & Yarats, 2018). This work is an additional step in this direction. In particular, we exploit the ubiquitous clustering structure of rich datasets used in deep learning to design a family of scalable variance reduced optimization procedures by combining existing optimizers (e.g., SGD+Momentum, Quasi Hyperbolic Momentum, Implicit Gradient Transport) with a multi-momentum strategy (Yuan et al., 2019). Our proposal leads to faster convergence than vanilla methods on standard benchmark datasets (e.g., CIFAR and ImageNet). It is robust to label noise and amenable to distributed optimization. We provide a parallel implementation in JAX.

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve mgg 1 lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its variance is more intricate due to the hierarchical sampling of blocks and data and the unique challenge of estimating hyper-gradient. We aim to achieve three nice properties for our algorithm: (a) matching the state-of-the-art complexity of standard BO problems with a single block; (b) achieving parallel speedup by sampling I blocks and sampling B samples for each sampled block per-iteration; (c) avoiding the computation of the inverse of a high-dimensional Hessian matrix estimator. However, it is non-trivial to achieve all of these by observing that existing works only achieve one or two of these properties. To address the involved challenges for achieving (a, b, c), we propose two stochastic algorithms by using advanced blockwise variance-reduction techniques for tracking the Hessian matrices (for low-dimensional problems) or the Hessian-vector products (for high-dimensional problems), and prove an iteration complexity of O(mepsilon^{-3I(I<m)}{II} + mepsilon^{-3}{IB}) for finding an epsilon-stationary point under appropriate conditions. We also conduct experiments to verify the effectiveness of the proposed algorithms comparing with existing MBBO algorithms.

Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of {ell_2} certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension d, proportionally decreasing at a rate of 1/d. This paper explores the feasibility of providing {ell_2} certified robustness for high-dimensional input through the utilization of dual smoothing in the lower-dimensional space. The proposed Dual Randomized Smoothing (DRS) down-samples the input image into two sub-images and smooths the two sub-images in lower dimensions. Theoretically, we prove that DRS guarantees a tight {ell_2} certified robustness radius for the original input and reveal that DRS attains a superior upper bound on the {ell_2} robustness radius, which decreases proportionally at a rate of (1/sqrt m + 1/sqrt n ) with m+n=d. Extensive experiments demonstrate the generalizability and effectiveness of DRS, which exhibits a notable capability to integrate with established methodologies, yielding substantial improvements in both accuracy and {ell_2} certified robustness baselines of RS on the CIFAR-10 and ImageNet datasets. Code is available at https://github.com/xiasong0501/DRS.

Vector similarity search presents significant challenges in terms of scalability for large and high-dimensional datasets, as well as in providing native support for hybrid queries. Serverless computing and cloud functions offer attractive benefits such as elasticity and cost-effectiveness, but are difficult to apply to data-intensive workloads. Jointly addressing these two main challenges, we present SQUASH, the first fully serverless vector search solution with rich support for hybrid queries. It features OSQ, an optimized and highly parallelizable quantization-based approach for vectors and attributes. Its segment-based storage mechanism enables significant compression in resource-constrained settings and offers efficient dimensional extraction operations. SQUASH performs a single distributed pass to guarantee the return of sufficiently many vectors satisfying the filter predicate, achieving high accuracy and avoiding redundant computation for vectors which fail the predicate. A multi-level search workflow is introduced to prune most vectors early to minimize the load on Function-as-a-Service (FaaS) instances. SQUASH is designed to identify and utilize retention of relevant data in re-used runtime containers, which eliminates redundant I/O and reduces costs. Finally, we demonstrate a new tree-based method for rapid FaaS invocation, enabling the bi-directional flow of data via request/response payloads. Experiments comparing SQUASH with state-of-the-art serverless vector search solutions and server-based baselines on vector search benchmarks confirm significant performance improvements at a lower cost.

The learning rate warmup heuristic achieves remarkable success in stabilizing training, accelerating convergence and improving generalization for adaptive stochastic optimization algorithms like RMSprop and Adam. Here, we study its mechanism in details. Pursuing the theory behind warmup, we identify a problem of the adaptive learning rate (i.e., it has problematically large variance in the early stage), suggest warmup works as a variance reduction technique, and provide both empirical and theoretical evidence to verify our hypothesis. We further propose RAdam, a new variant of Adam, by introducing a term to rectify the variance of the adaptive learning rate. Extensive experimental results on image classification, language modeling, and neural machine translation verify our intuition and demonstrate the effectiveness and robustness of our proposed method. All implementations are available at: https://github.com/LiyuanLucasLiu/RAdam.

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret performance compared to existing approaches. The first algorithm, although computationally inefficient, ensures a regret of mathcal{O}left(Kright), where K is the number of episodes. This is the first result with the optimal K dependence in the considered setting. The second algorithm, which is based on the policy optimization framework, guarantees a regret of mathcal{O}left(K^{3{4}} right) and is computationally efficient. Both our results significantly improve over the state-of-the-art: a computationally inefficient algorithm by Kong et al. [2023] with mathcal{O}left(K^{4{5}}+polyleft(1{lambda_{min}}right) right) regret, for some problem-dependent constant lambda_{min} that can be arbitrarily close to zero, and a computationally efficient algorithm by Sherman et al. [2023b] with mathcal{O}left(K^{6{7}} right) regret.

The development of an open and free RISC-V architecture is of great interest for a wide range of areas, including high-performance computing and numerical simulation in mathematics, physics, chemistry and other problem domains. In this paper, we discuss the possibilities of accelerating computations on available RISC-V processors by improving the vectorization of several computer vision and machine learning algorithms in the widely used OpenCV library. It is shown that improved vectorization speeds up computations on existing prototypes of RISC-V devices by tens of percent.

We show that classifiers trained with random region proposals achieve state-of-the-art Open-world Object Detection (OWOD): they can not only maintain the accuracy of the known objects (w/ training labels), but also considerably improve the recall of unknown ones (w/o training labels). Specifically, we propose RandBox, a Fast R-CNN based architecture trained on random proposals at each training iteration, surpassing existing Faster R-CNN and Transformer based OWOD. Its effectiveness stems from the following two benefits introduced by randomness. First, as the randomization is independent of the distribution of the limited known objects, the random proposals become the instrumental variable that prevents the training from being confounded by the known objects. Second, the unbiased training encourages more proposal explorations by using our proposed matching score that does not penalize the random proposals whose prediction scores do not match the known objects. On two benchmarks: Pascal-VOC/MS-COCO and LVIS, RandBox significantly outperforms the previous state-of-the-art in all metrics. We also detail the ablations on randomization and loss designs. Codes are available at https://github.com/scuwyh2000/RandBox.

