Daily Papers

The pursuit of a generalizable stereo matching model, capable of performing well across varying resolutions and disparity ranges without dataset-specific fine-tuning, has revealed a fundamental trade-off. Iterative local search methods achieve high scores on constrained benchmarks, but their core mechanism inherently limits the global consistency required for true generalization. However, global matching architectures, while theoretically more robust, have historically been rendered infeasible by prohibitive computational and memory costs. We resolve this dilemma with {S2M2}: a global matching architecture that achieves state-of-the-art accuracy and high efficiency without relying on cost volume filtering or deep refinement stacks. Our design integrates a multi-resolution transformer for robust long-range correspondence, trained with a novel loss function that concentrates probability on feasible matches. This approach enables a more robust joint estimation of disparity, occlusion, and confidence. {S2M2} establishes a new state of the art on Middlebury v3 and ETH3D benchmarks, significantly outperforming prior methods in most metrics while reconstructing high-quality details with competitive efficiency.

Recent improvements in text generation have leveraged human feedback to improve the quality of the generated output. However, human feedback is not always available, especially during inference. In this work, we propose an inference time optimization method FITO to use fine-grained actionable feedback in the form of error type, error location and severity level that are predicted by a learned error pinpoint model for iterative refinement. FITO starts with an initial output, then iteratively incorporates the feedback via a refinement model that generates an improved output conditioned on the feedback. Given the uncertainty of consistent refined samples at iterative steps, we formulate iterative refinement into a local search problem and develop a simulated annealing based algorithm that balances exploration of the search space and optimization for output quality. We conduct experiments on three text generation tasks, including machine translation, long-form question answering (QA) and topical summarization. We observe 0.8 and 0.7 MetricX gain on Chinese-English and English-German translation, 4.5 and 1.8 ROUGE-L gain at long form QA and topic summarization respectively, with a single iteration of refinement. With our simulated annealing algorithm, we see further quality improvements, including up to 1.7 MetricX improvements over the baseline approach.

Automated Program Repair (APR) attempts to fix software bugs without human intervention, which plays a crucial role in software development and maintenance. Recently, with the advances in Large Language Models (LLMs), a rapidly increasing number of APR techniques have been proposed with remarkable performance. However, existing LLM-based APR techniques typically adopt trial-and-error strategies, which suffer from two major drawbacks: (1) inherently limited patch effectiveness due to local exploration, and (2) low search efficiency due to redundant exploration. In this paper, we propose APRMCTS, which uses iterative tree search to improve LLM-based APR. APRMCTS incorporates Monte Carlo Tree Search (MCTS) into patch searching by performing a global evaluation of the explored patches and selecting the most promising one for subsequent refinement and generation. APRMCTS effectively resolves the problems of falling into local optima and thus helps improve the efficiency of patch searching. Our experiments on 835 bugs from Defects4J demonstrate that, when integrated with GPT-3.5, APRMCTS can fix a total of 201 bugs, which outperforms all state-of-the-art baselines. Besides, APRMCTS helps GPT-4o-mini, GPT-3.5, Yi-Coder-9B, and Qwen2.5-Coder-7B to fix 30, 27, 37, and 28 more bugs, respectively. More importantly, APRMCTS boasts a significant performance advantage while employing small patch size (16 and 32), notably fewer than the 500 and 10,000 patches adopted in previous studies. In terms of cost, compared to existing state-of-the-art LLM-based APR methods, APRMCTS has time and monetary costs of less than 20% and 50%, respectively. Our extensive study demonstrates that APRMCTS exhibits good effectiveness and efficiency, with particular advantages in addressing complex bugs.

Agentic search has recently emerged as a powerful paradigm, where an agent interleaves multi-step reasoning with on-demand retrieval to solve complex questions. Despite its success, how to design a retriever for agentic search remains largely underexplored. Existing search agents typically rely on similarity-based retrievers, while similar passages are not always useful for final answer generation. In this paper, we propose a novel retriever training framework tailored for agentic search. Unlike retrievers designed for single-turn retrieval-augmented generation (RAG) that only rely on local passage utility, we propose to use both local query-passage relevance and global answer correctness to measure passage utility in a multi-turn agentic search. We further introduce an iterative training strategy, where the search agent and the retriever are optimized bidirectionally and iteratively. Different from RAG retrievers that are only trained once with fixed questions, our retriever is continuously improved using evolving and higher-quality queries from the agent. Extensive experiments on seven single-hop and multi-hop QA benchmarks demonstrate that our retriever, termed , consistently outperforms strong baselines across different search agents. Our codes are available at: https://github.com/8421BCD/Agentic-R.

Designing user interfaces (UIs) is a critical step when launching products, building portfolios, or personalizing projects, yet end users without design expertise often struggle to articulate their intent and to trust design choices. Existing example-based tools either promote broad exploration, which can cause overwhelm and design drift, or require adapting a single example, risking design fixation. We present UI Remix, an interactive system that supports mobile UI design through an example-driven design workflow. Powered by a multimodal retrieval-augmented generation (MMRAG) model, UI Remix enables iterative search, selection, and adaptation of examples at both the global (whole interface) and local (component) level. To foster trust, it presents source transparency cues such as ratings, download counts, and developer information. In an empirical study with 24 end users, UI Remix significantly improved participants' ability to achieve their design goals, facilitated effective iteration, and encouraged exploration of alternative designs. Participants also reported that source transparency cues enhanced their confidence in adapting examples. Our findings suggest new directions for AI-assisted, example-driven systems that empower end users to design with greater control, trust, and openness to exploration.

This paper introduces KunLunBaizeRAG, a reinforcement learning-driven reasoning framework designed to enhance the reasoning capabilities of large language models (LLMs) in complex multi-hop question-answering tasks. The framework addresses key limitations of traditional RAG, such as retrieval drift, information redundancy, and strategy rigidity. Key innovations include the RAG-driven Reasoning Alignment (RDRA) mechanism, the Search-Think Iterative Enhancement (STIE) mechanism, the Network-Local Intelligent Routing (NLR) mechanism, and a progressive hybrid training strategy. Experimental results demonstrate significant improvements in exact match (EM) and LLM-judged score (LJ) across four benchmarks, highlighting the framework's robustness and effectiveness in complex reasoning scenarios.

Recent advances in large reasoning models (LRMs) have enabled agentic search systems to perform complex multi-step reasoning across multiple sources. However, most studies focus on general information retrieval and rarely explores vertical domains with unique challenges. In this work, we focus on local life services and introduce LocalSearchBench, which encompass diverse and complex business scenarios. Real-world queries in this domain are often ambiguous and require multi-hop reasoning across merchants and products, remaining challenging and not fully addressed. As the first comprehensive benchmark for agentic search in local life services, LocalSearchBench includes over 150,000 high-quality entries from various cities and business types. We construct 300 multi-hop QA tasks based on real user queries, challenging agents to understand questions and retrieve information in multiple steps. We also developed LocalPlayground, a unified environment integrating multiple tools for agent interaction. Experiments show that even state-of-the-art LRMs struggle on LocalSearchBench: the best model (DeepSeek-V3.1) achieves only 34.34% correctness, and most models have issues with completeness (average 77.33%) and faithfulness (average 61.99%). This highlights the need for specialized benchmarks and domain-specific agent training in local life services. Code, Benchmark, and Leaderboard are available at localsearchbench.github.io.

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.

We introduce iterative retrieval, a novel framework that empowers retrievers to make iterative decisions through policy optimization. Finding an optimal portfolio of retrieved items is a combinatorial optimization problem, generally considered NP-hard. This approach provides a learned approximation to such a solution, meeting specific task requirements under a given family of large language models (LLMs). We propose a training procedure based on reinforcement learning, incorporating feedback from LLMs. We instantiate an iterative retriever for composing in-context learning (ICL) exemplars and apply it to various semantic parsing tasks that demand synthesized programs as outputs. By adding only 4M additional parameters for state encoding, we convert an off-the-shelf dense retriever into a stateful iterative retriever, outperforming previous methods in selecting ICL exemplars on semantic parsing datasets such as CalFlow, TreeDST, and MTOP. Additionally, the trained iterative retriever generalizes across different inference LLMs beyond the one used during training.

We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

Iterative retrieval refers to the process in which the model continuously queries the retriever during generation to enhance the relevance of the retrieved knowledge, thereby improving the performance of Retrieval-Augmented Generation (RAG). Existing work typically employs few-shot prompting or manually constructed rules to implement iterative retrieval. This introduces additional inference overhead and overlooks the remarkable reasoning capabilities of Large Language Models (LLMs). In this paper, we introduce Auto-RAG, an autonomous iterative retrieval model centered on the LLM's powerful decision-making capabilities. Auto-RAG engages in multi-turn dialogues with the retriever, systematically planning retrievals and refining queries to acquire valuable knowledge. This process continues until sufficient external information is gathered, at which point the results are presented to the user. To this end, we develop a method for autonomously synthesizing reasoning-based decision-making instructions in iterative retrieval and fine-tuned the latest open-source LLMs. The experimental results indicate that Auto-RAG is capable of autonomous iterative interaction with the retriever, effectively leveraging the remarkable reasoning and decision-making abilities of LLMs, which lead to outstanding performance across six benchmarks. Further analysis reveals that Auto-RAG can autonomously adjust the number of iterations based on the difficulty of the questions and the utility of the retrieved knowledge, without requiring any human intervention. Moreover, Auto-RAG expresses the iterative retrieval process in natural language, enhancing interpretability while providing users with a more intuitive experienceCode is available at \url{https://github.com/ictnlp/Auto-RAG.

This paper investigates scaling laws for local SGD in LLM training, a distributed optimization algorithm that facilitates training on loosely connected devices. Through extensive experiments, we show that local SGD achieves competitive results compared to conventional methods, given equivalent model parameters, datasets, and computational resources. Furthermore, we explore the application of local SGD in various practical scenarios, including multi-cluster setups and edge computing environments. Our findings elucidate the necessary conditions for effective multi-cluster LLM training and examine the potential and limitations of leveraging edge computing resources in the LLM training process. This demonstrates its viability as an alternative to single large-cluster training.

Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a new one with a contrastive loss. We use graph attention networks and a richer set of features to further improve its performance.

We define and investigate the problem of c-approximate window search: approximate nearest neighbor search where each point in the dataset has a numeric label, and the goal is to find nearest neighbors to queries within arbitrary label ranges. Many semantic search problems, such as image and document search with timestamp filters, or product search with cost filters, are natural examples of this problem. We propose and theoretically analyze a modular tree-based framework for transforming an index that solves the traditional c-approximate nearest neighbor problem into a data structure that solves window search. On standard nearest neighbor benchmark datasets equipped with random label values, adversarially constructed embeddings, and image search embeddings with real timestamps, we obtain up to a 75times speedup over existing solutions at the same level of recall.

This paper presents a detailed analysis of the scalability and parallelization of local search algorithms for the Satisfiability problem. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequential version. Indeed, by approximating the runtime distribution of the sequential process with statistical methods, the runtime behavior of the parallel process can be predicted by a model based on order statistics. We apply this approach to study the parallel performance of two SAT local search solvers, namely Sparrow and CCASAT, and compare the predicted performances to the results of an actual experimentation on parallel hardware up to 384 cores. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of instances (random and crafted), we observe that the local search solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal.

