arXiv subjects

Yixin Cao

Publications and source records attributed to Yixin Cao.

At least 73 records · Page 4Linked to original sources

arXiv2025

CriticLean: Critic-Guided Reinforcement Learning for Mathematical Formalization

Translating natural language mathematical statements into formal, executable code is a fundamental challenge in automated theorem proving. While prior work has focused on generation and compilation success, little attention has been paid to the critic phase-the evaluation of whether generated formalizations truly capture the semantic intent of the original problem. In this paper, we introduce CriticLean, a novel critic-guided reinforcement learning framework that elevates the role of the critic from a passive validator to an active learning component. Specifically, first, we propose the CriticLeanGPT, trained via supervised fine-tuning and reinforcement learning, to rigorously assess the semantic fidelity of Lean 4 formalizations. Then, we introduce CriticLeanBench, a benchmark designed to measure models' ability to distinguish semantically correct from incorrect formalizations, and demonstrate that our trained CriticLeanGPT models can significantly outperform strong open- and closed-source baselines. Building on the CriticLean framework, we construct FineLeanCorpus, a dataset comprising over 285K problems that exhibits rich domain diversity, broad difficulty coverage, and high correctness based on human evaluation. Overall, our findings highlight that optimizing the critic phase is essential for producing reliable formalizations, and we hope our CriticLean will provide valuable insights for future advances in formal mathematical reasoning.

cs.CL↗

arXiv2025

S^3cMath: Spontaneous Step-level Self-correction Makes Large Language Models Better Mathematical Reasoners

Self-correction is a novel method that can stimulate the potential reasoning abilities of large language models (LLMs). It involves detecting and correcting errors during the inference process when LLMs solve reasoning problems. However, recent works do not regard self-correction as a spontaneous and intrinsic capability of LLMs. Instead, such correction is achieved through post-hoc generation, external knowledge introduction, multi-model collaboration, and similar techniques. In this paper, we propose a series of mathematical LLMs called S$^3$c-Math, which are able to perform Spontaneous Step-level Self-correction for Mathematical reasoning. This capability helps LLMs to recognize whether their ongoing inference tends to contain errors and simultaneously correct these errors to produce a more reliable response. We proposed a method, which employs a step-level sampling approach to construct step-wise self-correction data for achieving such ability. Additionally, we implement a training strategy that uses above constructed data to equip LLMs with spontaneous step-level self-correction capacities. Our data and methods have been demonstrated to be effective across various foundation LLMs, consistently showing significant progress in evaluations on GSM8K, MATH, and other mathematical benchmarks. To the best of our knowledge, we are the first to introduce the spontaneous step-level self-correction ability of LLMs in mathematical reasoning.

cs.CL↗

arXiv2025

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs

This paper explores the challenges of test-time scaling of large language models (LLMs), regarding both the data and inference efficiency. We highlight the diversity of multi-lingual reasoning based on our pilot studies, and then introduce a novel approach, $L^2$ multi-lingual unification learning with a decoding intervention strategy for further investigation. The basic idea of $L^2$ is that the reasoning process varies across different languages, which may be mutually beneficial to enhance both model performance and efficiency. In specific, there are two types of multi-lingual data: the entire long chain-of-thought annotations in different languages and the step-wise mixture of languages. By further tuning based on them, we show that even small amounts of data can significantly improve reasoning capabilities. Our findings suggest that multilingual learning reduces both the required data and the number of inference tokens while maintaining a comparable performance. Furthermore, $L^2$ is orthogonal to other data efficient methods. Thus, we also emphasize the importance of diverse data selection. The $L^2$ method offers a promising solution to the challenges of data collection and test-time compute efficiency in LLMs.

cs.CL↗

arXiv2025

Com$^2$: A Causal-Guided Benchmark for Exploring Complex Commonsense Reasoning in Large Language Models

Large language models (LLMs) have mastered abundant simple and explicit commonsense knowledge through pre-training, enabling them to achieve human-like performance in simple commonsense reasoning. Nevertheless, LLMs struggle to reason with complex and implicit commonsense knowledge that is derived from simple ones (such as understanding the long-term effects of certain events), an aspect humans tend to focus on more. Existing works focus on complex tasks like math and code, while complex commonsense reasoning remains underexplored due to its uncertainty and lack of structure. To fill this gap and align with real-world concerns, we propose a benchmark Com$^2$ focusing on complex commonsense reasoning. We first incorporate causal event graphs to serve as structured complex commonsense. Then we adopt causal theory~(e.g., intervention) to modify the causal event graphs and obtain different scenarios that meet human concerns. Finally, an LLM is employed to synthesize examples with slow thinking, which is guided by the logical relationships in the modified causal graphs. Furthermore, we use detective stories to construct a more challenging subset. Experiments show that LLMs struggle in reasoning depth and breadth, while post-training and slow thinking can alleviate this. The code and data are available at https://github.com/Waste-Wood/Com2.