Discrete diffusion or flow models could enable faster and more controllable sequence generation than autoregressive models. We show that na\"ive linear flow matching on the simplex is insufficient toward this goal since it suffers from discontinuities in the training target and further pathologies. To overcome this, we develop Dirichlet flow matching on the simplex based on mixtures of Dirichlet distributions as probability paths. In this framework, we derive a connection between the mixtures' scores and the flow's vector field that allows for classifier and classifier-free guidance. Further, we provide distilled Dirichlet flow matching, which enables one-step sequence generation with minimal performance hits, resulting in O(L) speedups compared to autoregressive models. On complex DNA sequence generation tasks, we demonstrate superior performance compared to all baselines in distributional metrics and in achieving desired design targets for generated sequences. Finally, we show that our classifier-free guidance approach improves unconditional generation and is effective for generating DNA that satisfies design targets. Code is available at https://github.com/HannesStark/dirichlet-flow-matching.

Diffusion models have shown great promise for image and video generation, but sampling from state-of-the-art models requires expensive numerical integration of a generative ODE. One approach for tackling this problem is rectified flows, which iteratively learn smooth ODE paths that are less susceptible to truncation error. However, rectified flows still require a relatively large number of function evaluations (NFEs). In this work, we propose improved techniques for training rectified flows, allowing them to compete with knowledge distillation methods even in the low NFE setting. Our main insight is that under realistic settings, a single iteration of the Reflow algorithm for training rectified flows is sufficient to learn nearly straight trajectories; hence, the current practice of using multiple Reflow iterations is unnecessary. We thus propose techniques to improve one-round training of rectified flows, including a U-shaped timestep distribution and LPIPS-Huber premetric. With these techniques, we improve the FID of the previous 2-rectified flow by up to 72% in the 1 NFE setting on CIFAR-10. On ImageNet 64times64, our improved rectified flow outperforms the state-of-the-art distillation methods such as consistency distillation and progressive distillation in both one-step and two-step settings and rivals the performance of improved consistency training (iCT) in FID. Code is available at https://github.com/sangyun884/rfpp.

Is the lottery ticket phenomenon an idiosyncrasy of gradient-based training or does it generalize to evolutionary optimization? In this paper we establish the existence of highly sparse trainable initializations for evolution strategies (ES) and characterize qualitative differences compared to gradient descent (GD)-based sparse training. We introduce a novel signal-to-noise iterative pruning procedure, which incorporates loss curvature information into the network pruning step. This can enable the discovery of even sparser trainable network initializations when using black-box evolution as compared to GD-based optimization. Furthermore, we find that these initializations encode an inductive bias, which transfers across different ES, related tasks and even to GD-based training. Finally, we compare the local optima resulting from the different optimization paradigms and sparsity levels. In contrast to GD, ES explore diverse and flat local optima and do not preserve linear mode connectivity across sparsity levels and independent runs. The results highlight qualitative differences between evolution and gradient-based learning dynamics, which can be uncovered by the study of iterative pruning procedures.

A recourse action aims to explain a particular algorithmic decision by showing one specific way in which the instance could be modified to receive an alternate outcome. Existing recourse generation methods often assume that the machine learning model does not change over time. However, this assumption does not always hold in practice because of data distribution shifts, and in this case, the recourse action may become invalid. To redress this shortcoming, we propose the Distributionally Robust Recourse Action (DiRRAc) framework, which generates a recourse action that has a high probability of being valid under a mixture of model shifts. We formulate the robustified recourse setup as a min-max optimization problem, where the max problem is specified by Gelbrich distance over an ambiguity set around the distribution of model parameters. Then we suggest a projected gradient descent algorithm to find a robust recourse according to the min-max objective. We show that our DiRRAc framework can be extended to hedge against the misspecification of the mixture weights. Numerical experiments with both synthetic and three real-world datasets demonstrate the benefits of our proposed framework over state-of-the-art recourse methods.

Training deep neural networks--and more recently, large models--demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (Make vAriance Reduction Shine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

Offline reinforcement learning (RL), where the agent aims to learn the optimal policy based on the data collected by a behavior policy, has attracted increasing attention in recent years. While offline RL with linear function approximation has been extensively studied with optimal results achieved under certain assumptions, many works shift their interest to offline RL with non-linear function approximation. However, limited works on offline RL with non-linear function approximation have instance-dependent regret guarantees. In this paper, we propose an oracle-efficient algorithm, dubbed Pessimistic Nonlinear Least-Square Value Iteration (PNLSVI), for offline RL with non-linear function approximation. Our algorithmic design comprises three innovative components: (1) a variance-based weighted regression scheme that can be applied to a wide range of function classes, (2) a subroutine for variance estimation, and (3) a planning phase that utilizes a pessimistic value iteration approach. Our algorithm enjoys a regret bound that has a tight dependency on the function class complexity and achieves minimax optimal instance-dependent regret when specialized to linear function approximation. Our work extends the previous instance-dependent results within simpler function classes, such as linear and differentiable function to a more general framework.

It has recently been conjectured that neural network solution sets reachable via stochastic gradient descent (SGD) are convex, considering permutation invariances (Entezari et al., 2022). This means that a linear path can connect two independent solutions with low loss, given the weights of one of the models are appropriately permuted. However, current methods to test this theory often require very wide networks to succeed. In this work, we conjecture that more generally, the SGD solution set is a "star domain" that contains a "star model" that is linearly connected to all the other solutions via paths with low loss values, modulo permutations. We propose the Starlight algorithm that finds a star model of a given learning task. We validate our claim by showing that this star model is linearly connected with other independently found solutions. As an additional benefit of our study, we demonstrate better uncertainty estimates on the Bayesian Model Averaging over the obtained star domain. Further, we demonstrate star models as potential substitutes for model ensembles. Our code is available at https://github.com/aktsonthalia/starlight.

Max sliced Wasserstein (Max-SW) distance has been widely known as a solution for less discriminative projections of sliced Wasserstein (SW) distance. In applications that have various independent pairs of probability measures, amortized projection optimization is utilized to predict the ``max" projecting directions given two input measures instead of using projected gradient ascent multiple times. Despite being efficient, Max-SW and its amortized version cannot guarantee metricity property due to the sub-optimality of the projected gradient ascent and the amortization gap. Therefore, we propose to replace Max-SW with distributional sliced Wasserstein distance with von Mises-Fisher (vMF) projecting distribution (v-DSW). Since v-DSW is a metric with any non-degenerate vMF distribution, its amortized version can guarantee the metricity when performing amortization. Furthermore, current amortized models are not permutation invariant and symmetric. To address the issue, we design amortized models based on self-attention architecture. In particular, we adopt efficient self-attention architectures to make the computation linear in the number of supports. With the two improvements, we derive self-attention amortized distributional projection optimization and show its appealing performance in point-cloud reconstruction and its downstream applications.