We propose a novel approach to scaling LLM inference for code generation. We frame code generation as a black box optimization problem within the code space, and employ optimization-inspired techniques to enhance exploration. Specifically, we introduce Scattered Forest Search to enhance solution diversity while searching for solutions. Our theoretical analysis illustrates how these methods avoid local optima during optimization. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance improvements. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our method scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

Diffusion large language models (dLLMs) represent a significant advancement in text generation, offering parallel token decoding capabilities. However, existing open-source implementations suffer from quality-speed trade-offs that impede their practical deployment. Conservative sampling strategies typically decode only the most confident token per step to ensure quality (i.e., greedy decoding), at the cost of inference efficiency due to repeated redundant refinement iterations--a phenomenon we term delayed decoding. Through systematic analysis of dLLM decoding dynamics, we characterize this delayed decoding behavior and propose a training-free adaptive parallel decoding strategy, named LocalLeap, to address these inefficiencies. LocalLeap is built on two fundamental empirical principles: local determinism propagation centered on high-confidence anchors and progressive spatial consistency decay. By applying these principles, LocalLeap identifies anchors and performs localized relaxed parallel decoding within bounded neighborhoods, achieving substantial inference step reduction through early commitment of already-determined tokens without compromising output quality. Comprehensive evaluation on various benchmarks demonstrates that LocalLeap achieves 6.94times throughput improvements and reduces decoding steps to just 14.2\% of the original requirement, achieving these gains with negligible performance impact. The source codes are available at: https://github.com/friedrichor/LocalLeap.

Agentic search, as a more autonomous and adaptive paradigm of retrieval augmentation, is driving the evolution of intelligent search systems. However, existing evaluation frameworks fail to align well with the goals of agentic search. First, the complex queries commonly used in current benchmarks often deviate from realistic user search scenarios. Second, prior approaches tend to introduce noise when extracting ground truth for end-to-end evaluations, leading to distorted assessments at a fine-grained level. Third, most current frameworks focus solely on the quality of final answers, neglecting the evaluation of the iterative process inherent to agentic search. To address these limitations, we propose RAVine -- a Reality-Aligned eValuation framework for agentic LLMs with search. RAVine targets multi-point queries and long-form answers that better reflect user intents, and introduces an attributable ground truth construction strategy to enhance the accuracy of fine-grained evaluation. Moreover, RAVine examines model's interaction with search tools throughout the iterative process, and accounts for factors of efficiency. We benchmark a series of models using RAVine and derive several insights, which we hope will contribute to advancing the development of agentic search systems. The code and datasets are available at https://github.com/SwordFaith/RAVine.

This paper re-examines a continuous optimization framework dubbed NOTEARS for learning Bayesian networks. We first generalize existing algebraic characterizations of acyclicity to a class of matrix polynomials. Next, focusing on a one-parameter-per-edge setting, it is shown that the Karush-Kuhn-Tucker (KKT) optimality conditions for the NOTEARS formulation cannot be satisfied except in a trivial case, which explains a behavior of the associated algorithm. We then derive the KKT conditions for an equivalent reformulation, show that they are indeed necessary, and relate them to explicit constraints that certain edges be absent from the graph. If the score function is convex, these KKT conditions are also sufficient for local minimality despite the non-convexity of the constraint. Informed by the KKT conditions, a local search post-processing algorithm is proposed and shown to substantially and universally improve the structural Hamming distance of all tested algorithms, typically by a factor of 2 or more. Some combinations with local search are both more accurate and more efficient than the original NOTEARS.

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.

Increasing demand for Large Language Models (LLMs) services imposes substantial deployment and computation costs on providers. LLM routing offers a cost-efficient solution by directing queries to the optimal LLM based on model and query features. However, existing works primarily focus on offline scenarios and struggle to adapt to online settings with high query volume and constrained token budgets. In this work, we introduce the first training-free algorithm for online routing scenarios. Our algorithm leverages approximate nearest neighbor search to efficiently estimate query features and performs a one-time optimization over a small set of initial queries to learn a routing strategy that guides future routing. We provide theoretical guarantees demonstrating that our algorithm achieves a competitive ratio of 1 - o(1) under natural assumptions, which is further validated by extensive experiments across 3 benchmark datasets and 8 baselines, showing an average improvement of 3.55times in overall performance, 1.85times in cost efficiency, and nearly 4.25times in throughput. Our code is available at https://github.com/fzwark/PORT.

Recently, the retrieval models based on dense representations have been gradually applied in the first stage of the document retrieval tasks, showing better performance than traditional sparse vector space models. To obtain high efficiency, the basic structure of these models is Bi-encoder in most cases. However, this simple structure may cause serious information loss during the encoding of documents since the queries are agnostic. To address this problem, we design a method to mimic the queries on each of the documents by an iterative clustering process and represent the documents by multiple pseudo queries (i.e., the cluster centroids). To boost the retrieval process using approximate nearest neighbor search library, we also optimize the matching function with a two-step score calculation procedure. Experimental results on several popular ranking and QA datasets show that our model can achieve state-of-the-art results.

Large language models are transitioning from generalpurpose knowledge engines to realworld problem solvers, yet optimizing them for deep search tasks remains challenging. The central bottleneck lies in the extreme sparsity of highquality search trajectories and reward signals, arising from the difficulty of scalable longhorizon task construction and the high cost of interactionheavy rollouts involving external tool calls. To address these challenges, we propose REDSearcher, a unified framework that codesigns complex task synthesis, midtraining, and posttraining for scalable searchagent optimization. Specifically, REDSearcher introduces the following improvements: (1) We frame task synthesis as a dualconstrained optimization, where task difficulty is precisely governed by graph topology and evidence dispersion, allowing scalable generation of complex, highquality tasks. (2) We introduce toolaugmented queries to encourage proactive tool use rather than passive recall.(3) During midtraining, we strengthen core atomic capabilities knowledge, planning, and function calling substantially reducing the cost of collecting highquality trajectories for downstream training. (4) We build a local simulated environment that enables rapid, lowcost algorithmic iteration for reinforcement learning experiments. Across both textonly and multimodal searchagent benchmarks, our approach achieves stateoftheart performance. To facilitate future research on longhorizon search agents, we will release 10K highquality complex text search trajectories, 5K multimodal trajectories and 1K text RL query set, and together with code and model checkpoints.

Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources of greedy decoding due to wasteful search strategies, making them difficult to be deployed in practical applications. This study introduces a novel guided tree search algorithm with dynamic node selection and node-level exploration budget (maximum number of children) calculation to tackle this issue. By considering the search progress towards the final answer (history) and the guidance from a value network (future) trained without any step-wise annotations, our algorithm iteratively selects the most promising tree node before expanding it within the boundaries of the allocated computational budget. Experiments conducted on the GSM8K and TabMWP datasets demonstrate that our approach not only offers competitive performance but also enjoys significantly lower computational costs compared to baseline methods.

We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced by Zermelo almost a century ago. Here we describe an alternative and similarly simple iteration that provably returns identical results but does so much faster -- over a hundred times faster in some cases. We demonstrate this algorithm with applications to a range of example data sets and derive a number of results regarding its convergence.

In this paper, we consider the problem of Iterative Machine Teaching (IMT), where the teacher provides examples to the learner iteratively such that the learner can achieve fast convergence to a target model. However, existing IMT algorithms are solely based on parameterized families of target models. They mainly focus on convergence in the parameter space, resulting in difficulty when the target models are defined to be functions without dependency on parameters. To address such a limitation, we study a more general task -- Nonparametric Iterative Machine Teaching (NIMT), which aims to teach nonparametric target models to learners in an iterative fashion. Unlike parametric IMT that merely operates in the parameter space, we cast NIMT as a functional optimization problem in the function space. To solve it, we propose both random and greedy functional teaching algorithms. We obtain the iterative teaching dimension (ITD) of the random teaching algorithm under proper assumptions, which serves as a uniform upper bound of ITD in NIMT. Further, the greedy teaching algorithm has a significantly lower ITD, which reaches a tighter upper bound of ITD in NIMT. Finally, we verify the correctness of our theoretical findings with extensive experiments in nonparametric scenarios.

Many fields use search algorithms, which automatically explore a search space to find high-performing solutions: chemists search through the space of molecules to discover new drugs; engineers search for stronger, cheaper, safer designs, scientists search for models that best explain data, etc. The goal of search algorithms has traditionally been to return the single highest-performing solution in a search space. Here we describe a new, fundamentally different type of algorithm that is more useful because it provides a holistic view of how high-performing solutions are distributed throughout a search space. It creates a map of high-performing solutions at each point in a space defined by dimensions of variation that a user gets to choose. This Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) algorithm illuminates search spaces, allowing researchers to understand how interesting attributes of solutions combine to affect performance, either positively or, equally of interest, negatively. For example, a drug company may wish to understand how performance changes as the size of molecules and their cost-to-produce vary. MAP-Elites produces a large diversity of high-performing, yet qualitatively different solutions, which can be more helpful than a single, high-performing solution. Interestingly, because MAP-Elites explores more of the search space, it also tends to find a better overall solution than state-of-the-art search algorithms. We demonstrate the benefits of this new algorithm in three different problem domains ranging from producing modular neural networks to designing simulated and real soft robots. Because MAP- Elites (1) illuminates the relationship between performance and dimensions of interest in solutions, (2) returns a set of high-performing, yet diverse solutions, and (3) improves finding a single, best solution, it will advance science and engineering.

Structural pruning enhances hardware-agnostic inference efficiency for large language models (LLMs) yet often fails to maintain comparable performance. Local pruning performs efficient layer-by-layer compression but ignores global topology. Although global pruning aims to identify an optimal sparse model, intuitive methods typically adopt a two-stage paradigm that first evaluates substructure saliency and then applies global pruning, which ignores inter-structure dependencies and fails to achieve end-to-end optimization. To address these limitations, we propose T\'yr-the-Pruner, an efficient end-to-end search-based global structural pruning framework. This framework constructs a supernet by repeatedly applying local pruning across a range of sparsity ratios to each layer in an LLM, with the core goal of determining the optimal sparsity distribution under a target overall sparsity ratio. Concretely, we introduce an effective local pruning and an expectation error accumulation approach to improve supernet construction. Furthermore, we employ an iterative prune-and-search strategy with coarse-to-fine sparsity granularity to ensure efficient search convergence. Experimental results show that T\'yr-the-Pruner achieves state-of-the-art structural pruning, retaining 97% of the dense model's performance while removing a challenging 50% of Llama-3.1-70B's parameters. Code will be available at https://github.com/AMD-AGI/Tyr-the-Pruner.

This paper tackles optimization problems whose objective and constraints involve a trained Neural Network (NN), where the goal is to maximize f(Phi(x)) subject to c(Phi(x)) leq 0, with f smooth, c general and non-stringent, and Phi an already trained and possibly nonwhite-box NN. We address two challenges regarding this problem: identifying ascent directions for local search, and ensuring reliable convergence towards relevant local solutions. To this end, we re-purpose the notion of directional NN attacks as efficient optimization subroutines, since directional NN attacks use the neural structure of Phi to compute perturbations of x that steer Phi(x) in prescribed directions. Precisely, we develop an attack operator that computes attacks of Phi at any x along the direction nabla f(Phi(x)). Then, we propose a hybrid algorithm combining the attack operator with derivative-free optimization (DFO) techniques, designed for numerical reliability by remaining oblivious to the structure of the problem. We consider the cDSM algorithm, which offers asymptotic guarantees to converge to a local solution under mild assumptions on the problem. The resulting method alternates between attack-based steps for heuristic yet fast local intensification and cDSM steps for certified convergence and numerical reliability. Experiments on three problems show that this hybrid approach consistently outperforms standard DFO baselines.

We present a novel framework for training large language models with continuously adjustable internal representations that span the full spectrum from localist (interpretable, rule-based) to distributed (generalizable, efficient) encodings. The key innovation is a locality dial, a tunable parameter that dynamically controls the degree of localization during both training and inference without requiring model retraining. This is achieved through group sparsity penalties on attention mechanisms, information-theoretic anchor design, and dynamic rule injection. We provide rigorous mathematical proofs establishing explicit threshold conditions under which attention provably concentrates on semantically relevant blocks, with exponential bounds on attention entropy and pointer fidelity. Specifically, we prove that when group sparsity penalties exceed certain threshold values, the model's attention mechanisms concentrate on semantically relevant blocks, achieving low entropy and high fidelity with negligible error. This framework enables practitioners to continuously interpolate between interpretable and high-performance modes, supporting applications in regulated domains requiring both transparency and capability.