cs.CL↗

arXiv2025

Towards Storage-Efficient Visual Document Retrieval: An Empirical Study on Reducing Patch-Level Embeddings

Despite the strong performance of ColPali/ColQwen2 in Visualized Document Retrieval (VDR), it encodes each page into multiple patch-level embeddings and leads to excessive memory usage. This empirical study investigates methods to reduce patch embeddings per page at minimum performance degradation. We evaluate two token-reduction strategies: token pruning and token merging. Regarding token pruning, we surprisingly observe that a simple random strategy outperforms other sophisticated pruning methods, though still far from satisfactory. Further analysis reveals that pruning is inherently unsuitable for VDR as it requires removing certain page embeddings without query-specific information. Turning to token merging (more suitable for VDR), we search for the optimal combinations of merging strategy across three dimensions and develop Light-ColPali/ColQwen2. It maintains 98.2% of retrieval performance with only 11.8% of original memory usage, and preserves 94.6% effectiveness at 2.8% memory footprint. We expect our empirical findings and resulting Light-ColPali/ColQwen2 offer valuable insights and establish a competitive baseline for future research towards efficient VDR.

cs.IR↗

arXiv2025

Long or short CoT? Investigating Instance-level Switch of Large Reasoning Models

With the rapid advancement of large reasoning models, long Chain-of-Thought (CoT) prompting has demonstrated strong performance on complex tasks. However, this often comes with a significant increase in token usage. In this paper, we conduct a comprehensive empirical analysis comparing long and short CoT strategies. Our findings reveal that while long CoT can lead to performance improvements, its benefits are often marginal relative to its significantly higher token consumption. Specifically, long CoT tends to outperform when ample generation budgets are available, whereas short CoT is more effective under tighter budget constraints. These insights underscore the need for a dynamic approach that selects the proper CoT strategy based on task context and resource availability. To address this, we propose SwitchCoT, an automatic framework that adaptively chooses between long and short CoT strategies to balance reasoning accuracy and computational efficiency. Moreover, SwitchCoT is designed to be budget-aware, making it broadly applicable across scenarios with varying resource constraints. Experimental results demonstrate that SwitchCoT can reduce inference costs by up to 50% while maintaining high accuracy. Notably, under limited token budgets, it achieves performance comparable to, or even exceeding, that of using either long or short CoT alone.

cs.CL↗

arXiv2025

Knowledge Graph Completion by Intermediate Variables Regularization

Knowledge graph completion (KGC) can be framed as a 3-order binary tensor completion task. Tensor decomposition-based (TDB) models have demonstrated strong performance in KGC. In this paper, we provide a summary of existing TDB models and derive a general form for them, serving as a foundation for further exploration of TDB models. Despite the expressiveness of TDB models, they are prone to overfitting. Existing regularization methods merely minimize the norms of embeddings to regularize the model, leading to suboptimal performance. Therefore, we propose a novel regularization method for TDB models that addresses this limitation. The regularization is applicable to most TDB models and ensures tractable computation. Our method minimizes the norms of intermediate variables involved in the different ways of computing the predicted tensor. To support our regularization method, we provide a theoretical analysis that proves its effect in promoting low trace norm of the predicted tensor to reduce overfitting. Finally, we conduct experiments to verify the effectiveness of our regularization technique as well as the reliability of our theoretical analysis. The code is available at https://github.com/changyi7231/IVR.

cs.LG↗

arXiv2025

BNPO: Beta Normalization Policy Optimization

Recent studies, including DeepSeek-R1 and Kimi-k1.5, have demonstrated that reinforcement learning with rule-based, binary-valued reward functions can significantly enhance the reasoning capabilities of large language models. These models primarily utilize REINFORCE-based policy optimization techniques, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation remains: current policy optimization methods either neglect reward normalization or employ static normalization strategies, which fail to adapt to the dynamic nature of policy updates during training. This may result in unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel policy optimization method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. BNPO aligns the normalization with the changing policy distribution, enabling more precise and lower-variance gradient estimation, which in turn promotes stable training dynamics. We provide theoretical analysis demonstrating BNPO's variance-reducing properties and show that it generalizes both REINFORCE and GRPO under binary-valued reward settings. Furthermore, we introduce an advantage decomposition mechanism to extend BNPO's applicability to more complex reward systems. Experimental results confirm that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks. The code is available at https://github.com/changyi7231/BNPO.