Robust routing under uncertainty is central to real-world logistics, yet most benchmarks assume static, idealized settings. We present SVRPBench, the first open benchmark to capture high-fidelity stochastic dynamics in vehicle routing at urban scale. Spanning more than 500 instances with up to 1000 customers, it simulates realistic delivery conditions: time-dependent congestion, log-normal delays, probabilistic accidents, and empirically grounded time windows for residential and commercial clients. Our pipeline generates diverse, constraint-rich scenarios, including multi-depot and multi-vehicle setups. Benchmarking reveals that state-of-the-art RL solvers like POMO and AM degrade by over 20% under distributional shift, while classical and metaheuristic methods remain robust. To enable reproducible research, we release the dataset and evaluation suite. SVRPBench challenges the community to design solvers that generalize beyond synthetic assumptions and adapt to real-world uncertainty.

We consider the optimization problem of the form min_{x in R^d} f(x) triangleq E_{xi} [F(x; xi)], where the component F(x;xi) is L-mean-squared Lipschitz but possibly nonconvex and nonsmooth. The recently proposed gradient-free method requires at most O( L^4 d^{3/2} epsilon^{-4} + Delta L^3 d^{3/2} delta^{-1} epsilon^{-4}) stochastic zeroth-order oracle complexity to find a (delta,epsilon)-Goldstein stationary point of objective function, where Delta = f(x_0) - inf_{x in R^d} f(x) and x_0 is the initial point of the algorithm. This paper proposes a more efficient algorithm using stochastic recursive gradient estimators, which improves the complexity to O(L^3 d^{3/2} epsilon^{-3}+ Delta L^2 d^{3/2} delta^{-1} epsilon^{-3}).

Vector Symbolic Architectures (VSAs) give a way to represent a complex object as a single fixed-length vector, so that similar objects have similar vector representations. These vector representations then become easy to use for machine learning or nearest-neighbor search. We review a previously proposed VSA method, MBAT (Matrix Binding of Additive Terms), which uses multiplication by random matrices for binding related terms. However, multiplying by such matrices introduces instabilities which can harm performance. Making the random matrices be orthogonal matrices provably fixes this problem. With respect to larger scale applications, we see how to apply MBAT vector representations for any data expressed in JSON. JSON is used in numerous programming languages to express complex data, but its native format appears highly unsuited for machine learning. Expressing JSON as a fixed-length vector makes it readily usable for machine learning and nearest-neighbor search. Creating such JSON vectors also shows that a VSA needs to employ binding operations that are non-commutative. VSAs are now ready to try with full-scale practical applications, including healthcare, pharmaceuticals, and genomics. Keywords: MBAT (Matrix Binding of Additive Terms), VSA (Vector Symbolic Architecture), HDC (Hyperdimensional Computing), Distributed Representations, Binding, Orthogonal Matrices, Recurrent Connections, Machine Learning, Search, JSON, VSA Applications

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization. Our presentation of black-box optimization, strongly influenced by Nesterov's seminal book and Nemirovski's lecture notes, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. We also pay special attention to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging) and discuss their relevance in machine learning. We provide a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization we discuss stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. We also briefly touch upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures.

Neural Architecture Search (NAS) has been a source of dramatic improvements in neural network design, with recent results meeting or exceeding the performance of hand-tuned architectures. However, our understanding of how to represent the search space for neural net architectures and how to search that space efficiently are both still in their infancy. We have performed an in-depth analysis to identify limitations in a widely used search space and a recent architecture search method, Differentiable Architecture Search (DARTS). These findings led us to introduce novel network blocks with a more general, balanced, and consistent design; a better-optimized Cosine Power Annealing learning rate schedule; and other improvements. Our resulting sharpDARTS search is 50% faster with a 20-30% relative improvement in final model error on CIFAR-10 when compared to DARTS. Our best single model run has 1.93% (1.98+/-0.07) validation error on CIFAR-10 and 5.5% error (5.8+/-0.3) on the recently released CIFAR-10.1 test set. To our knowledge, both are state of the art for models of similar size. This model also generalizes competitively to ImageNet at 25.1% top-1 (7.8% top-5) error. We found improvements for existing search spaces but does DARTS generalize to new domains? We propose Differentiable Hyperparameter Grid Search and the HyperCuboid search space, which are representations designed to leverage DARTS for more general parameter optimization. Here we find that DARTS fails to generalize when compared against a human's one shot choice of models. We look back to the DARTS and sharpDARTS search spaces to understand why, and an ablation study reveals an unusual generalization gap. We finally propose Max-W regularization to solve this problem, which proves significantly better than the handmade design. Code will be made available.

Novel computer vision architectures monopolize the spotlight, but the impact of the model architecture is often conflated with simultaneous changes to training methodology and scaling strategies. Our work revisits the canonical ResNet (He et al., 2015) and studies these three aspects in an effort to disentangle them. Perhaps surprisingly, we find that training and scaling strategies may matter more than architectural changes, and further, that the resulting ResNets match recent state-of-the-art models. We show that the best performing scaling strategy depends on the training regime and offer two new scaling strategies: (1) scale model depth in regimes where overfitting can occur (width scaling is preferable otherwise); (2) increase image resolution more slowly than previously recommended (Tan & Le, 2019). Using improved training and scaling strategies, we design a family of ResNet architectures, ResNet-RS, which are 1.7x - 2.7x faster than EfficientNets on TPUs, while achieving similar accuracies on ImageNet. In a large-scale semi-supervised learning setup, ResNet-RS achieves 86.2% top-1 ImageNet accuracy, while being 4.7x faster than EfficientNet NoisyStudent. The training techniques improve transfer performance on a suite of downstream tasks (rivaling state-of-the-art self-supervised algorithms) and extend to video classification on Kinetics-400. We recommend practitioners use these simple revised ResNets as baselines for future research.

Reinforcement learning has been applied in operation research and has shown promise in solving large combinatorial optimization problems. However, existing works focus on developing neural network architectures for certain problems. These works lack the flexibility to incorporate recent advances in reinforcement learning, as well as the flexibility of customizing model architectures for operation research problems. In this work, we analyze the end-to-end autoregressive models for vehicle routing problems and show that these models can benefit from the recent advances in reinforcement learning with a careful re-implementation of the model architecture. In particular, we re-implemented the Attention Model and trained it with Proximal Policy Optimization (PPO) in CleanRL, showing at least 8 times speed up in training time. We hereby introduce RLOR, a flexible framework for Deep Reinforcement Learning for Operation Research. We believe that a flexible framework is key to developing deep reinforcement learning models for operation research problems. The code of our work is publicly available at https://github.com/cpwan/RLOR.