We introduce a unified framework for iterative reasoning that leverages non-Euclidean geometry via Bregman divergences, higher-order operator averaging, and adaptive feedback mechanisms. Our analysis establishes that, under mild smoothness and contractivity assumptions, a generalized update scheme not only unifies classical methods such as mirror descent and dynamic programming but also captures modern chain-of-thought reasoning processes in large language models. In particular, we prove that our accelerated iterative update achieves an O(1/t^2) convergence rate in the absence of persistent perturbations, and we further demonstrate that feedback (iterative) architectures are necessary to approximate certain fixed-point functions efficiently. These theoretical insights bridge classical acceleration techniques with contemporary applications in neural computation and optimization.

Current literature, aiming to surpass the "Chain-of-Thought" approach, often resorts to an external modus operandi involving halting, modifying, and then resuming the generation process to boost Large Language Models' (LLMs) reasoning capacities. This mode escalates the number of query requests, leading to increased costs, memory, and computational overheads. Addressing this, we propose the Algorithm of Thoughts -- a novel strategy that propels LLMs through algorithmic reasoning pathways, pioneering a new mode of in-context learning. By employing algorithmic examples, we exploit the innate recurrence dynamics of LLMs, expanding their idea exploration with merely one or a few queries. Our technique outperforms earlier single-query methods and stands on par with a recent multi-query strategy that employs an extensive tree search algorithm. Intriguingly, our results suggest that instructing an LLM using an algorithm can lead to performance surpassing that of the algorithm itself, hinting at LLM's inherent ability to weave its intuition into optimized searches. We probe into the underpinnings of our method's efficacy and its nuances in application.

This work delved into the realm of automatic text generation, exploring a variety of techniques ranging from traditional deterministic approaches to more modern stochastic methods. Through analysis of greedy search, beam search, top-k sampling, top-p sampling, contrastive searching, and locally typical searching, this work has provided valuable insights into the strengths, weaknesses, and potential applications of each method. Each text-generating method is evaluated using several standard metrics and a comparative study has been made on the performance of the approaches. Finally, some future directions of research in the field of automatic text generation are also identified.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

We present Adjacent Possible Exploration (APE), a simple yet effective method for adapting large language models to specific tasks using minimal computational resources. Unlike traditional fine-tuning that requires extensive compute, APE iteratively fine-tunes models on small, carefully selected data batches (200 examples), retaining only improvements. On news summarization, APE achieves 40 percent BLEU improvement using just a T4 GPU in 60 minutes, matching or exceeding more complex methods like LoRA while remaining conceptually simple. Our approach is particularly valuable for researchers and practitioners with limited computational resources. We provide open-source code and demonstrate APE's effectiveness through both automatic metrics and human evaluation. While inspired by evolutionary theory's "adjacent possible", APE's core insight has a very practical application: small, iterative data perturbations can efficiently guide LLMs toward task-specific performance without expensive retraining.

Large Language Model (LLM)-based search agents have shown remarkable capabilities in solving complex tasks by dynamically decomposing problems and addressing them through interleaved reasoning and retrieval. However, this interleaved paradigm introduces substantial efficiency bottlenecks. First, we observe that both highly accurate and overly approximate retrieval methods degrade system efficiency: exact search incurs significant retrieval overhead, while coarse retrieval requires additional reasoning steps during generation. Second, we identify inefficiencies in system design, including improper scheduling and frequent retrieval stalls, which lead to cascading latency -- where even minor delays in retrieval amplify end-to-end inference time. To address these challenges, we introduce SearchAgent-X, a high-efficiency inference framework for LLM-based search agents. SearchAgent-X leverages high-recall approximate retrieval and incorporates two key techniques: priority-aware scheduling and non-stall retrieval. Extensive experiments demonstrate that SearchAgent-X consistently outperforms state-of-the-art systems such as vLLM and HNSW-based retrieval across diverse tasks, achieving up to 3.4times higher throughput and 5times lower latency, without compromising generation quality. SearchAgent-X is available at https://github.com/tiannuo-yang/SearchAgent-X.

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.

Mixed-integer programming (MIP) is a powerful paradigm for modeling and solving various important combinatorial optimization problems. Recently, learning-based approaches have shown a potential to speed up MIP solving via offline training that then guides important design decisions during the search. However, a significant drawback of these methods is their heavy reliance on offline training, which requires collecting training datasets and computationally costly training epochs yet offering only limited generalization to unseen (larger) instances. In this paper, we propose Balans, an adaptive meta-solver for MIPs with online learning capability that does not require any supervision or apriori training. At its core, Balans is based on adaptive large-neighborhood search, operating on top of an MIP solver by successive applications of destroy and repair neighborhood operators. During the search, the selection among different neighborhood definitions is guided on the fly for the instance at hand via multi-armed bandit algorithms. Our extensive experiments on hard optimization instances show that Balans offers significant performance gains over the default MIP solver, is better than committing to any single best neighborhood, and improves over the state-of-the-art large-neighborhood search for MIPs. Finally, we release Balans as a highly configurable, MIP solver agnostic, open-source software.

We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only. We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems, without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem statements, we achieve state-of-the-art on the miniF2F benchmark, automatically solving multiple challenging problems drawn from high school olympiads.

Vector databases typically rely on approximate nearest neighbor (ANN) search to retrieve the top-k closest vectors to a query in embedding space. While effective, this approach often yields semantically redundant results, missing the diversity and contextual richness required by applications such as retrieval-augmented generation (RAG), multi-hop QA, and memory-augmented agents. We introduce a new retrieval paradigm: semantic compression, which aims to select a compact, representative set of vectors that captures the broader semantic structure around a query. We formalize this objective using principles from submodular optimization and information geometry, and show that it generalizes traditional top-k retrieval by prioritizing coverage and diversity. To operationalize this idea, we propose graph-augmented vector retrieval, which overlays semantic graphs (e.g., kNN or knowledge-based links) atop vector spaces to enable multi-hop, context-aware search. We theoretically analyze the limitations of proximity-based retrieval under high-dimensional concentration and highlight how graph structures can improve semantic coverage. Our work outlines a foundation for meaning-centric vector search systems, emphasizing hybrid indexing, diversity-aware querying, and structured semantic retrieval. We make our implementation publicly available to foster future research in this area.

The field of Automatic Machine Learning (AutoML) has recently attained impressive results, including the discovery of state-of-the-art machine learning solutions, such as neural image classifiers. This is often done by applying an evolutionary search method, which samples multiple candidate solutions from a large space and evaluates the quality of each candidate through a long training process. As a result, the search tends to be slow. In this paper, we show that large efficiency gains can be obtained by employing a fast unified functional hash, especially through the functional equivalence caching technique, which we also present. The central idea is to detect by hashing when the search method produces equivalent candidates, which occurs very frequently, and this way avoid their costly re-evaluation. Our hash is "functional" in that it identifies equivalent candidates even if they were represented or coded differently, and it is "unified" in that the same algorithm can hash arbitrary representations; e.g. compute graphs, imperative code, or lambda functions. As evidence, we show dramatic improvements on multiple AutoML domains, including neural architecture search and algorithm discovery. Finally, we consider the effect of hash collisions, evaluation noise, and search distribution through empirical analysis. Altogether, we hope this paper may serve as a guide to hashing techniques in AutoML.

Modular approaches, which use a different composition of modules for each problem and avoid forgetting by design, have been shown to be a promising direction in continual learning (CL). However, searching through the large, discrete space of possible module compositions is a challenge because evaluating a composition's performance requires a round of neural network training. To address this challenge, we develop a modular CL framework, called PICLE, that accelerates search by using a probabilistic model to cheaply compute the fitness of each composition. The model combines prior knowledge about good module compositions with dataset-specific information. Its use is complemented by splitting up the search space into subsets, such as perceptual and latent subsets. We show that PICLE is the first modular CL algorithm to achieve different types of transfer while scaling to large search spaces. We evaluate it on two benchmark suites designed to capture different desiderata of CL techniques. On these benchmarks, PICLE offers significantly better performance than state-of-the-art CL baselines.

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

Large language models (LLMs) demonstrate exceptional performance in numerous tasks but still heavily rely on knowledge stored in their parameters. Moreover, updating this knowledge incurs high training costs. Retrieval-augmented generation (RAG) methods address this issue by integrating external knowledge. The model can answer questions it couldn't previously by retrieving knowledge relevant to the query. This approach improves performance in certain scenarios for specific tasks. However, if irrelevant texts are retrieved, it may impair model performance. In this paper, we propose Retrieval Augmented Iterative Self-Feedback (RA-ISF), a framework that iteratively decomposes tasks and processes them in three submodules to enhance the model's problem-solving capabilities. Experiments show that our method outperforms existing benchmarks, performing well on models like GPT3.5, Llama2, significantly enhancing factual reasoning capabilities and reducing hallucinations.

We provide a reproducible, end-to-end demonstration of vector search with OpenAI embeddings using Lucene on the popular MS MARCO passage ranking test collection. The main goal of our work is to challenge the prevailing narrative that a dedicated vector store is necessary to take advantage of recent advances in deep neural networks as applied to search. Quite the contrary, we show that hierarchical navigable small-world network (HNSW) indexes in Lucene are adequate to provide vector search capabilities in a standard bi-encoder architecture. This suggests that, from a simple cost-benefit analysis, there does not appear to be a compelling reason to introduce a dedicated vector store into a modern "AI stack" for search, since such applications have already received substantial investments in existing, widely deployed infrastructure.

This paper presents first successful steps in designing search agents that learn meta-strategies for iterative query refinement in information-seeking tasks. Our approach uses machine reading to guide the selection of refinement terms from aggregated search results. Agents are then empowered with simple but effective search operators to exert fine-grained and transparent control over queries and search results. We develop a novel way of generating synthetic search sessions, which leverages the power of transformer-based language models through (self-)supervised learning. We also present a reinforcement learning agent with dynamically constrained actions that learns interactive search strategies from scratch. Our search agents obtain retrieval and answer quality performance comparable to recent neural methods, using only a traditional term-based BM25 ranking function and interpretable discrete reranking and filtering actions.

This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with O(n^3) runtime and O(n^2) space complexity or sample a large volume of random spanning trees, thus are difficult to scale to large graphs. In this work, we propose an improvement based on the online relaxation technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret O(n^{1+gamma}) when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying O(kn^{1+gamma}) regret based on this relaxation. The key of FastONL is a generalized local push method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is O(vol({S})log 1/epsilon) locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.

Iterative preference optimization methods have recently been shown to perform well for general instruction tuning tasks, but typically make little improvement on reasoning tasks (Yuan et al., 2024, Chen et al., 2024). In this work we develop an iterative approach that optimizes the preference between competing generated Chain-of-Thought (CoT) candidates by optimizing for winning vs. losing reasoning steps that lead to the correct answer. We train using a modified DPO loss (Rafailov et al., 2023) with an additional negative log-likelihood term, which we find to be crucial. We show reasoning improves across repeated iterations of this scheme. While only relying on examples in the training set, our approach results in increasing accuracy for Llama-2-70B-Chat from 55.6% to 81.6% on GSM8K (and 88.7% with majority voting out of 32 samples), from 12.5% to 20.8% on MATH, and from 77.8% to 86.7% on ARC-Challenge, which outperforms other Llama-2-based models not relying on additionally sourced datasets.

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how they differ from meta-learning is lacking. In this paper, we propose a framework to analyze such learning-based acceleration approaches, where one can immediately identify a departure from classical meta-learning. We show that this departure may lead to arbitrary deterioration of model performance. Based on our analysis, we introduce a novel training method for learning-based acceleration of iterative methods. Furthermore, we theoretically prove that the proposed method improves upon the existing methods, and demonstrate its significant advantage and versatility through various numerical applications.

