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Dec 26

ProofBridge: Auto-Formalization of Natural Language Proofs in Lean via Joint Embeddings

Translating human-written mathematical theorems and proofs from natural language (NL) into formal languages (FLs) like Lean 4 has long been a significant challenge for AI. Most state-of-the-art methods address this separately, first translating theorems and then generating proofs, creating a fundamental disconnect vis-a-vis true proof auto-formalization. This two-step process and its limitations were evident even in AlphaProof's silver-medal performance at the 2024 IMO, where problem statements needed manual translation before automated proof synthesis. We present ProofBridge, a unified framework for automatically translating entire NL theorems and proofs into Lean 4. At its core is a joint embedding model that aligns NL and FL (NL-FL) theorem-proof pairs in a shared semantic space, enabling cross-modal retrieval of semantically relevant FL examples to guide translation. Our training ensures that NL-FL theorems (and their proofs) are mapped close together in this space if and only if the NL-FL pairs are semantically equivalent. ProofBridge integrates retrieval-augmented fine-tuning with iterative proof repair, leveraging Lean's type checker and semantic equivalence feedback to ensure both syntactic correctness and semantic fidelity. Experiments show substantial improvements in proof auto-formalization over strong baselines (including GPT-5, Gemini-2.5, Kimina-Prover, DeepSeek-Prover), with our retrieval-augmented approach yielding significant gains in semantic correctness (SC, via proving bi-directional equivalence) and type correctness (TC, via type-checking theorem+proof) across pass@k metrics on miniF2F-Test-PF, a dataset we curated. In particular, ProofBridge improves cross-modal retrieval quality by up to 3.28x Recall@1 over all-MiniLM-L6-v2, and achieves +31.14% SC and +1.64% TC (pass@32) compared to the baseline Kimina-Prover-RL-1.7B.

  • 6 authors
·
Oct 17 1

Better Fit: Accommodate Variations in Clothing Types for Virtual Try-on

Image-based virtual try-on aims to transfer target in-shop clothing to a dressed model image, the objectives of which are totally taking off original clothing while preserving the contents outside of the try-on area, naturally wearing target clothing and correctly inpainting the gap between target clothing and original clothing. Tremendous efforts have been made to facilitate this popular research area, but cannot keep the type of target clothing with the try-on area affected by original clothing. In this paper, we focus on the unpaired virtual try-on situation where target clothing and original clothing on the model are different, i.e., the practical scenario. To break the correlation between the try-on area and the original clothing and make the model learn the correct information to inpaint, we propose an adaptive mask training paradigm that dynamically adjusts training masks. It not only improves the alignment and fit of clothing but also significantly enhances the fidelity of virtual try-on experience. Furthermore, we for the first time propose two metrics for unpaired try-on evaluation, the Semantic-Densepose-Ratio (SDR) and Skeleton-LPIPS (S-LPIPS), to evaluate the correctness of clothing type and the accuracy of clothing texture. For unpaired try-on validation, we construct a comprehensive cross-try-on benchmark (Cross-27) with distinctive clothing items and model physiques, covering a broad try-on scenarios. Experiments demonstrate the effectiveness of the proposed methods, contributing to the advancement of virtual try-on technology and offering new insights and tools for future research in the field. The code, model and benchmark will be publicly released.

  • 6 authors
·
Mar 13, 2024

ProJudge: A Multi-Modal Multi-Discipline Benchmark and Instruction-Tuning Dataset for MLLM-based Process Judges

As multi-modal large language models (MLLMs) frequently exhibit errors when solving scientific problems, evaluating the validity of their reasoning processes is critical for ensuring reliability and uncovering fine-grained model weaknesses. Since human evaluation is laborious and costly, prompting MLLMs as automated process judges has become a common practice. However, the reliability of these model-based judges remains uncertain. To address this, we introduce ProJudgeBench, the first comprehensive benchmark specifically designed for evaluating abilities of MLLM-based process judges. ProJudgeBench comprises 2,400 test cases and 50,118 step-level labels, spanning four scientific disciplines with diverse difficulty levels and multi-modal content. In ProJudgeBench, each step is meticulously annotated by human experts for correctness, error type, and explanation, enabling a systematic evaluation of judges' capabilities to detect, classify and diagnose errors. Evaluation on ProJudgeBench reveals a significant performance gap between open-source and proprietary models. To bridge this gap, we further propose ProJudge-173k, a large-scale instruction-tuning dataset, and a Dynamic Dual-Phase fine-tuning strategy that encourages models to explicitly reason through problem-solving before assessing solutions. Both contributions significantly enhance the process evaluation capabilities of open-source models. All the resources will be released to foster future research of reliable multi-modal process evaluation.