Maximizing a monotone submodular function under cardinality constraint k is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction, exemplar clustering, and coverage problems. We study this classic problem in the fully dynamic model where a stream of insertions and deletions of elements of an underlying ground set is given and the goal is to maintain an approximate solution using a fast update time. A recent paper at NeurIPS'20 by Lattanzi, Mitrovic, Norouzi{-}Fard, Tarnawski, Zadimoghaddam claims to obtain a dynamic algorithm for this problem with a 1{2} -epsilon approximation ratio and a query complexity bounded by poly(log(n),log(k),epsilon^{-1}). However, as we explain in this paper, the analysis has some important gaps. Having a dynamic algorithm for the problem with polylogarithmic update time is even more important in light of a recent result by Chen and Peng at STOC'22 who show a matching lower bound for the problem -- any randomized algorithm with a 1{2}+epsilon approximation ratio must have an amortized query complexity that is polynomial in n. In this paper, we develop a simpler algorithm for the problem that maintains a (1{2}-epsilon)-approximate solution for submodular maximization under cardinality constraint k using a polylogarithmic amortized update time.

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear system Atheta = b for which A and b can only be accessed through random estimates {({bf A}_n, {bf b}_n): n in N^*}. Our analysis is based on new results regarding moments and high probability bounds for products of matrices which are shown to be tight. We derive high probability bounds on the performance of LSA under weaker conditions on the sequence {({bf A}_n, {bf b}_n): n in N^*} than previous works. However, in contrast, we establish polynomial concentration bounds with order depending on the stepsize. We show that our conclusions cannot be improved without additional assumptions on the sequence of random matrices {{bf A}_n: n in N^*}, and in particular that no Gaussian or exponential high probability bounds can hold. Finally, we pay a particular attention to establishing bounds with sharp order with respect to the number of iterations and the stepsize and whose leading terms contain the covariance matrices appearing in the central limit theorems.

Look-up table(LUT)-based methods have shown the great efficacy in single image super-resolution (SR) task. However, previous methods ignore the essential reason of restricted receptive field (RF) size in LUT, which is caused by the interaction of space and channel features in vanilla convolution. They can only increase the RF at the cost of linearly increasing LUT size. To enlarge RF with contained LUT sizes, we propose a novel Reconstructed Convolution(RC) module, which decouples channel-wise and spatial calculation. It can be formulated as n^2 1D LUTs to maintain ntimes n receptive field, which is obviously smaller than ntimes nD LUT formulated before. The LUT generated by our RC module reaches less than 1/10000 storage compared with SR-LUT baseline. The proposed Reconstructed Convolution module based LUT method, termed as RCLUT, can enlarge the RF size by 9 times than the state-of-the-art LUT-based SR method and achieve superior performance on five popular benchmark dataset. Moreover, the efficient and robust RC module can be used as a plugin to improve other LUT-based SR methods. The code is available at https://github.com/liuguandu/RC-LUT.

Traditional white-box methods for creating adversarial perturbations against LLMs typically rely only on gradient computation from the targeted model, ignoring the internal mechanisms responsible for attack success or failure. Conversely, interpretability studies that analyze these internal mechanisms lack practical applications beyond runtime interventions. We bridge this gap by introducing a novel white-box approach that leverages mechanistic interpretability techniques to craft practical adversarial inputs. Specifically, we first identify acceptance subspaces - sets of feature vectors that do not trigger the model's refusal mechanisms - then use gradient-based optimization to reroute embeddings from refusal subspaces to acceptance subspaces, effectively achieving jailbreaks. This targeted approach significantly reduces computation cost, achieving attack success rates of 80-95\% on state-of-the-art models including Gemma2, Llama3.2, and Qwen2.5 within minutes or even seconds, compared to existing techniques that often fail or require hours of computation. We believe this approach opens a new direction for both attack research and defense development. Furthermore, it showcases a practical application of mechanistic interpretability where other methods are less efficient, which highlights its utility. The code and generated datasets are available at https://github.com/Sckathach/subspace-rerouting.

Learning-based decision-making has the potential to enable generalizable Autonomous Driving (AD) policies, reducing the engineering overhead of rule-based approaches. Imitation Learning (IL) remains the dominant paradigm, benefiting from large-scale human demonstration datasets, but it suffers from inherent limitations such as distribution shift and imitation gaps. Reinforcement Learning (RL) presents a promising alternative, yet its adoption in AD remains limited due to the lack of standardized and efficient research frameworks. To this end, we introduce V-Max, an open research framework providing all the necessary tools to make RL practical for AD. V-Max is built on Waymax, a hardware-accelerated AD simulator designed for large-scale experimentation. We extend it using ScenarioNet's approach, enabling the fast simulation of diverse AD datasets.

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

When considering a model architecture, there are several ways to reduce its memory footprint. Historically, popular approaches included selecting smaller architectures and creating sparse networks through pruning. More recently, randomized parameter-sharing (RPS) methods have gained traction for model compression at start of training. In this paper, we comprehensively assess the trade-off between memory and accuracy across RPS, pruning techniques, and building smaller models. Our findings demonstrate that RPS, which is both data and model-agnostic, consistently outperforms/matches smaller models and all moderately informed pruning strategies, such as MAG, SNIP, SYNFLOW, and GRASP, across the entire compression range. This advantage becomes particularly pronounced in higher compression scenarios. Notably, even when compared to highly informed pruning techniques like Lottery Ticket Rewinding (LTR), RPS exhibits superior performance in high compression settings. This points out inherent capacity advantage that RPS enjoys over sparse models. Theoretically, we establish RPS as a superior technique in terms of memory-efficient representation when compared to pruning for linear models. This paper argues in favor of paradigm shift towards RPS based models. During our rigorous evaluation of RPS, we identified issues in the state-of-the-art RPS technique ROAST, specifically regarding stability (ROAST's sensitivity to initialization hyperparameters, often leading to divergence) and Pareto-continuity (ROAST's inability to recover the accuracy of the original model at zero compression). We provably address both of these issues. We refer to the modified RPS, which incorporates our improvements, as STABLE-RPS.