This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdos, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

Augmenting large language models (LLMs) with external retrieval has become a standard method to address their inherent knowledge cutoff limitations. However, traditional retrieval-augmented generation methods employ static, pre-inference retrieval strategies, making them inadequate for complex tasks involving ambiguous, multi-step, or evolving information needs. Recent advances in test-time scaling techniques have demonstrated significant potential in enabling LLMs to dynamically interact with external tools, motivating the shift toward adaptive inference-time retrieval. Inspired by Information Foraging Theory (IFT), we propose InForage, a reinforcement learning framework that formalizes retrieval-augmented reasoning as a dynamic information-seeking process. Unlike existing approaches, InForage explicitly rewards intermediate retrieval quality, encouraging LLMs to iteratively gather and integrate information through adaptive search behaviors. To facilitate training, we construct a human-guided dataset capturing iterative search and reasoning trajectories for complex, real-world web tasks. Extensive evaluations across general question answering, multi-hop reasoning tasks, and a newly developed real-time web QA dataset demonstrate InForage's superior performance over baseline methods. These results highlight InForage's effectiveness in building robust, adaptive, and efficient reasoning agents.

Large language model (LLM)-based search agents have proven promising for addressing knowledge-intensive problems by incorporating information retrieval capabilities. Existing works largely focus on optimizing the reasoning paradigms of search agents, yet the quality of intermediate search queries during reasoning remains overlooked. As a result, the generated queries often remain inaccurate, leading to unexpected retrieval results and ultimately limiting search agents' overall effectiveness. To mitigate this issue, we introduce SmartSearch, a framework built upon two key mechanisms: (1) Process rewards, which provide fine-grained supervision for the quality of each intermediate search query through Dual-Level Credit Assessment. (2) Query refinement, which promotes the optimization of query generation by selectively refining low-quality search queries and regenerating subsequent search rounds based on these refinements. To enable the search agent to progressively internalize the ability to improve query quality under the guidance of process rewards, we design a three-stage curriculum learning framework. This framework guides the agent through a progression from imitation, to alignment, and ultimately to generalization. Experimental results show that SmartSearch consistently surpasses existing baselines, and additional quantitative analyses further confirm its significant gains in both search efficiency and query quality. The code is available at https://github.com/MYVAE/SmartSearch.

Recent efforts in fine-tuning language models often rely on automatic data selection, commonly using Nearest Neighbors retrieval from large datasets. However, we theoretically show that this approach tends to select redundant data, limiting its effectiveness or even hurting performance. To address this, we introduce SIFT, a data selection algorithm designed to reduce uncertainty about the model's response given a prompt, which unifies ideas from retrieval and active learning. Whereas Nearest Neighbor retrieval typically fails in the presence of information duplication, SIFT accounts for information duplication and optimizes the overall information gain of the selected examples. We focus our evaluations on fine-tuning at test-time for prompt-specific language modeling on the Pile dataset, and show that SIFT consistently outperforms Nearest Neighbor retrieval, with minimal computational overhead. Moreover, we show that our uncertainty estimates can predict the performance gain of test-time fine-tuning, and use this to develop an adaptive algorithm that invests test-time compute proportional to realized performance gains. We provide the activeft (Active Fine-Tuning) library which can be used as a drop-in replacement for Nearest Neighbor retrieval.

Generative retrieval has emerged as a powerful paradigm for LLM-based recommendation. However, industrial recommender systems often benefit from restricting the output space to a constrained subset of items based on business logic (e.g. enforcing content freshness or product category), which standard autoregressive decoding cannot natively support. Moreover, existing constrained decoding methods that make use of prefix trees (Tries) incur severe latency penalties on hardware accelerators (TPUs/GPUs). In this work, we introduce STATIC (Sparse Transition Matrix-Accelerated Trie Index for Constrained Decoding), an efficient and scalable constrained decoding technique designed specifically for high-throughput LLM-based generative retrieval on TPUs/GPUs. By flattening the prefix tree into a static Compressed Sparse Row (CSR) matrix, we transform irregular tree traversals into fully vectorized sparse matrix operations, unlocking massive efficiency gains on hardware accelerators. We deploy STATIC on a large-scale industrial video recommendation platform serving billions of users. STATIC produces significant product metric impact with minimal latency overhead (0.033 ms per step and 0.25% of inference time), achieving a 948x speedup over a CPU trie implementation and a 47-1033x speedup over a hardware-accelerated binary-search baseline. Furthermore, the runtime overhead of STATIC remains extremely low across a wide range of practical configurations. To the best of our knowledge, STATIC enables the first production-scale deployment of strictly constrained generative retrieval. In addition, evaluation on academic benchmarks demonstrates that STATIC can considerably improve cold-start performance for generative retrieval. Our code is available at https://github.com/youtube/static-constraint-decoding.

Efficiently ranking relevant items from large candidate pools is a cornerstone of modern information retrieval systems -- such as web search, recommendation, and retrieval-augmented generation. Listwise rerankers, which improve relevance by jointly considering multiple candidates, are often limited in practice: either by model input size constraints, or by degraded quality when processing large sets. We propose a model-agnostic method for fast reranking large sets that exceed a model input limits. The method first partitions candidate items into overlapping blocks, each of which is ranked independently in parallel. Implicit pairwise comparisons are then derived from these local rankings. Finally, these comparisons are aggregated to construct a global ranking using algorithms such as Winrate or PageRank. Experiments on TREC DL-2019 show that our method achieves an nDCG@10 of 70.88 compared to the 57.68 for full-context listwise approach using gpt-4.1-mini as long-context model, while reducing latency from 21 to 8 seconds. The implementation of the algorithm and the experiments is available in the repository: https://github.com/V3RGANz/jointrank

Vector search systems, pivotal in AI applications, often rely on the Hierarchical Navigable Small Worlds (HNSW) algorithm. However, the behaviour of HNSW under real-world scenarios using vectors generated with deep learning models remains under-explored. Existing Approximate Nearest Neighbours (ANN) benchmarks and research typically has an over-reliance on simplistic datasets like MNIST or SIFT1M and fail to reflect the complexity of current use-cases. Our investigation focuses on HNSW's efficacy across a spectrum of datasets, including synthetic vectors tailored to mimic specific intrinsic dimensionalities, widely-used retrieval benchmarks with popular embedding models, and proprietary e-commerce image data with CLIP models. We survey the most popular HNSW vector databases and collate their default parameters to provide a realistic fixed parameterisation for the duration of the paper. We discover that the recall of approximate HNSW search, in comparison to exact K Nearest Neighbours (KNN) search, is linked to the vector space's intrinsic dimensionality and significantly influenced by the data insertion sequence. Our methodology highlights how insertion order, informed by measurable properties such as the pointwise Local Intrinsic Dimensionality (LID) or known categories, can shift recall by up to 12 percentage points. We also observe that running popular benchmark datasets with HNSW instead of KNN can shift rankings by up to three positions for some models. This work underscores the need for more nuanced benchmarks and design considerations in developing robust vector search systems using approximate vector search algorithms. This study presents a number of scenarios with varying real world applicability which aim to better increase understanding and future development of ANN algorithms and embedding

Transformer architectures have achieved remarkable success in various domains. While efficient alternatives to Softmax Attention have been widely studied, the search for more expressive mechanisms grounded in theoretical insight-even at greater computational cost-has been relatively underexplored. In this work, we bridge this gap by proposing Local Linear Attention (LLA), a novel attention mechanism derived from nonparametric statistics through the lens of test-time regression. First, we show that LLA offers theoretical advantages over Linear and Softmax Attention for associative memory via a bias-variance trade-off analysis. Next, we address its computational challenges and propose two memory-efficient primitives to tackle the Theta(n^2 d) and Theta(n d^2) complexity. We then introduce FlashLLA, a hardware-efficient, blockwise algorithm that enables scalable and parallel computation on modern accelerators. In addition, we implement and profile a customized inference kernel that significantly reduces memory overheads. Finally, we empirically validate the advantages and limitations of LLA on test-time regression, in-context regression, associative recall and state tracking tasks. Experiment results demonstrate that LLA effectively adapts to non-stationarity, outperforming strong baselines in test-time training and in-context learning, and exhibiting promising evidence for its scalability and applicability in large-scale models. Code is available at https://github.com/Yifei-Zuo/Flash-LLA.

Recent advancements in Large Language Models have transformed ML/AI development, necessitating a reevaluation of AutoML principles for the Retrieval-Augmented Generation (RAG) systems. To address the challenges of hyper-parameter optimization and online adaptation in RAG, we propose the AutoRAG-HP framework, which formulates the hyper-parameter tuning as an online multi-armed bandit (MAB) problem and introduces a novel two-level Hierarchical MAB (Hier-MAB) method for efficient exploration of large search spaces. We conduct extensive experiments on tuning hyper-parameters, such as top-k retrieved documents, prompt compression ratio, and embedding methods, using the ALCE-ASQA and Natural Questions datasets. Our evaluation from jointly optimization all three hyper-parameters demonstrate that MAB-based online learning methods can achieve Recall@5 approx 0.8 for scenarios with prominent gradients in search space, using only sim20% of the LLM API calls required by the Grid Search approach. Additionally, the proposed Hier-MAB approach outperforms other baselines in more challenging optimization scenarios. The code will be made available at https://aka.ms/autorag.

In this paper, we examine how large language models (LLMs) solve multi-step problems under a language agent framework with three components: a generator, a discriminator, and a planning method. We investigate the practical utility of two advanced planning methods, iterative correction and tree search. We present a comprehensive analysis of how discrimination accuracy affects the overall performance of agents when using these two methods or a simpler method, re-ranking. Experiments on two tasks, text-to-SQL parsing and mathematical reasoning, show that: (1) advanced planning methods demand discriminators with at least 90% accuracy to achieve significant improvements over re-ranking; (2) current LLMs' discrimination abilities have not met the needs of advanced planning methods to achieve such improvements; (3) with LLM-based discriminators, advanced planning methods may not adequately balance accuracy and efficiency. For example, compared to the other two methods, tree search is at least 10--20 times slower but leads to negligible performance gains, which hinders its real-world applications. Code and data will be released at https://github.com/OSU-NLP-Group/llm-planning-eval.

Iterative refinement has been a promising paradigm to enable large language models (LLMs) to resolve difficult reasoning and problem-solving tasks. One of the key challenges, however, is how to effectively search through the enormous search space of possible refinements. Existing methods typically fall back on predefined heuristics, which are troubled by the exploration-exploitation dilemma and cannot adapt based on past refinement outcomes. We introduce Tree-Guided Policy Refinement (TGPR), a novel framework that combines GRPO with a Thompson-Sampling-based tree search. TGPR explores both failed and successful refinement paths actively, with denser training trajectories and more adaptive policies. On HumanEval, MBPP, and APPS benchmarks, our method achieves up to +4.2 percentage points absolute improvement in pass@1 (on MBPP) and up to +12.51 percentage points absolute improvement in pass@10 (on APPS) compared to a competitive GRPO baseline. Apart from debugging code, TGPR focuses on a principled approach to combining learned policies with structured search methods, offering a general framework for enhancing iterative refinement and stateful reasoning in LLMs.

We consider the problem where an agent wants to find a hidden object that is randomly located in some vertex of a directed acyclic graph (DAG) according to a fixed but possibly unknown distribution. The agent can only examine vertices whose in-neighbors have already been examined. In this paper, we address a learning setting where we allow the agent to stop before having found the object and restart searching on a new independent instance of the same problem. Our goal is to maximize the total number of hidden objects found given a time budget. The agent can thus skip an instance after realizing that it would spend too much time on it. Our contributions are both to the search theory and multi-armed bandits. If the distribution is known, we provide a quasi-optimal and efficient stationary strategy. If the distribution is unknown, we additionally show how to sequentially approximate it and, at the same time, act near-optimally in order to collect as many hidden objects as possible.