cs.LG↗

arXiv2025

Disentangling Language and Culture for Evaluating Multilingual Large Language Models

This paper introduces a Dual Evaluation Framework to comprehensively assess the multilingual capabilities of LLMs. By decomposing the evaluation along the dimensions of linguistic medium and cultural context, this framework enables a nuanced analysis of LLMs' ability to process questions within both native and cross-cultural contexts cross-lingually. Extensive evaluations are conducted on a wide range of models, revealing a notable "CulturalLinguistic Synergy" phenomenon, where models exhibit better performance when questions are culturally aligned with the language. This phenomenon is further explored through interpretability probing, which shows that a higher proportion of specific neurons are activated in a language's cultural context. This activation proportion could serve as a potential indicator for evaluating multilingual performance during model training. Our findings challenge the prevailing notion that LLMs, primarily trained on English data, perform uniformly across languages and highlight the necessity of culturally and linguistically model evaluations. Our code can be found at https://yingjiahao14. github.io/Dual-Evaluation/.

cs.CL↗

arXiv2025

Model Utility Law: Evaluating LLMs beyond Performance through Mechanism Interpretable Metric

Large Language Models (LLMs) have become indispensable across academia, industry, and daily applications, yet current evaluation methods struggle to keep pace with their rapid development. One core challenge of evaluation in the large language model (LLM) era is the generalization issue: how to infer a model's near-unbounded abilities from inevitably bounded benchmarks. We address this challenge by proposing Model Utilization Index (MUI), a mechanism interpretability enhanced metric that complements traditional performance scores. MUI quantifies the effort a model expends on a task, defined as the proportion of activated neurons or features during inference. Intuitively, a truly capable model should achieve higher performance with lower effort. Extensive experiments across popular LLMs reveal a consistent inverse logarithmic relationship between MUI and performance, which we formulate as the Utility Law. From this law we derive four practical corollaries that (i) guide training diagnostics, (ii) expose data contamination issue, (iii) enable fairer model comparisons, and (iv) design model-specific dataset diversity. Our code can be found at https://github.com/ALEX-nlp/MUI-Eva.

cs.CL↗

arXiv2025

Teach2Eval: An Indirect Evaluation Method for LLM by Judging How It Teaches

Recent progress in large language models (LLMs) has outpaced the development of effective evaluation methods. Traditional benchmarks rely on task-specific metrics and static datasets, which often suffer from fairness issues, limited scalability, and contamination risks. In this paper, we introduce Teach2Eval, an indirect evaluation framework inspired by the Feynman Technique. Instead of directly testing LLMs on predefined tasks, our method evaluates a model's multiple abilities to teach weaker student models to perform tasks effectively. By converting open-ended tasks into standardized multiple-choice questions (MCQs) through teacher-generated feedback, Teach2Eval enables scalable, automated, and multi-dimensional assessment. Our approach not only avoids data leakage and memorization but also captures a broad range of cognitive abilities that are orthogonal to current benchmarks. Experimental results across 26 leading LLMs show strong alignment with existing human and model-based dynamic rankings, while offering additional interpretability for training guidance.

cs.CL↗

arXiv2025

Characterization of Circular-arc Graphs: II. McConnell Flipping

McConnell [FOCS 2001] presented a flipping transformation from circular-arc graphs to interval graphs with certain patterns of representations. Beyond its algorithmic implications, this transformation is instrumental in identifying all minimal graphs that are not circular-arc graphs. We conduct a structural study of this transformation, and for $C_{4}$-free graphs, we achieve a complete characterization of these patterns. This characterization allows us, among other things, to identify all minimal chordal graphs that are not circular-arc graphs in a companion paper.

math.CO↗

arXiv2025

Toward Generalizable Evaluation in the LLM Era: A Survey Beyond Benchmarks

Large Language Models (LLMs) are advancing at an amazing speed and have become indispensable across academia, industry, and daily applications. To keep pace with the status quo, this survey probes the core challenges that the rise of LLMs poses for evaluation. We identify and analyze two pivotal transitions: (i) from task-specific to capability-based evaluation, which reorganizes benchmarks around core competencies such as knowledge, reasoning, instruction following, multi-modal understanding, and safety; and (ii) from manual to automated evaluation, encompassing dynamic dataset curation and "LLM-as-a-judge" scoring. Yet, even with these transitions, a crucial obstacle persists: the evaluation generalization issue. Bounded test sets cannot scale alongside models whose abilities grow seemingly without limit. We will dissect this issue, along with the core challenges of the above two transitions, from the perspectives of methods, datasets, evaluators, and metrics. Due to the fast evolving of this field, we will maintain a living GitHub repository (links are in each section) to crowd-source updates and corrections, and warmly invite contributors and collaborators.