Learning neural operators for solving partial differential equations (PDEs) has attracted great attention due to its high inference efficiency. However, training such operators requires generating a substantial amount of labeled data, i.e., PDE problems together with their solutions. The data generation process is exceptionally time-consuming, as it involves solving numerous systems of linear equations to obtain numerical solutions to the PDEs. Many existing methods solve these systems independently without considering their inherent similarities, resulting in extremely redundant computations. To tackle this problem, we propose a novel method, namely Sorting Krylov Recycling (SKR), to boost the efficiency of solving these systems, thus significantly accelerating data generation for neural operators training. To the best of our knowledge, SKR is the first attempt to address the time-consuming nature of data generation for learning neural operators. The working horse of SKR is Krylov subspace recycling, a powerful technique for solving a series of interrelated systems by leveraging their inherent similarities. Specifically, SKR employs a sorting algorithm to arrange these systems in a sequence, where adjacent systems exhibit high similarities. Then it equips a solver with Krylov subspace recycling to solve the systems sequentially instead of independently, thus effectively enhancing the solving efficiency. Both theoretical analysis and extensive experiments demonstrate that SKR can significantly accelerate neural operator data generation, achieving a remarkable speedup of up to 13.9 times.

We develop a variant of the stochastic prox-linear method for minimizing the Conditional Value-at-Risk (CVaR) objective. CVaR is a risk measure focused on minimizing worst-case performance, defined as the average of the top quantile of the losses. In machine learning, such a risk measure is useful to train more robust models. Although the stochastic subgradient method (SGM) is a natural choice for minimizing the CVaR objective, we show that our stochastic prox-linear (SPL+) algorithm can better exploit the structure of the objective, while still providing a convenient closed form update. Our SPL+ method also adapts to the scaling of the loss function, which allows for easier tuning. We then specialize a general convergence theorem for SPL+ to our setting, and show that it allows for a wider selection of step sizes compared to SGM. We support this theoretical finding experimentally.

Optimization with matrix gradient orthogonalization has recently demonstrated impressive results in the training of deep neural networks (Jordan et al., 2024; Liu et al., 2025). In this paper, we provide a theoretical analysis of this approach. In particular, we show that the orthogonalized gradient method can be seen as a first-order trust-region optimization method, where the trust-region is defined in terms of the matrix spectral norm. Motivated by this observation, we develop the stochastic non-Euclidean trust-region gradient method with momentum, which recovers the Muon optimizer (Jordan et al., 2024) as a special case, along with normalized SGD and signSGD with momentum (Cutkosky and Mehta, 2020; Sun et al., 2023). In addition, we prove state-of-the-art convergence results for the proposed algorithm in a range of scenarios, which involve arbitrary non-Euclidean norms, constrained and composite problems, and non-convex, star-convex, first- and second-order smooth functions. Finally, our theoretical findings provide an explanation for several practical observations, including the practical superiority of Muon compared to the Orthogonal-SGDM algorithm of Tuddenham et al. (2022) and the importance of weight decay in the training of large-scale language models.

Real-world Super-Resolution (Real-SR) methods focus on dealing with diverse real-world images and have attracted increasing attention in recent years. The key idea is to use a complex and high-order degradation model to mimic real-world degradations. Although they have achieved impressive results in various scenarios, they are faced with the obstacle of evaluation. Currently, these methods are only assessed by their average performance on a small set of degradation cases randomly selected from a large space, which fails to provide a comprehensive understanding of their overall performance and often yields inconsistent and potentially misleading results. To overcome the limitation in evaluation, we propose SEAL, a framework for systematic evaluation of real-SR. In particular, we cluster the extensive degradation space to create a set of representative degradation cases, which serves as a comprehensive test set. Next, we propose a coarse-to-fine evaluation protocol to measure the distributed and relative performance of real-SR methods on the test set. The protocol incorporates two new metrics: acceptance rate (AR) and relative performance ratio (RPR), derived from acceptance and excellence lines. Under SEAL, we benchmark existing real-SR methods, obtain new observations and insights into their performance, and develop a new strong baseline. We consider SEAL as the first step towards creating a comprehensive real-SR evaluation platform, which can promote the development of real-SR. The source code is available at https://github.com/XPixelGroup/SEAL

Learning rate schedules used in practice bear little resemblance to those recommended by theory. We close much of this theory/practice gap, and as a consequence are able to derive new problem-adaptive learning rate schedules. Our key technical contribution is a refined analysis of learning rate schedules for a wide class of optimization algorithms (including SGD). In contrast to most prior works that study the convergence of the average iterate, we study the last iterate, which is what most people use in practice. When considering only worst-case analysis, our theory predicts that the best choice is the linear decay schedule: a popular choice in practice that sets the stepsize proportionally to 1 - t/T, where t is the current iteration and T is the total number of steps. To go beyond this worst-case analysis, we use the observed gradient norms to derive schedules refined for any particular task. These refined schedules exhibit learning rate warm-up and rapid learning rate annealing near the end of training. Ours is the first systematic approach to automatically yield both of these properties. We perform the most comprehensive evaluation of learning rate schedules to date, evaluating across 10 diverse deep learning problems, a series of LLMs, and a suite of logistic regression problems. We validate that overall, the linear-decay schedule matches or outperforms all commonly used default schedules including cosine annealing, and that our schedule refinement method gives further improvements.

We propose a new dataset distillation algorithm using reparameterization and convexification of implicit gradients (RCIG), that substantially improves the state-of-the-art. To this end, we first formulate dataset distillation as a bi-level optimization problem. Then, we show how implicit gradients can be effectively used to compute meta-gradient updates. We further equip the algorithm with a convexified approximation that corresponds to learning on top of a frozen finite-width neural tangent kernel. Finally, we improve bias in implicit gradients by parameterizing the neural network to enable analytical computation of final-layer parameters given the body parameters. RCIG establishes the new state-of-the-art on a diverse series of dataset distillation tasks. Notably, with one image per class, on resized ImageNet, RCIG sees on average a 108% improvement over the previous state-of-the-art distillation algorithm. Similarly, we observed a 66% gain over SOTA on Tiny-ImageNet and 37% on CIFAR-100.

We propose a tuning-free dynamic SGD step size formula, which we call Distance over Gradients (DoG). The DoG step sizes depend on simple empirical quantities (distance from the initial point and norms of gradients) and have no ``learning rate'' parameter. Theoretically, we show that a slight variation of the DoG formula enjoys strong parameter-free convergence guarantees for stochastic convex optimization assuming only locally bounded stochastic gradients. Empirically, we consider a broad range of vision and language transfer learning tasks, and show that DoG's performance is close to that of SGD with tuned learning rate. We also propose a per-layer variant of DoG that generally outperforms tuned SGD, approaching the performance of tuned Adam. A PyTorch implementation is available at https://github.com/formll/dog

We propose a method that achieves near-optimal rates for smooth stochastic convex optimization and requires essentially no prior knowledge of problem parameters. This improves on prior work which requires knowing at least the initial distance to optimality d0. Our method, U-DoG, combines UniXGrad (Kavis et al., 2019) and DoG (Ivgi et al., 2023) with novel iterate stabilization techniques. It requires only loose bounds on d0 and the noise magnitude, provides high probability guarantees under sub-Gaussian noise, and is also near-optimal in the non-smooth case. Our experiments show consistent, strong performance on convex problems and mixed results on neural network training.