Decoding for many NLP tasks requires an effective heuristic algorithm for approximating exact search since the problem of searching the full output space is often intractable, or impractical in many settings. The default algorithm for this job is beam search -- a pruned version of breadth-first search. Quite surprisingly, beam search often returns better results than exact inference due to beneficial search bias for NLP tasks. In this work, we show that the standard implementation of beam search can be made up to 10x faster in practice. Our method assumes that the scoring function is monotonic in the sequence length, which allows us to safely prune hypotheses that cannot be in the final set of hypotheses early on. We devise effective monotonic approximations to popular nonmonontic scoring functions, including length normalization and mutual information decoding. Lastly, we propose a memory-reduced variant of Best-First Beam Search, which has a similar beneficial search bias in terms of downstream performance, but runs in a fraction of the time.

Greedy search methods like Greedy Best-First Search (GBFS) and Enforced Hill-Climbing (EHC) often struggle when faced with Uninformed Heuristic Regions (UHRs) like heuristic local minima or plateaus. In this work, we theoretically and empirically compare two popular methods for escaping UHRs in breadth-first search (BrFS) and restarting random walks (RRWs). We first derive the expected runtime of escaping a UHR using BrFS and RRWs, based on properties of the UHR and the random walk procedure, and then use these results to identify when RRWs will be faster in expectation than BrFS. We then evaluate these methods for escaping UHRs by comparing standard EHC, which uses BrFS to escape UHRs, to variants of EHC called EHC-RRW, which use RRWs for that purpose. EHC-RRW is shown to have strong expected runtime guarantees in cases where EHC has previously been shown to be effective. We also run experiments with these approaches on PDDL planning benchmarks to better understand their relative effectiveness for escaping UHRs.

Recent advances in deep-research agents have shown promise for autonomous knowledge construction through dynamic reasoning over external sources. However, existing approaches rely on a mono-contextual paradigm that accumulates all information in a single, expanding context window, leading to context suffocation and noise contamination that limit their effectiveness on long-horizon tasks. We introduce IterResearch, a novel iterative deep-research paradigm that reformulates long-horizon research as a Markov Decision Process with strategic workspace reconstruction. By maintaining an evolving report as memory and periodically synthesizing insights, our approach preserves consistent reasoning capacity across arbitrary exploration depths. We further develop Efficiency-Aware Policy Optimization (EAPO), a reinforcement learning framework that incentivizes efficient exploration through geometric reward discounting and enables stable distributed training via adaptive downsampling. Extensive experiments demonstrate that IterResearch achieves substantial improvements over existing open-source agents with average +14.5pp across six benchmarks and narrows the gap with frontier proprietary systems. Remarkably, our paradigm exhibits unprecedented interaction scaling, extending to 2048 interactions with dramatic performance gains (from 3.5\% to 42.5\%), and serves as an effective prompting strategy, improving frontier models by up to 19.2pp over ReAct on long-horizon tasks. These findings position IterResearch as a versatile solution for long-horizon reasoning, effective both as a trained agent and as a prompting paradigm for frontier models.

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.

Neural embedding models have become a fundamental component of modern information retrieval (IR) pipelines. These models produce a single embedding x in R^d per data-point, allowing for fast retrieval via highly optimized maximum inner product search (MIPS) algorithms. Recently, beginning with the landmark ColBERT paper, multi-vector models, which produce a set of embedding per data point, have achieved markedly superior performance for IR tasks. Unfortunately, using these models for IR is computationally expensive due to the increased complexity of multi-vector retrieval and scoring. In this paper, we introduce MUVERA (MUlti-VEctor Retrieval Algorithm), a retrieval mechanism which reduces multi-vector similarity search to single-vector similarity search. This enables the usage of off-the-shelf MIPS solvers for multi-vector retrieval. MUVERA asymmetrically generates Fixed Dimensional Encodings (FDEs) of queries and documents, which are vectors whose inner product approximates multi-vector similarity. We prove that FDEs give high-quality epsilon-approximations, thus providing the first single-vector proxy for multi-vector similarity with theoretical guarantees. Empirically, we find that FDEs achieve the same recall as prior state-of-the-art heuristics while retrieving 2-5times fewer candidates. Compared to prior state of the art implementations, MUVERA achieves consistently good end-to-end recall and latency across a diverse set of the BEIR retrieval datasets, achieving an average of 10% improved recall with 90% lower latency.

Modern IR systems are increasingly tasked with answering complex, multi-faceted queries that require deep reasoning rather than simple keyword or semantic matching. While LLM-based IR has shown great promise, the prevailing retrieve-then-rerank paradigm inherits the limitations of embedding-based retrieval; parametric generative approaches are difficult to update with new information; and long-context methods that place the entire corpus in context are computationally infeasible for large document collections. To address these challenges, we introduce LATTICE, a hierarchical retrieval framework that enables an LLM to reason over and navigate large corpora with logarithmic search complexity by imposing a semantic tree structure on the corpus. Our approach consists of two stages: (1) an offline phase that organizes the corpus into a semantic hierarchy via either a bottom-up agglomerative strategy or a top-down divisive strategy using multi-level summaries and (2) an online traversal phase where a search LLM navigates this tree. A central challenge in such LLM-guided search is that the model's relevance judgments are noisy, context-dependent, and unaware of the hierarchy, making cross-branch and cross-level comparisons difficult. To overcome this, we propose a traversal algorithm that estimates calibrated latent relevance scores from local LLM outputs and aggregates them into a global path relevance metric. Our training-free framework achieves state-of-the-art zero-shot performance on the reasoning-intensive BRIGHT benchmark, demonstrating up to 9% improvement in Recall@100 and 5% in nDCG@10 over the next best zero-shot baseline. Furthermore, compared to the fine-tuned SOTA method DIVER-v2, LATTICE attains comparable results on BRIGHT subsets that use a static corpus for evaluation.

As user content and queries become increasingly multi-modal, the need for effective multi-modal search systems has grown. Traditional search systems often rely on textual and metadata annotations for indexed images, while multi-modal embeddings like CLIP enable direct search using text and image embeddings. However, embedding-based approaches face challenges in integrating contextual features such as user locale and recency. Building a scalable multi-modal search system requires fine-tuning several components. This paper presents a multi-modal search architecture and a series of AB tests that optimize embeddings and multi-modal technologies in Adobe Express template search. We address considerations such as embedding model selection, the roles of embeddings in matching and ranking, and the balance between dense and sparse embeddings. Our iterative approach demonstrates how utilizing sparse, dense, and contextual features enhances short and long query search, significantly reduces null rates (over 70\%), and increases click-through rates (CTR). Our findings provide insights into developing robust multi-modal search systems, thereby enhancing relevance for complex queries.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

Tensor network (TN) is a powerful framework in machine learning, but selecting a good TN model, known as TN structure search (TN-SS), is a challenging and computationally intensive task. The recent approach TNLS~li2022permutation showed promising results for this task, however, its computational efficiency is still unaffordable, requiring too many evaluations of the objective function. We propose TnALE, a new algorithm that updates each structure-related variable alternately by local enumeration, greatly reducing the number of evaluations compared to TNLS. We theoretically investigate the descent steps for TNLS and TnALE, proving that both algorithms can achieve linear convergence up to a constant if a sufficient reduction of the objective is reached in each neighborhood. We also compare the evaluation efficiency of TNLS and TnALE, revealing that Omega(2^N) evaluations are typically required in TNLS for reaching the objective reduction in the neighborhood, while ideally O(N^2R) evaluations are sufficient in TnALE, where N denotes the tensor order and R reflects the ``low-rankness'' of the neighborhood. Experimental results verify that TnALE can find practically good TN-ranks and permutations with vastly fewer evaluations than the state-of-the-art algorithms.

The efficacy of large language models (LLMs) in understanding and generating natural language has aroused a wide interest in developing prompt-based methods to harness the power of black-box LLMs. Existing methodologies usually prioritize a global optimization for finding the global optimum, which however will perform poorly in certain tasks. This thus motivates us to re-think the necessity of finding a global optimum in prompt optimization. To answer this, we conduct a thorough empirical study on prompt optimization and draw two major insights. Contrasting with the rarity of global optimum, local optima are usually prevalent and well-performed, which can be more worthwhile for efficient prompt optimization (Insight I). The choice of the input domain, covering both the generation and the representation of prompts, affects the identification of well-performing local optima (Insight II). Inspired by these insights, we propose a novel algorithm, namely localized zeroth-order prompt optimization (ZOPO), which incorporates a Neural Tangent Kernel-based derived Gaussian process into standard zeroth-order optimization for an efficient search of well-performing local optima in prompt optimization. Remarkably, ZOPO outperforms existing baselines in terms of both the optimization performance and the query efficiency, which we demonstrate through extensive experiments.

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with generalization guarantees) by formulating constrained learning problems that can then be tackled by dual ascent algorithms. Yet, though these algorithms converge in objective value, even in non-convex settings, they cannot guarantee that their outcome is feasible. Doing so requires randomizing over all iterates, which is impractical in virtually any modern applications. Still, final iterates have been observed to perform well in practice. In this work, we address this gap between theory and practice by characterizing the constraint violation of Lagrangian minimizers associated with optimal dual variables, despite lack of convexity. To do this, we leverage the fact that non-convex, finite-dimensional constrained learning problems can be seen as parametrizations of convex, functional problems. Our results show that rich parametrizations effectively mitigate the issue of feasibility in dual methods, shedding light on prior empirical successes of dual learning. We illustrate our findings in fair learning tasks.

Heuristic functions are essential to the performance of tree search algorithms such as A*, where their accuracy and efficiency directly impact search outcomes. Traditionally, such heuristics are handcrafted, requiring significant expertise. Recent advances in large language models (LLMs) and evolutionary frameworks have opened the door to automating heuristic design. In this paper, we extend the Evolution of Heuristics (EoH) framework to investigate the automated generation of guiding heuristics for A* search. We introduce a novel domain-agnostic prompt augmentation strategy that includes the A* code into the prompt to leverage in-context learning, named Algorithmic - Contextual EoH (A-CEoH). To evaluate the effectiveness of A-CeoH, we study two problem domains: the Unit-Load Pre-Marshalling Problem (UPMP), a niche problem from warehouse logistics, and the classical sliding puzzle problem (SPP). Our computational experiments show that A-CEoH can significantly improve the quality of the generated heuristics and even outperform expert-designed heuristics.

This paper introduces MR-Search, an in-context meta reinforcement learning (RL) formulation for agentic search with self-reflection. Instead of optimizing a policy within a single independent episode with sparse rewards, MR-Search trains a policy that conditions on past episodes and adapts its search strategy across episodes. MR-Search learns to learn a search strategy with self-reflection, allowing search agents to improve in-context exploration at test-time. Specifically, MR-Search performs cross-episode exploration by generating explicit self-reflections after each episode and leveraging them as additional context to guide subsequent attempts, thereby promoting more effective exploration during test-time. We further introduce a multi-turn RL algorithm that estimates a dense relative advantage at the turn level, enabling fine-grained credit assignment on each episode. Empirical results across various benchmarks demonstrate the advantages of MR-Search over baselines based RL, showing strong generalization and relative improvements of 9.2% to 19.3% across eight benchmarks. Our code and data are available at https://github.com/tengxiao1/MR-Search.

Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities within these models. However, the progress of discovering effective prompts has been slow, driving a desire for general prompt optimization methods. Unfortunately, few existing prompt learning methods satisfy the criteria of being truly "general", i.e., automatic, discrete, black-box, gradient-free, and interpretable all at once. In this paper, we introduce metaheuristics, a branch of discrete non-convex optimization methods with over 100 options, as a promising approach to prompt learning. Within our paradigm, we test six typical methods: hill climbing, simulated annealing, genetic algorithms with/without crossover, tabu search, and harmony search, demonstrating their effectiveness in black-box prompt learning and Chain-of-Thought prompt tuning. Furthermore, we show that these methods can be used to discover more human-understandable prompts that were previously unknown, opening the door to a cornucopia of possibilities in prompt optimization. We release all the codes in https://github.com/research4pan/Plum.

Prompt-based learning has been an effective paradigm for large pretrained language models (LLM), enabling few-shot or even zero-shot learning. Black-box prompt search has received growing interest recently for its distinctive properties of gradient-free optimization, proven particularly useful and powerful for model-as-a-service usage. However, the discrete nature and the complexity of combinatorial optimization hinder the efficiency of modern black-box approaches. Despite extensive research on search algorithms, the crucial aspect of search space design and optimization has been largely overlooked. In this paper, we first conduct a sensitivity analysis by prompting LLM, revealing that only a small number of tokens exert a disproportionate amount of influence on LLM predictions. Leveraging this insight, we propose the Clustering and Pruning for Efficient Black-box Prompt Search (ClaPS), a simple black-box search method that first clusters and prunes the search space to focus exclusively on influential prompt tokens. By employing even simple search methods within the pruned search space, ClaPS achieves state-of-the-art performance across various tasks and LLMs, surpassing the performance of complex approaches while significantly reducing search costs. Our findings underscore the critical role of search space design and optimization in enhancing both the usefulness and the efficiency of black-box prompt-based learning.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

Finding the optimal Retrieval-Augmented Generation (RAG) configuration for a given use case can be complex and expensive. Motivated by this challenge, frameworks for RAG hyper-parameter optimization (HPO) have recently emerged, yet their effectiveness has not been rigorously benchmarked. To address this gap, we present a comprehensive study involving 5 HPO algorithms over 5 datasets from diverse domains, including a new one collected for this work on real-world product documentation. Our study explores the largest HPO search space considered to date, with two optimized evaluation metrics. Analysis of the results shows that RAG HPO can be done efficiently, either greedily or with iterative random search, and that it significantly boosts RAG performance for all datasets. For greedy HPO approaches, we show that optimizing models first is preferable to the prevalent practice of optimizing sequentially according to the RAG pipeline order.

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to optimal control, to PDE-constrained optimization. We develop an adaptive inexact Newton method for this problem class. In each iteration, we solve the Lagrangian Newton system inexactly via a randomized iterative sketching solver, and select a suitable stepsize by performing line search on an exact augmented Lagrangian merit function. The randomized solvers have advantages over deterministic linear system solvers by significantly reducing per-iteration flops complexity and storage cost, when equipped with suitable sketching matrices. Our method adaptively controls the accuracy of the randomized solver and the penalty parameters of the exact augmented Lagrangian, to ensure that the inexact Newton direction is a descent direction of the exact augmented Lagrangian. This allows us to establish a global almost sure convergence. We also show that a unit stepsize is admissible locally, so that our method exhibits a local linear convergence. Furthermore, we prove that the linear convergence can be strengthened to superlinear convergence if we gradually sharpen the adaptive accuracy condition on the randomized solver. We demonstrate the superior performance of our method on benchmark nonlinear problems in CUTEst test set, constrained logistic regression with data from LIBSVM, and a PDE-constrained problem.

Users may strive to formulate an adequate textual query for their information need. Search engines assist the users by presenting query suggestions. To preserve the original search intent, suggestions should be context-aware and account for the previous queries issued by the user. Achieving context awareness is challenging due to data sparsity. We present a probabilistic suggestion model that is able to account for sequences of previous queries of arbitrary lengths. Our novel hierarchical recurrent encoder-decoder architecture allows the model to be sensitive to the order of queries in the context while avoiding data sparsity. Additionally, our model can suggest for rare, or long-tail, queries. The produced suggestions are synthetic and are sampled one word at a time, using computationally cheap decoding techniques. This is in contrast to current synthetic suggestion models relying upon machine learning pipelines and hand-engineered feature sets. Results show that it outperforms existing context-aware approaches in a next query prediction setting. In addition to query suggestion, our model is general enough to be used in a variety of other applications.

The remarkable capability of large language models (LLMs) for in-context learning (ICL) needs to be activated by demonstration examples. Prior work has extensively explored the selection of examples for ICL, predominantly following the "select then organize" paradigm, such approaches often neglect the internal relationships between examples and exist an inconsistency between the training and inference. In this paper, we formulate the problem as a sequential selection problem and introduce Se^2, a sequential-aware method that leverages the LLM's feedback on varying context, aiding in capturing inter-relationships and sequential information among examples, significantly enriching the contextuality and relevance of ICL prompts. Meanwhile, we utilize beam search to seek and construct example sequences, enhancing both quality and diversity. Extensive experiments across 23 NLP tasks from 8 distinct categories illustrate that Se^2 markedly surpasses competitive baselines and achieves 42% relative improvement over random selection. Further in-depth analysis show the effectiveness of proposed strategies, highlighting Se^2's exceptional stability and adaptability across various scenarios. Our code will be released to facilitate future research.

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 present Neural Attention Search (NAtS), a framework that automatically evaluates the importance of each token within a sequence and determines if the corresponding token can be dropped after several steps. This approach can efficiently reduce the KV cache sizes required by transformer-based models during inference and thus reduce inference costs. In this paper, we design a search space that contains three token types: (i) Global Tokens will be preserved and queried by all the following tokens. (ii) Local Tokens survive until the next global token appears. (iii) Sliding Window Tokens have an impact on the inference of a fixed size of the next following tokens. Similar to the One-Shot Neural Architecture Search approach, this token-type information can be learned jointly with the architecture weights via a learnable attention mask. Experiments on both training a new transformer from scratch and fine-tuning existing large language models show that NAtS can efficiently reduce the KV cache size required for the models while maintaining the models' performance.

Learning to search is the task of building artificial agents that learn to autonomously use a search box to find information. So far, it has been shown that current language models can learn symbolic query reformulation policies, in combination with traditional term-based retrieval, but fall short of outperforming neural retrievers. We extend the previous learning to search setup to a hybrid environment, which accepts discrete query refinement operations, after a first-pass retrieval step via a dual encoder. Experiments on the BEIR task show that search agents, trained via behavioral cloning, outperform the underlying search system based on a combined dual encoder retriever and cross encoder reranker. Furthermore, we find that simple heuristic Hybrid Retrieval Environments (HRE) can improve baseline performance by several nDCG points. The search agent based on HRE (HARE) matches state-of-the-art performance, balanced in both zero-shot and in-domain evaluations, via interpretable actions, and at twice the speed.

Product search is a crucial component of modern e-commerce platforms, with billions of user queries every day. In product search systems, first-stage retrieval should achieve high recall while ensuring efficient online deployment. Sparse retrieval is particularly attractive in this context due to its interpretability and storage efficiency. However, sparse retrieval methods suffer from severe vocabulary mismatch issues, leading to suboptimal performance in product search scenarios. With their potential for semantic analysis, large language models (LLMs) offer a promising avenue for mitigating vocabulary mismatch issues and thereby improving retrieval quality. Directly applying LLMs to sparse retrieval in product search exposes two key challenges:(1)Queries and product titles are typically short and highly susceptible to LLM-induced hallucinations, such as generating irrelevant expansion terms or underweighting critical literal terms like brand names and model numbers;(2)The large vocabulary space of LLMs leads to difficulty in initializing training effectively, making it challenging to learn meaningful sparse representations in such ultra-high-dimensional spaces.To address these challenges, we propose PROSPER, a framework for PROduct search leveraging LLMs as SParsE Retrievers. PROSPER incorporates: (1)A literal residual network that alleviates hallucination in lexical expansion by reinforcing underweighted literal terms through a residual compensation mechanism; and (2)A lexical focusing window that facilitates effective training initialization via a coarse-to-fine sparsification strategy.Extensive offline and online experiments show that PROSPER significantly outperforms sparse baselines and achieves recall performance comparable to advanced dense retrievers, while also achieving revenue increments online.

Motivated by reducing the computational and storage costs of LLMs, model compression and KV cache compression have attracted much attention from researchers. However, current methods predominantly emphasize maintaining the performance of compressed LLMs, as measured by perplexity or simple accuracy on tasks of common sense knowledge QA and basic arithmetic reasoning. In this blog, we present a brief review of recent advancements in LLMs related to retrieval-augmented generation, multi-step reasoning, external tools, and computational expressivity, all of which substantially enhance LLM performance. Then, we propose a lottery LLM hypothesis suggesting that for a given LLM and task, there exists a smaller lottery LLM capable of producing the same performance as the original LLM with the assistance of multi-step reasoning and external tools. Based on the review of current progress in LLMs, we discuss and summarize the essential capabilities that the lottery LLM and KV cache compression must possess, which are currently overlooked in existing methods.

The lottery ticket hypothesis (LTH) has increased attention to pruning neural networks at initialization. We study this problem in the linear setting. We show that finding a sparse mask at initialization is equivalent to the sketching problem introduced for efficient matrix multiplication. This gives us tools to analyze the LTH problem and gain insights into it. Specifically, using the mask found at initialization, we bound the approximation error of the pruned linear model at the end of training. We theoretically justify previous empirical evidence that the search for sparse networks may be data independent. By using the sketching perspective, we suggest a generic improvement to existing algorithms for pruning at initialization, which we show to be beneficial in the data-independent case.

Large language models (LLMs) have recently achieved remarkable results in complex multi-step tasks, such as mathematical reasoning and agentic software engineering. However, they often struggle to maintain consistent performance across multiple solution attempts. One effective approach to narrow the gap between average-case and best-case performance is guided test-time search, which explores multiple solution paths to identify the most promising one. Unfortunately, effective search techniques (e.g. MCTS) are often unsuitable for non-serializable RL environments, such as Docker containers, where intermediate environment states cannot be easily saved and restored. We investigate two complementary search strategies applicable to such environments: 1-step lookahead and trajectory selection, both guided by a learned action-value function estimator. On the SWE-bench Verified benchmark, a key testbed for agentic software engineering, we find these methods to double the average success rate of a fine-tuned Qwen-72B model, achieving 40.8%, the new state-of-the-art for open-weights models. Additionally, we show that these techniques are transferable to more advanced closed models, yielding similar improvements with GPT-4o.

Many program synthesis tasks prove too challenging for even state-of-the-art language models to solve in single attempts. Search-based evolutionary methods offer a promising alternative by exploring solution spaces iteratively, but their effectiveness remain limited by the fixed capabilities of the underlying generative model. We propose SOAR, a method that learns program synthesis by integrating language models into a self-improving evolutionary loop. SOAR alternates between (1) an evolutionary search that uses an LLM to sample and refine candidate solutions, and (2) a hindsight learning phase that converts search attempts into valid problem-solution pairs used to fine-tune the LLM's sampling and refinement capabilities\, -- \,enabling increasingly effective search in subsequent iterations. On the challenging ARC-AGI benchmark, SOAR achieves significant performance gains across model scales and iterations, leveraging positive transfer between the sampling and refinement finetuning tasks. These improvements carry over to test-time adaptation, enabling SOAR to solve 52\% of the public test set. Our code is open-sourced at: https://github.com/flowersteam/SOAR

Recent advancements in large language models have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling sequential, linearized exploration via long chain-of-thought (CoT) generation. However, this is not the only strategy for scaling test-time compute: parallel sampling with best-of-n selection provides an alternative that generates diverse solutions simultaneously. Despite the growing adoption of sequential search, its advantages over parallel sampling--especially under a fixed compute budget remain poorly understood. In this paper, we systematically compare these two approaches on two challenging reasoning tasks: CountDown and Sudoku. Surprisingly, we find that sequential search underperforms parallel sampling on CountDown but outperforms it on Sudoku, suggesting that backtracking is not universally beneficial. We identify two factors that can cause backtracking to degrade performance: (1) training on fixed search traces can lock models into suboptimal strategies, and (2) explicit CoT supervision can discourage "implicit" (non-verbalized) reasoning. Extending our analysis to reinforcement learning (RL), we show that models with backtracking capabilities benefit significantly from RL fine-tuning, while models without backtracking see limited, mixed gains. Together, these findings challenge the assumption that backtracking universally enhances LLM reasoning, instead revealing a complex interaction between task structure, training data, model scale, and learning paradigm.