cs.CL↗

arXiv2025

Precise Localization of Memories: A Fine-grained Neuron-level Knowledge Editing Technique for LLMs

Knowledge editing aims to update outdated information in Large Language Models (LLMs). A representative line of study is locate-then-edit methods, which typically employ causal tracing to identify the modules responsible for recalling factual knowledge about entities. However, we find these methods are often sensitive only to changes in the subject entity, leaving them less effective at adapting to changes in relations. This limitation results in poor editing locality, which can lead to the persistence of irrelevant or inaccurate facts, ultimately compromising the reliability of LLMs. We believe this issue arises from the insufficient precision of knowledge localization. To address this, we propose a Fine-grained Neuron-level Knowledge Editing (FiNE) method that enhances editing locality without affecting overall success rates. By precisely identifying and modifying specific neurons within feed-forward networks, FiNE significantly improves knowledge localization and editing. Quantitative experiments demonstrate that FiNE efficiently achieves better overall performance compared to existing techniques, providing new insights into the localization and modification of knowledge within LLMs.

cs.CL↗

arXiv2025

Characterization of Chordal Circular-arc Graphs: I. Split Graphs

The most elusive problem around the class of circular-arc graphs is identifying all minimal graphs that are not in this class. The main obstacle is the lack of a systematic way of enumerating these minimal graphs. McConnell [FOCS 2001] presented a transformation from circular-arc graphs to interval graphs with certain patterns of representations. We fully characterize these interval patterns for circular-arc graphs that are split graphs, thereby building a connection between minimal split graphs that are not circular-arc graphs and minimal non-interval graphs. This connection enables us to identify all minimal split graphs that are not circular-arc graphs. As a byproduct, we develop a linear-time certifying recognition algorithm for circular-arc graphs when the input is a split graph.

math.CO↗

arXiv2025

Characterization of Circular-arc Graphs: III. Chordal Graphs

We identify all minimal chordal graphs that are not circular-arc graphs, thereby resolving one of ``the main open problems'' concerning the structures of circular-arc graphs as posed by Dur{á}n, Grippo, and Safe in 2011. The problem had been attempted even earlier, and previous efforts have yielded partial results, particularly for claw-free graphs and graphs with an independence number of at most four. The answers turn out to have very simple structures: all the nontrivial ones belong to a single family. Our findings are based on a structural study of McConnell's flipping, which transforms circular-arc graphs into interval graphs with certain representation patterns.

math.CO↗

arXiv2025

PairJudge RM: Perform Best-of-N Sampling with Knockout Tournament

Best-of-N (BoN) sampling, a common strategy for test-time scaling of Large Language Models (LLMs), relies on reward models to select the best candidate solution from multiple generations. However, traditional reward models often assign arbitrary and inconsistent scores, limiting their effectiveness. To address this, we propose a Pairwise Judge Reward Model (PariJudge RM) combined with a knockout tournament for BoN sampling. Instead of assigning absolute scores, given one math problem, PariJudge RM judges two candidate solutions' correctness with chain-of-thought reasoning simultaneously. This approach eliminates the need for scoring and enables cross-validation of solutions through parallel judgment. In the knockout tournament, PariJudge RM conducts pairwise Judgment between candidate solutions and eliminates the incorrect ones iteratively. We construct PairJudge-432K, a large-scale dataset of 432K pairwise judgments derived from NumiaMath and annotated using \texttt{gemini-1.5-flash}, and train the PariJudge RM via supervised fine-tuning. Experiments on MATH-500 and the Olympiad Bench demonstrate significant improvements over baseline reward models. And a 40\% to 60\% relative improvement is achieved on the top 50\% challenging problems.

cs.CL↗

arXiv2024

Long Context vs. RAG for LLMs: An Evaluation and Revisits

Extending context windows (i.e., Long Context, LC) and using retrievers to selectively access relevant information (i.e., Retrieval-Augmented Generation, RAG) are the two main strategies to enable LLMs to incorporate extremely long external contexts. This paper revisits recent studies on this topic, highlighting their key insights and discrepancies. We then provide a more comprehensive evaluation by filtering out questions answerable without external context, identifying the most effective retrieval methods, and expanding the datasets. We show that LC generally outperforms RAG in question-answering benchmarks, especially for Wikipedia-based questions. Summarization-based retrieval performs comparably to LC, while chunk-based retrieval lags behind. However, RAG has advantages in dialogue-based and general question queries. These insights underscore the trade-offs between RAG and LC strategies, offering guidance for future optimization of LLMs with external knowledge sources. We also provide an in-depth discussion on this topic, highlighting the overlooked importance of context relevance in existing studies.

cs.CL↗