Approximating Stochastic Gradient Descent (SGD) as a Stochastic Differential Equation (SDE) has allowed researchers to enjoy the benefits of studying a continuous optimization trajectory while carefully preserving the stochasticity of SGD. Analogous study of adaptive gradient methods, such as RMSprop and Adam, has been challenging because there were no rigorously proven SDE approximations for these methods. This paper derives the SDE approximations for RMSprop and Adam, giving theoretical guarantees of their correctness as well as experimental validation of their applicability to common large-scaling vision and language settings. A key practical result is the derivation of a square root scaling rule to adjust the optimization hyperparameters of RMSprop and Adam when changing batch size, and its empirical validation in deep learning settings.

We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. Specifically, we propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP), which incorporates both model-based and value-based incarnations. In particular, LOOP features a novel construction of confidence sets and a low-switching policy updating scheme, which are tailored to the average-reward and function approximation setting. Moreover, for AMDPs, we propose a novel complexity measure -- average-reward generalized eluder coefficient (AGEC) -- which captures the challenge of exploration in AMDPs with general function approximation. Such a complexity measure encompasses almost all previously known tractable AMDP models, such as linear AMDPs and linear mixture AMDPs, and also includes newly identified cases such as kernel AMDPs and AMDPs with Bellman eluder dimensions. Using AGEC, we prove that LOOP achieves a sublinear mathcal{O}(poly(d, sp(V^*)) Tbeta ) regret, where d and beta correspond to AGEC and log-covering number of the hypothesis class respectively, sp(V^*) is the span of the optimal state bias function, T denotes the number of steps, and mathcal{O} (cdot) omits logarithmic factors. When specialized to concrete AMDP models, our regret bounds are comparable to those established by the existing algorithms designed specifically for these special cases. To the best of our knowledge, this paper presents the first comprehensive theoretical framework capable of handling nearly all AMDPs.

We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or even better performance as evaluated on several real-world networks on various downstream tasks. We observe that most network embedding methods consist of two components: construct a node similarity matrix and then apply dimension reduction techniques to this matrix. We show that the success of these methods should be attributed to the proper construction of this similarity matrix, rather than the dimension reduction method employed. FastRP is proposed as a scalable algorithm for network embeddings. Two key features of FastRP are: 1) it explicitly constructs a node similarity matrix that captures transitive relationships in a graph and normalizes matrix entries based on node degrees; 2) it utilizes very sparse random projection, which is a scalable optimization-free method for dimension reduction. An extra benefit from combining these two design choices is that it allows the iterative computation of node embeddings so that the similarity matrix need not be explicitly constructed, which further speeds up FastRP. FastRP is also advantageous for its ease of implementation, parallelization and hyperparameter tuning. The source code is available at https://github.com/GTmac/FastRP.

Layer normalization (LayerNorm) has been successfully applied to various deep neural networks to help stabilize training and boost model convergence because of its capability in handling re-centering and re-scaling of both inputs and weight matrix. However, the computational overhead introduced by LayerNorm makes these improvements expensive and significantly slows the underlying network, e.g. RNN in particular. In this paper, we hypothesize that re-centering invariance in LayerNorm is dispensable and propose root mean square layer normalization, or RMSNorm. RMSNorm regularizes the summed inputs to a neuron in one layer according to root mean square (RMS), giving the model re-scaling invariance property and implicit learning rate adaptation ability. RMSNorm is computationally simpler and thus more efficient than LayerNorm. We also present partial RMSNorm, or pRMSNorm where the RMS is estimated from p% of the summed inputs without breaking the above properties. Extensive experiments on several tasks using diverse network architectures show that RMSNorm achieves comparable performance against LayerNorm but reduces the running time by 7%~64% on different models. Source code is available at https://github.com/bzhangGo/rmsnorm.

Recently, Qiao, Duan, and Cheng~(2019) proposed a distributed nearest-neighbor classification method, in which a massive dataset is split into smaller groups, each processed with a k-nearest-neighbor classifier, and the final class label is predicted by a majority vote among these groupwise class labels. This paper shows that the distributed algorithm with k=1 over a sufficiently large number of groups attains a minimax optimal error rate up to a multiplicative logarithmic factor under some regularity conditions, for both regression and classification problems. Roughly speaking, distributed 1-nearest-neighbor rules with M groups has a performance comparable to standard Theta(M)-nearest-neighbor rules. In the analysis, alternative rules with a refined aggregation method are proposed and shown to attain exact minimax optimal rates.

We propose a new differentiable probabilistic model over DAGs (DP-DAG). DP-DAG allows fast and differentiable DAG sampling suited to continuous optimization. To this end, DP-DAG samples a DAG by successively (1) sampling a linear ordering of the node and (2) sampling edges consistent with the sampled linear ordering. We further propose VI-DP-DAG, a new method for DAG learning from observational data which combines DP-DAG with variational inference. Hence,VI-DP-DAG approximates the posterior probability over DAG edges given the observed data. VI-DP-DAG is guaranteed to output a valid DAG at any time during training and does not require any complex augmented Lagrangian optimization scheme in contrast to existing differentiable DAG learning approaches. In our extensive experiments, we compare VI-DP-DAG to other differentiable DAG learning baselines on synthetic and real datasets. VI-DP-DAG significantly improves DAG structure and causal mechanism learning while training faster than competitors.

Regret minimization in streaming multi-armed bandits (MABs) has been studied extensively in recent years. In the single-pass setting with K arms and T trials, a regret lower bound of Omega(T^{2/3}) has been proved for any algorithm with o(K) memory (Maiti et al. [NeurIPS'21]; Agarwal at al. [COLT'22]). On the other hand, however, the previous best regret upper bound is still O(K^{1/3} T^{2/3}log^{1/3}(T)), which is achieved by the streaming implementation of the simple uniform exploration. The O(K^{1/3}log^{1/3}(T)) gap leaves the open question of the tight regret bound in the single-pass MABs with sublinear arm memory. In this paper, we answer this open problem and complete the picture of regret minimization in single-pass streaming MABs. We first improve the regret lower bound to Omega(K^{1/3}T^{2/3}) for algorithms with o(K) memory, which matches the uniform exploration regret up to a logarithm factor in T. We then show that the log^{1/3}(T) factor is not necessary, and we can achieve O(K^{1/3}T^{2/3}) regret by finding an varepsilon-best arm and committing to it in the rest of the trials. For regret minimization with high constant probability, we can apply the single-memory varepsilon-best arm algorithms in Jin et al. [ICML'21] to obtain the optimal bound. Furthermore, for the expected regret minimization, we design an algorithm with a single-arm memory that achieves O(K^{1/3} T^{2/3}log(K)) regret, and an algorithm with O(log^{*}(n))-memory with the optimal O(K^{1/3} T^{2/3}) regret following the varepsilon-best arm algorithm in Assadi and Wang [STOC'20]. We further tested the empirical performances of our algorithms. The simulation results show that the proposed algorithms consistently outperform the benchmark uniform exploration algorithm by a large margin, and on occasion, reduce the regret by up to 70%.