Collecting ground truth task completion rewards or human demonstrations for multi-step reasoning tasks is often cost-prohibitive and time-consuming, especially in interactive domains like web tasks. To address this bottleneck, we present self-taught lookahead, a self-supervised method that leverages state-transition dynamics to train a value model capable of effectively guiding language model-controlled search. We find that moderately sized (8 billion parameters) open-weight value models improved with self-taught lookahead can match the performance of using a frontier LLM such as gpt-4o as the value model. Furthermore, we find that self-taught lookahead improves performance by 20% while reducing costs 37x compared to previous LLM-based tree search, without relying on ground truth rewards.

Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating proof search spaces. While the existing approaches primarily rely on value functions and Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Search (BFS) remains underexplored. This paper investigates whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM's policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a score of 71.31 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

Generative AI search is reshaping information retrieval by offering end-to-end answers to complex queries, reducing users' reliance on manually browsing and summarizing multiple web pages. However, while this paradigm enhances convenience, it disrupts the feedback-driven improvement loop that has historically powered the evolution of traditional Web search. Web search can continuously improve their ranking models by collecting large-scale, fine-grained user feedback (e.g., clicks, dwell time) at the document level. In contrast, generative AI search operates through a much longer search pipeline, spanning query decomposition, document retrieval, and answer generation, yet typically receives only coarse-grained feedback on the final answer. This introduces a feedback loop disconnect, where user feedback for the final output cannot be effectively mapped back to specific system components, making it difficult to improve each intermediate stage and sustain the feedback loop. In this paper, we envision NExT-Search, a next-generation paradigm designed to reintroduce fine-grained, process-level feedback into generative AI search. NExT-Search integrates two complementary modes: User Debug Mode, which allows engaged users to intervene at key stages; and Shadow User Mode, where a personalized user agent simulates user preferences and provides AI-assisted feedback for less interactive users. Furthermore, we envision how these feedback signals can be leveraged through online adaptation, which refines current search outputs in real-time, and offline update, which aggregates interaction logs to periodically fine-tune query decomposition, retrieval, and generation models. By restoring human control over key stages of the generative AI search pipeline, we believe NExT-Search offers a promising direction for building feedback-rich AI search systems that can evolve continuously alongside human feedback.

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.

Local graph clustering methods aim to detect small clusters in very large graphs without the need to process the whole graph. They are fundamental and scalable tools for a wide range of tasks such as local community detection, node ranking and node embedding. While prior work on local graph clustering mainly focuses on graphs without node attributes, modern real-world graph datasets typically come with node attributes that provide valuable additional information. We present a simple local graph clustering algorithm for graphs with node attributes, based on the idea of diffusing mass locally in the graph while accounting for both structural and attribute proximities. Using high-dimensional concentration results, we provide statistical guarantees on the performance of the algorithm for the recovery of a target cluster with a single seed node. We give conditions under which a target cluster generated from a fairly general contextual random graph model, which includes both the stochastic block model and the planted cluster model as special cases, can be fully recovered with bounded false positives. Empirically, we validate all theoretical claims using synthetic data, and we show that incorporating node attributes leads to superior local clustering performances using real-world graph datasets.

We introduce LOCORE, Long-Context Re-ranker, a model that takes as input local descriptors corresponding to an image query and a list of gallery images and outputs similarity scores between the query and each gallery image. This model is used for image retrieval, where typically a first ranking is performed with an efficient similarity measure, and then a shortlist of top-ranked images is re-ranked based on a more fine-grained similarity measure. Compared to existing methods that perform pair-wise similarity estimation with local descriptors or list-wise re-ranking with global descriptors, LOCORE is the first method to perform list-wise re-ranking with local descriptors. To achieve this, we leverage efficient long-context sequence models to effectively capture the dependencies between query and gallery images at the local-descriptor level. During testing, we process long shortlists with a sliding window strategy that is tailored to overcome the context size limitations of sequence models. Our approach achieves superior performance compared with other re-rankers on established image retrieval benchmarks of landmarks (ROxf and RPar), products (SOP), fashion items (In-Shop), and bird species (CUB-200) while having comparable latency to the pair-wise local descriptor re-rankers.

Optimizing GPU kernels is critical for efficient modern machine learning systems yet remains challenging due to the complex interplay of design factors and rapid hardware evolution. Existing automated approaches typically treat Large Language Models (LLMs) merely as stochastic code generators within heuristic-guided evolutionary loops. These methods often struggle with complex kernels requiring coordinated, multi-step structural transformations, as they lack explicit planning capabilities and frequently discard promising strategies due to inefficient or incorrect intermediate implementations. To address this, we propose Search via Co-Evolving World Model and build K-Search based on this method. By replacing static search heuristics with a co-evolving world model, our framework leverages LLMs' prior domain knowledge to guide the search, actively exploring the optimization space. This approach explicitly decouples high-level algorithmic planning from low-level program instantiation, enabling the system to navigate non-monotonic optimization paths while remaining resilient to temporary implementation defects. We evaluate K-Search on diverse, complex kernels from FlashInfer, including GQA, MLA, and MoE kernels. Our results show that K-Search significantly outperforms state-of-the-art evolutionary search methods, achieving an average 2.10x improvement and up to a 14.3x gain on complex MoE kernels. On the GPUMode TriMul task, K-Search achieves state-of-the-art performance on H100, reaching 1030us and surpassing both prior evolution and human-designed solutions.

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.

Deep research agents rely on iterative retrieval and reasoning to answer complex queries, but scaling test-time computation raises significant efficiency concerns. We study how to allocate reasoning budget in deep search pipelines, focusing on the role of listwise reranking. Using the BrowseComp-Plus benchmark, we analyze tradeoffs between model scale, reasoning effort, reranking depth, and total token cost via a novel effective token cost (ETC) metric. Our results show that reranking consistently improves retrieval and end-to-end accuracy, and that moderate reranking often yields larger gains than increasing search-time reasoning, achieving comparable accuracy at substantially lower cost. All our code is available at https://github.com/texttron/BrowseComp-Plus.git

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a 1{{sigma(mu^star)}}(1-e^{-{sigma(mu^star)}})-approximation of an optimal merge sequence, where {sigma(mu^star)} is the total backward curvature with respect to the optimal merge sequence mu^star. Empirically the lower bound of the approximation is approx 0.37. We provide a faster implementation of BPE which improves the runtime complexity from Oleft(N Mright) to Oleft(N log Mright), where N is the sequence length and M is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.

Embedding-based search is widely used in applications such as recommendation and retrieval-augmented generation (RAG). Recently, there is a growing demand to support these capabilities over personal data stored locally on devices. However, maintaining the necessary data structure associated with the embedding-based search is often infeasible due to its high storage overhead. For example, indexing 100 GB of raw data requires 150 to 700 GB of storage, making local deployment impractical. Reducing this overhead while maintaining search quality and latency becomes a critical challenge. In this paper, we present LEANN, a storage-efficient approximate nearest neighbor (ANN) search index optimized for resource-constrained personal devices. LEANN combines a compact graph-based structure with an efficient on-the-fly recomputation strategy to enable fast and accurate retrieval with minimal storage overhead. Our evaluation shows that LEANN reduces index size to under 5% of the original raw data, achieving up to 50 times smaller storage than standard indexes, while maintaining 90% top-3 recall in under 2 seconds on real-world question answering benchmarks.

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Although this tuning process can require large computational costs, recent work has shown that these costs can be reduced by line search methods that iteratively adjust the stepsize. We propose an alternative approach to stochastic line search by using a new algorithm based on forward step model building. This model building step incorporates second-order information that allows adjusting not only the stepsize but also the search direction. Noting that deep learning model parameters come in groups (layers of tensors), our method builds its model and calculates a new step for each parameter group. This novel diagonalization approach makes the selected step lengths adaptive. We provide convergence rate analysis, and experimentally show that the proposed algorithm achieves faster convergence and better generalization in well-known test problems. More precisely, SMB requires less tuning, and shows comparable performance to other adaptive methods.

Efficient k-nearest neighbor search is a fundamental task, foundational for many problems in NLP. When the similarity is measured by dot-product between dual-encoder vectors or ell_2-distance, there already exist many scalable and efficient search methods. But not so when similarity is measured by more accurate and expensive black-box neural similarity models, such as cross-encoders, which jointly encode the query and candidate neighbor. The cross-encoders' high computational cost typically limits their use to reranking candidates retrieved by a cheaper model, such as dual encoder or TF-IDF. However, the accuracy of such a two-stage approach is upper-bounded by the recall of the initial candidate set, and potentially requires additional training to align the auxiliary retrieval model with the cross-encoder model. In this paper, we present an approach that avoids the use of a dual-encoder for retrieval, relying solely on the cross-encoder. Retrieval is made efficient with CUR decomposition, a matrix decomposition approach that approximates all pairwise cross-encoder distances from a small subset of rows and columns of the distance matrix. Indexing items using our approach is computationally cheaper than training an auxiliary dual-encoder model through distillation. Empirically, for k > 10, our approach provides test-time recall-vs-computational cost trade-offs superior to the current widely-used methods that re-rank items retrieved using a dual-encoder or TF-IDF.

Discovering efficient algorithms for solving complex problems has been an outstanding challenge in mathematics and computer science, requiring substantial human expertise over the years. Recent advancements in evolutionary search with large language models (LLMs) have shown promise in accelerating the discovery of algorithms across various domains, particularly in mathematics and optimization. However, existing approaches treat the LLM as a static generator, missing the opportunity to update the model with the signal obtained from evolutionary exploration. In this work, we propose to augment LLM-based evolutionary search by continuously refining the search operator - the LLM - through reinforcement learning (RL) fine-tuning. Our method leverages evolutionary search as an exploration strategy to discover improved algorithms, while RL optimizes the LLM policy based on these discoveries. Our experiments on three combinatorial optimization tasks - bin packing, traveling salesman, and the flatpack problem - show that combining RL and evolutionary search improves discovery efficiency of improved algorithms, showcasing the potential of RL-enhanced evolutionary strategies to assist computer scientists and mathematicians for more efficient algorithm design.

The emergent abilities of large language models (LLMs) have demonstrated great potential in solving medical questions. They can possess considerable medical knowledge, but may still hallucinate and are inflexible in the knowledge updates. While Retrieval-Augmented Generation (RAG) has been proposed to enhance the medical question-answering capabilities of LLMs with external knowledge bases, it may still fail in complex cases where multiple rounds of information-seeking are required. To address such an issue, we propose iterative RAG for medicine (i-MedRAG), where LLMs can iteratively ask follow-up queries based on previous information-seeking attempts. In each iteration of i-MedRAG, the follow-up queries will be answered by a vanilla RAG system and they will be further used to guide the query generation in the next iteration. Our experiments show the improved performance of various LLMs brought by i-MedRAG compared with vanilla RAG on complex questions from clinical vignettes in the United States Medical Licensing Examination (USMLE), as well as various knowledge tests in the Massive Multitask Language Understanding (MMLU) dataset. Notably, our zero-shot i-MedRAG outperforms all existing prompt engineering and fine-tuning methods on GPT-3.5, achieving an accuracy of 69.68\% on the MedQA dataset. In addition, we characterize the scaling properties of i-MedRAG with different iterations of follow-up queries and different numbers of queries per iteration. Our case studies show that i-MedRAG can flexibly ask follow-up queries to form reasoning chains, providing an in-depth analysis of medical questions. To the best of our knowledge, this is the first-of-its-kind study on incorporating follow-up queries into medical RAG.