Simple regret is a natural and parameter-free performance criterion for pure exploration in multi-armed bandits yet is less popular than the probability of missing the best arm or an epsilon-good arm, perhaps due to lack of easy ways to characterize it. In this paper, we make significant progress on minimizing simple regret in both data-rich (Tge n) and data-poor regime (T le n) where n is the number of arms, and T is the number of samples. At its heart is our improved instance-dependent analysis of the well-known Sequential Halving (SH) algorithm, where we bound the probability of returning an arm whose mean reward is not within epsilon from the best (i.e., not epsilon-good) for any choice of epsilon>0, although epsilon is not an input to SH. Our bound not only leads to an optimal worst-case simple regret bound of n/T up to logarithmic factors but also essentially matches the instance-dependent lower bound for returning an epsilon-good arm reported by Katz-Samuels and Jamieson (2020). For the more challenging data-poor regime, we propose Bracketing SH (BSH) that enjoys the same improvement even without sampling each arm at least once. Our empirical study shows that BSH outperforms existing methods on real-world tasks.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods with a provable improvement of the condition number, cutting the gaps between highest eigenvalues, without explicit knowledge of the actual spectrum. We give a stochastic interpretation of this preconditioning in terms of coordinate volume sampling and compare it with other classical approaches, including the Chebyshev polynomials. We show how to incorporate a polynomial preconditioning into the Gradient and Fast Gradient Methods and establish the corresponding global complexity bounds. Finally, we propose a simple adaptive search procedure that automatically chooses the best possible polynomial preconditioning for the Gradient Method, minimizing the objective along a low-dimensional Krylov subspace. Numerical experiments confirm the efficiency of our preconditioning strategies for solving various machine learning problems.

Learning Rate Rewinding (LRR) has been established as a strong variant of Iterative Magnitude Pruning (IMP) to find lottery tickets in deep overparameterized neural networks. While both iterative pruning schemes couple structure and parameter learning, understanding how LRR excels in both aspects can bring us closer to the design of more flexible deep learning algorithms that can optimize diverse sets of sparse architectures. To this end, we conduct experiments that disentangle the effect of mask learning and parameter optimization and how both benefit from overparameterization. The ability of LRR to flip parameter signs early and stay robust to sign perturbations seems to make it not only more effective in mask identification but also in optimizing diverse sets of masks, including random ones. In support of this hypothesis, we prove in a simplified single hidden neuron setting that LRR succeeds in more cases than IMP, as it can escape initially problematic sign configurations.

CIFAR-10 is among the most widely used datasets in machine learning, facilitating thousands of research projects per year. To accelerate research and reduce the cost of experiments, we introduce training methods for CIFAR-10 which reach 94% accuracy in 3.29 seconds, 95% in 10.4 seconds, and 96% in 46.3 seconds, when run on a single NVIDIA A100 GPU. As one factor contributing to these training speeds, we propose a derandomized variant of horizontal flipping augmentation, which we show improves over the standard method in every case where flipping is beneficial over no flipping at all. Our code is released at https://github.com/KellerJordan/cifar10-airbench.

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals' outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that involves retrospective reshuffling of participants across experimental arms at the end of an RCT. We identify conditions under which such reassignments are permissible and can be leveraged to construct counterfactual trials, whose outcomes can be accurately ascertained, for free. We prove theoretically that such an estimator is more accurate than common estimators based on sample means -- we show that it returns an unbiased estimate and simultaneously reduces variance. We demonstrate the value of our approach through empirical experiments on synthetic, semi-synthetic as well as real case study data and show improved estimation accuracy across the board.

Given a K-vertex simplex in a d-dimensional space, suppose we measure n points on the simplex with noise (hence, some of the observed points fall outside the simplex). Vertex hunting is the problem of estimating the K vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). However, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest.

This paper reports Deep LOGISMOS approach to 3D tumor segmentation by incorporating boundary information derived from deep contextual learning to LOGISMOS - layered optimal graph image segmentation of multiple objects and surfaces. Accurate and reliable tumor segmentation is essential to tumor growth analysis and treatment selection. A fully convolutional network (FCN), UNet, is first trained using three adjacent 2D patches centered at the tumor, providing contextual UNet segmentation and probability map for each 2D patch. The UNet segmentation is then refined by Gaussian Mixture Model (GMM) and morphological operations. The refined UNet segmentation is used to provide the initial shape boundary to build a segmentation graph. The cost for each node of the graph is determined by the UNet probability maps. Finally, a max-flow algorithm is employed to find the globally optimal solution thus obtaining the final segmentation. For evaluation, we applied the method to pancreatic tumor segmentation on a dataset of 51 CT scans, among which 30 scans were used for training and 21 for testing. With Deep LOGISMOS, DICE Similarity Coefficient (DSC) and Relative Volume Difference (RVD) reached 83.2+-7.8% and 18.6+-17.4% respectively, both are significantly improved (p<0.05) compared with contextual UNet and/or LOGISMOS alone.

We study convergence lower bounds of without-replacement stochastic gradient descent (SGD) for solving smooth (strongly-)convex finite-sum minimization problems. Unlike most existing results focusing on final iterate lower bounds in terms of the number of components n and the number of epochs K, we seek bounds for arbitrary weighted average iterates that are tight in all factors including the condition number kappa. For SGD with Random Reshuffling, we present lower bounds that have tighter kappa dependencies than existing bounds. Our results are the first to perfectly close the gap between lower and upper bounds for weighted average iterates in both strongly-convex and convex cases. We also prove weighted average iterate lower bounds for arbitrary permutation-based SGD, which apply to all variants that carefully choose the best permutation. Our bounds improve the existing bounds in factors of n and kappa and thereby match the upper bounds shown for a recently proposed algorithm called GraB.