With increasing demands for efficiency, information retrieval has developed a branch of sparse retrieval, further advancing towards inference-free retrieval where the documents are encoded during indexing time and there is no model-inference for queries. Existing sparse retrieval models rely on FLOPS regularization for sparsification, while this mechanism was originally designed for Siamese encoders, it is considered to be suboptimal in inference-free scenarios which is asymmetric. Previous attempts to adapt FLOPS for inference-free scenarios have been limited to rule-based methods, leaving the potential of sparsification approaches for inference-free retrieval models largely unexplored. In this paper, we explore ell_0 inspired sparsification manner for inference-free retrievers. Through comprehensive out-of-domain evaluation on the BEIR benchmark, our method achieves state-of-the-art performance among inference-free sparse retrieval models and is comparable to leading Siamese sparse retrieval models. Furthermore, we provide insights into the trade-off between retrieval effectiveness and computational efficiency, demonstrating practical value for real-world applications.

Local stochastic gradient descent (Local-SGD), also referred to as federated averaging, is an approach to distributed optimization where each device performs more than one SGD update per communication. This work presents an empirical study of {\it asynchronous} Local-SGD for training language models; that is, each worker updates the global parameters as soon as it has finished its SGD steps. We conduct a comprehensive investigation by examining how worker hardware heterogeneity, model size, number of workers, and optimizer could impact the learning performance. We find that with naive implementations, asynchronous Local-SGD takes more iterations to converge than its synchronous counterpart despite updating the (global) model parameters more frequently. We identify momentum acceleration on the global parameters when worker gradients are stale as a key challenge. We propose a novel method that utilizes a delayed Nesterov momentum update and adjusts the workers' local training steps based on their computation speed. This approach, evaluated with models up to 150M parameters on the C4 dataset, matches the performance of synchronous Local-SGD in terms of perplexity per update step, and significantly surpasses it in terms of wall clock time.

State-of-the-art large language models (LLMs) exhibit impressive problem-solving capabilities but may struggle with complex reasoning and factual correctness. Existing methods harness the strengths of chain-of-thought and retrieval-augmented generation (RAG) to decompose a complex problem into simpler steps and apply retrieval to improve factual correctness. These methods work well on straightforward reasoning tasks but often falter on challenging tasks such as competitive programming and mathematics, due to frequent reasoning errors and irrelevant knowledge retrieval. To address this, we introduce Critic-guided planning with Retrieval-augmentation, CR-Planner, a novel framework that leverages fine-tuned critic models to guide both reasoning and retrieval processes through planning. CR-Planner solves a problem by iteratively selecting and executing sub-goals. Initially, it identifies the most promising sub-goal from reasoning, query generation, and retrieval, guided by rewards given by a critic model named sub-goal critic. It then executes this sub-goal through sampling and selecting the optimal output based on evaluations from another critic model named execution critic. This iterative process, informed by retrieved information and critic models, enables CR-Planner to effectively navigate the solution space towards the final answer. We employ Monte Carlo Tree Search to collect the data for training the critic models, allowing for a systematic exploration of action sequences and their long-term impacts. We validate CR-Planner on challenging domain-knowledge-intensive and reasoning-heavy tasks, including competitive programming, theorem-driven math reasoning, and complex domain retrieval problems. Our experiments demonstrate that CR-Planner significantly outperforms baselines, highlighting its effectiveness in addressing challenging problems by improving both reasoning and retrieval.

Tackling complex optimization problems often relies on expert-designed heuristics, typically crafted through extensive trial and error. Recent advances demonstrate that large language models (LLMs), when integrated into well-designed evolutionary search frameworks, can autonomously discover high-performing heuristics at a fraction of the traditional cost. However, existing approaches predominantly rely on verbal guidance, i.e., manipulating the prompt generation process, to steer the evolution of heuristics, without adapting the underlying LLM. We propose a hybrid framework that combines verbal and numerical guidance, the latter achieved by fine-tuning the LLM via reinforcement learning based on the quality of generated heuristics. This joint optimization allows the LLM to co-evolve with the search process. Our method outperforms state-of-the-art (SOTA) baselines across various optimization tasks, running locally on a single 24GB GPU using a 7B model with INT4 quantization. It surpasses methods that rely solely on verbal guidance, even when those use significantly more powerful API-based models.

Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pre-trained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pre-trained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamcl2r.

Large language models have made significant progress in complex but easy-to-verify problems, yet they still struggle with discovering the unknown. In this paper, we present AlphaResearch, an autonomous research agent designed to discover new algorithms on open-ended problems. To synergize the feasibility and innovation of the discovery process, we construct a novel dual research environment by combining the execution-based verify and simulated real-world peer review environment. AlphaResearch discovers new algorithm by iteratively running the following steps: (1) propose new ideas (2) verify the ideas in the dual research environment (3) optimize the research proposals for better performance. To promote a transparent evaluation process, we construct AlphaResearchComp, a new evaluation benchmark that includes an eight open-ended algorithmic problems competition, with each problem carefully curated and verified through executable pipelines, objective metrics, and reproducibility checks. AlphaResearch gets a 2/8 win rate in head-to-head comparison with human researchers, demonstrate the possibility of accelerating algorithm discovery with LLMs. Notably, the algorithm discovered by AlphaResearch on the ``packing circles'' problem achieves the best-of-known performance, surpassing the results of human researchers and strong baselines from recent work (e.g., AlphaEvolve). Additionally, we conduct a comprehensive analysis of the remaining challenges of the 6/8 failure cases, providing valuable insights for future research.

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting the search space to fixed heuristic forms. Such designs offer limited capacity for structural exploration, making it difficult to escape deep local optima in complex Combinatorial Optimization Problems (COPs). In this work, we propose G-LNS, a generative evolutionary framework that extends LLM-based AHD to the automated design of Large Neighborhood Search (LNS) operators. Unlike prior methods that evolve heuristics in isolation, G-LNS leverages LLMs to co-evolve tightly coupled pairs of destroy and repair operators. A cooperative evaluation mechanism explicitly captures their interaction, enabling the discovery of complementary operator logic that jointly performs effective structural disruption and reconstruction. Extensive experiments on challenging COP benchmarks, such as Traveling Salesman Problems (TSP) and Capacitated Vehicle Routing Problems (CVRP), demonstrate that G-LNS significantly outperforms LLM-based AHD methods as well as strong classical solvers. The discovered heuristics not only achieve near-optimal solutions with reduced computational budgets but also exhibit robust generalization across diverse and unseen instance distributions.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

Learned sparse retrieval systems aim to combine the effectiveness of contextualized language models with the scalability of conventional data structures such as inverted indexes. Nevertheless, the indexes generated by these systems exhibit significant deviations from the ones that use traditional retrieval models, leading to a discrepancy in the performance of existing query optimizations that were specifically developed for traditional structures. These disparities arise from structural variations in query and document statistics, including sub-word tokenization, leading to longer queries, smaller vocabularies, and different score distributions within posting lists. This paper introduces Block-Max Pruning (BMP), an innovative dynamic pruning strategy tailored for indexes arising in learned sparse retrieval environments. BMP employs a block filtering mechanism to divide the document space into small, consecutive document ranges, which are then aggregated and sorted on the fly, and fully processed only as necessary, guided by a defined safe early termination criterion or based on approximate retrieval requirements. Through rigorous experimentation, we show that BMP substantially outperforms existing dynamic pruning strategies, offering unparalleled efficiency in safe retrieval contexts and improved tradeoffs between precision and efficiency in approximate retrieval tasks.

We present a novel framework for training large language models with continuously adjustable internal representations that span the full spectrum from localist (interpretable, rule-based) to distributed (generalizable, efficient) encodings. The key innovations are (1) a locality dial, a tunable parameter that dynamically controls the degree of localization during both training and inference without requiring model retraining, (2) an information-theoretic recruitment mechanism that adaptively allocates semantic blocks as needed, eliminating the requirement for complete domain knowledge at initialization, and (3) a hierarchical recruitment framework that extends capacity allocation to entire specialized LLMs, enabling multi-granularity architectural adaptation. This is achieved through group sparsity penalties on attention mechanisms, information-theoretic anchor design, dynamic rule injection, and principled recruitment criteria based on penalized likelihood with explicit units. We provide rigorous mathematical results establishing explicit threshold conditions under which attention provably concentrates on semantically relevant blocks at stationary points, with exact bounds on attention entropy and pointer fidelity. The hierarchical recruitment mechanism provides convergence guarantees at both the block level (fine-grained, within-LLM) and the LLM level (coarse-grained, cross-domain), ensuring the system discovers semantic partitions that balance model complexity against data encoding efficiency. This framework enables practitioners to continuously interpolate between interpretable and high-performance modes while adapting architectural capacity at multiple granularities, supporting applications in regulated domains requiring both transparency and capability.

Graph-based Retrieval-Augmented Generation (GraphRAG) frameworks face a trade-off between the comprehensiveness of global search and the efficiency of local search. Existing methods are often challenged by navigating large-scale hierarchical graphs, optimizing retrieval paths, and balancing exploration-exploitation dynamics, frequently lacking robust multi-stage re-ranking. To overcome these deficits, we propose Deep GraphRAG, a framework designed for a balanced approach to hierarchical retrieval and adaptive integration. It introduces a hierarchical global-to-local retrieval strategy that integrates macroscopic inter-community and microscopic intra-community contextual relations. This strategy employs a three-stage process: (1) inter-community filtering, which prunes the search space using local context; (2) community-level refinement, which prioritizes relevant subgraphs via entity-interaction analysis; and (3) entity-level fine-grained search within target communities. A beam search-optimized dynamic re-ranking module guides this process, continuously filtering candidates to balance efficiency and global comprehensiveness. Deep GraphRAG also features a Knowledge Integration Module leveraging a compact LLM, trained with Dynamic Weighting Reward GRPO (DW-GRPO). This novel reinforcement learning approach dynamically adjusts reward weights to balance three key objectives: relevance, faithfulness, and conciseness. This training enables compact models (1.5B) to approach the performance of large models (70B) in the integration task. Evaluations on Natural Questions and HotpotQA demonstrate that Deep GraphRAG significantly outperforms baseline graph retrieval methods in both accuracy and efficiency.

Compatible features enable the direct comparison of old and new learned features allowing to use them interchangeably over time. In visual search systems, this eliminates the need to extract new features from the gallery-set when the representation model is upgraded with novel data. This has a big value in real applications as re-indexing the gallery-set can be computationally expensive when the gallery-set is large, or even infeasible due to privacy or other concerns of the application. In this paper, we propose CoReS, a new training procedure to learn representations that are compatible with those previously learned, grounding on the stationarity of the features as provided by fixed classifiers based on polytopes. With this solution, classes are maximally separated in the representation space and maintain their spatial configuration stationary as new classes are added, so that there is no need to learn any mappings between representations nor to impose pairwise training with the previously learned model. We demonstrate that our training procedure largely outperforms the current state of the art and is particularly effective in the case of multiple upgrades of the training-set, which is the typical case in real applications.

This paper presents a parallel random-search method for reducing additive complexity in fast matrix multiplication. The approach replaces expensive exact evaluation with fast heuristic scoring, including the new Greedy-Intersections strategy. The method runs many independent common subexpression elimination processes in parallel, exploring the search space through random pair substitutions and diverse selection strategies while sharing promising partial solutions. Tested on 164 ternary-coefficient schemes, the method achieves lower addition counts than the state-of-the-art Greedy-Potential on 103 schemes, matches it on 59, and is outperformed on 2. For most schemes, it gives equal or better results while being much faster, making it practical for algorithm exploration. All software and results are open source.