The non-convexity of the artificial neural network (ANN) training landscape brings inherent optimization difficulties. While the traditional back-propagation stochastic gradient descent (SGD) algorithm and its variants are effective in certain cases, they can become stuck at spurious local minima and are sensitive to initializations and hyperparameters. Recent work has shown that the training of an ANN with ReLU activations can be reformulated as a convex program, bringing hope to globally optimizing interpretable ANNs. However, naively solving the convex training formulation has an exponential complexity, and even an approximation heuristic requires cubic time. In this work, we characterize the quality of this approximation and develop two efficient algorithms that train ANNs with global convergence guarantees. The first algorithm is based on the alternating direction method of multiplier (ADMM). It solves both the exact convex formulation and the approximate counterpart. Linear global convergence is achieved, and the initial several iterations often yield a solution with high prediction accuracy. When solving the approximate formulation, the per-iteration time complexity is quadratic. The second algorithm, based on the "sampled convex programs" theory, is simpler to implement. It solves unconstrained convex formulations and converges to an approximately globally optimal classifier. The non-convexity of the ANN training landscape exacerbates when adversarial training is considered. We apply the robust convex optimization theory to convex training and develop convex formulations that train ANNs robust to adversarial inputs. Our analysis explicitly focuses on one-hidden-layer fully connected ANNs, but can extend to more sophisticated architectures.

The proposed method, Discriminator Guidance, aims to improve sample generation of pre-trained diffusion models. The approach introduces a discriminator that gives explicit supervision to a denoising sample path whether it is realistic or not. Unlike GANs, our approach does not require joint training of score and discriminator networks. Instead, we train the discriminator after score training, making discriminator training stable and fast to converge. In sample generation, we add an auxiliary term to the pre-trained score to deceive the discriminator. This term corrects the model score to the data score at the optimal discriminator, which implies that the discriminator helps better score estimation in a complementary way. Using our algorithm, we achive state-of-the-art results on ImageNet 256x256 with FID 1.83 and recall 0.64, similar to the validation data's FID (1.68) and recall (0.66). We release the code at https://github.com/alsdudrla10/DG.

Remote Sensing Image Dehazing (RSID) poses significant challenges in real-world scenarios due to the complex atmospheric conditions and severe color distortions that degrade image quality. The scarcity of real-world remote sensing hazy image pairs has compelled existing methods to rely primarily on synthetic datasets. However, these methods struggle with real-world applications due to the inherent domain gap between synthetic and real data. To address this, we introduce Real-World Remote Sensing Hazy Image Dataset (RRSHID), the first large-scale dataset featuring real-world hazy and dehazed image pairs across diverse atmospheric conditions. Based on this, we propose MCAF-Net, a novel framework tailored for real-world RSID. Its effectiveness arises from three innovative components: Multi-branch Feature Integration Block Aggregator (MFIBA), which enables robust feature extraction through cascaded integration blocks and parallel multi-branch processing; Color-Calibrated Self-Supervised Attention Module (CSAM), which mitigates complex color distortions via self-supervised learning and attention-guided refinement; and Multi-Scale Feature Adaptive Fusion Module (MFAFM), which integrates features effectively while preserving local details and global context. Extensive experiments validate that MCAF-Net demonstrates state-of-the-art performance in real-world RSID, while maintaining competitive performance on synthetic datasets. The introduction of RRSHID and MCAF-Net sets new benchmarks for real-world RSID research, advancing practical solutions for this complex task. The code and dataset are publicly available at https://github.com/lwCVer/RRSHID.

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

Recently, the impressive empirical success of policy gradient (PG) methods has catalyzed the development of their theoretical foundations. Despite the huge efforts directed at the design of efficient stochastic PG-type algorithms, the understanding of their convergence to a globally optimal policy is still limited. In this work, we develop improved global convergence guarantees for a general class of Fisher-non-degenerate parameterized policies which allows to address the case of continuous state action spaces. First, we propose a Normalized Policy Gradient method with Implicit Gradient Transport (N-PG-IGT) and derive a mathcal{O}(varepsilon^{-2.5}) sample complexity of this method for finding a global varepsilon-optimal policy. Improving over the previously known mathcal{O}(varepsilon^{-3}) complexity, this algorithm does not require the use of importance sampling or second-order information and samples only one trajectory per iteration. Second, we further improve this complexity to mathcal{mathcal{O} }(varepsilon^{-2}) by considering a Hessian-Aided Recursive Policy Gradient ((N)-HARPG) algorithm enhanced with a correction based on a Hessian-vector product. Interestingly, both algorithms are (i) simple and easy to implement: single-loop, do not require large batches of trajectories and sample at most two trajectories per iteration; (ii) computationally and memory efficient: they do not require expensive subroutines at each iteration and can be implemented with memory linear in the dimension of parameters.

Rectified-flow-based diffusion transformers, such as FLUX and OpenSora, have demonstrated exceptional performance in the field of image and video generation. Despite their robust generative capabilities, these models often suffer from inaccurate inversion, which could further limit their effectiveness in downstream tasks such as image and video editing. To address this issue, we propose RF-Solver, a novel training-free sampler that enhances inversion precision by reducing errors in the process of solving rectified flow ODEs. Specifically, we derive the exact formulation of the rectified flow ODE and perform a high-order Taylor expansion to estimate its nonlinear components, significantly decreasing the approximation error at each timestep. Building upon RF-Solver, we further design RF-Edit, which comprises specialized sub-modules for image and video editing. By sharing self-attention layer features during the editing process, RF-Edit effectively preserves the structural information of the source image or video while achieving high-quality editing results. Our approach is compatible with any pre-trained rectified-flow-based models for image and video tasks, requiring no additional training or optimization. Extensive experiments on text-to-image generation, image & video inversion, and image & video editing demonstrate the robust performance and adaptability of our methods. Code is available at https://github.com/wangjiangshan0725/RF-Solver-Edit.

We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As regular RFs for non-graph kernels, they provide means to scale up kernel methods defined on graphs to larger networks. Importantly, they give substantial computational gains also for smaller graphs, while applied in downstream applications. Consequently, GRFs address the notoriously difficult problem of cubic (in the number of the nodes of the graph) time complexity of graph kernels algorithms. We provide a detailed theoretical analysis of GRFs and an extensive empirical evaluation: from speed tests, through Frobenius relative error analysis to kmeans graph-clustering with graph kernels. We show that the computation of GRFs admits an embarrassingly simple distributed algorithm that can be applied if the graph under consideration needs to be split across several machines. We also introduce a (still unbiased) quasi Monte Carlo variant of GRFs, q-GRFs, relying on the so-called reinforced random walks, that might be used to optimize the variance of GRFs. As a byproduct, we obtain a novel approach to solve certain classes of linear equations with positive and symmetric matrices.