Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This survey examines the development of mathematical reasoning abilities in LLMs through two high-level cognitive phases: comprehension, where models gain mathematical understanding via diverse pretraining strategies, and answer generation, which has progressed from direct prediction to step-by-step Chain-of-Thought (CoT) reasoning. We review methods for enhancing mathematical reasoning, ranging from training-free prompting to fine-tuning approaches such as supervised fine-tuning and reinforcement learning, and discuss recent work on extended CoT and "test-time scaling". Despite notable progress, fundamental challenges remain in terms of capacity, efficiency, and generalization. To address these issues, we highlight promising research directions, including advanced pretraining and knowledge augmentation techniques, formal reasoning frameworks, and meta-generalization through principled learning paradigms. This survey tries to provide some insights for researchers interested in enhancing reasoning capabilities of LLMs and for those seeking to apply these techniques to other domains.

Most existing structured pruning methods for Large Language Models (LLMs) require substantial computational and data resources for retraining to reestablish the corrupted correlations, making them prohibitively expensive. To address this, we propose a pruning framework for LLMs called Orthogonal decomposition and Linear Calibration (Olica), which eliminates the need for retraining. A key observation is that the multi-head attention (MHA) layer depends on two types of matrix products. By treating these matrix products as unified entities and applying principal component analysis (PCA), we extract the most important information to compress LLMs without sacrificing accuracy or disrupting their original structure. Consequently, retraining becomes unnecessary. A fast decomposition method is devised, reducing the complexity of PCA by a factor of the square of the number of attention heads. Additionally, to mitigate error accumulation problem caused by pruning the feed-forward network (FFN) layer, we introduce a linear calibration method to reconstruct the residual errors of pruned layers using low-rank matrices. By leveraging singular value decomposition (SVD) on the solution of the least-squares problem, these matrices are obtained without requiring retraining. Extensive experiments show that the proposed Olica is efficient in terms of data usage, GPU memory, and running time, while delivering superior performance across multiple benchmarks.

As large language models (LLMs) continue to advance, there is a growing urgency to enhance the interpretability of their internal knowledge mechanisms. Consequently, many interpretation methods have emerged, aiming to unravel the knowledge mechanisms of LLMs from various perspectives. However, current interpretation methods differ in input data formats and interpreting outputs. The tools integrating these methods are only capable of supporting tasks with specific inputs, significantly constraining their practical applications. To address these challenges, we present an open-source Knowledge Mechanisms Revealer&Interpreter (Know-MRI) designed to analyze the knowledge mechanisms within LLMs systematically. Specifically, we have developed an extensible core module that can automatically match different input data with interpretation methods and consolidate the interpreting outputs. It enables users to freely choose appropriate interpretation methods based on the inputs, making it easier to comprehensively diagnose the model's internal knowledge mechanisms from multiple perspectives. Our code is available at https://github.com/nlpkeg/Know-MRI. We also provide a demonstration video on https://youtu.be/NVWZABJ43Bs.

Leveraging more test-time computation has proven to be an effective way to boost the reasoning capabilities of large language models (LLMs). Among various methods, the verify-and-improve paradigm stands out for enabling dynamic solution exploration and feedback incorporation. However, existing approaches often suffer from restricted feedback spaces and lack of coordinated training of different parties, leading to suboptimal performance. To address this, we model this multi-turn refinement process as a Markov Decision Process and introduce DPSDP (Direct Policy Search by Dynamic Programming), a reinforcement learning algorithm that trains an actor-critic LLM system to iteratively refine answers via direct preference learning on self-generated data. Theoretically, DPSDP can match the performance of any policy within the training distribution. Empirically, we instantiate DPSDP with various base models and show improvements on both in- and out-of-distribution benchmarks. For example, on benchmark MATH 500, majority voting over five refinement steps increases first-turn accuracy from 58.2% to 63.2% with Ministral-based models. An ablation study further confirms the benefits of multi-agent collaboration and out-of-distribution generalization.

Deep speech classification tasks, including keyword spotting and speaker verification, are vital in speech-based human-computer interaction. Recently, the security of these technologies has been revealed to be susceptible to backdoor attacks. Specifically, attackers use noisy disruption triggers and speech element triggers to produce poisoned speech samples that train models to become vulnerable. However, these methods typically create only a limited number of backdoors due to the inherent constraints of the trigger function. In this paper, we propose that speech backdoor attacks can strategically focus on speech elements such as timbre and emotion, leveraging the Speech Large Language Model (SLLM) to generate diverse triggers. Increasing the number of triggers may disproportionately elevate the poisoning rate, resulting in higher attack costs and a lower success rate per trigger. We introduce the Multiple Gradient Descent Algorithm (MGDA) as a mitigation strategy to address this challenge. The proposed attack is called the Speech Prompt Backdoor Attack (SPBA). Building on this foundation, we conducted attack experiments on two speech classification tasks, demonstrating that SPBA shows significant trigger effectiveness and achieves exceptional performance in attack metrics.

We present LeanTutor, a Large Language Model (LLM)-based tutoring system for math proofs. LeanTutor interacts with the student in natural language, formally verifies student-written math proofs in Lean, generates correct next steps, and provides the appropriate instructional guidance. LeanTutor is composed of three modules: (i) an autoformalizer/proof-checker, (ii) a next-step generator, and (iii) a natural language feedback generator. The first module faithfully autoformalizes student proofs into Lean and verifies proof accuracy via successful code compilation. If the proof has an error, the incorrect step is identified. The next-step generator module outputs a valid next Lean tactic for incorrect proofs via LLM-based candidate generation and proof search. The feedback generator module leverages Lean data to produce a pedagogically-motivated natural language hint for the student user. To evaluate our system, we introduce PeanoBench, a human-written dataset derived from the Natural Numbers Game, consisting of 371 Peano Arithmetic proofs, where each natural language proof step is paired with the corresponding logically equivalent tactic in Lean. The Autoformalizer correctly formalizes 57% of tactics in correct proofs and accurately identifies the incorrect step in 30% of incorrect proofs. In generating natural language hints for erroneous proofs, LeanTutor outperforms a simple baseline on accuracy and relevance metrics.

With the advent of large language models (LLMs), software engineering agents (SWE agents) have emerged as a powerful paradigm for automating a range of software tasks -- from code generation and repair to test case synthesis. These agents operate autonomously by interpreting user input and responding to environmental feedback. While various agent architectures have demonstrated strong empirical performance, the internal decision-making worfklows that drive their behavior remain poorly understood. Deeper insight into these workflows hold promise for improving both agent reliability and efficiency. In this work, we present the first systematic study of SWE agent behavior through the lens of execution traces. Our contributions are as follows: (1) we propose the first taxonomy of decision-making pathways across five representative agents; (2) using this taxonomy, we identify three core components essential to agent success -- bug localization, patch generation, and reproduction test generation -- and study each in depth; (3) we study the impact of test generation on successful patch production; and analyze strategies that can lead to successful test generation; (4) we further conduct the first large-scale code clone analysis comparing agent-generated and developer-written patches and provide a qualitative study revealing structural and stylistic differences in patch content. Together, these findings offer novel insights into agent design and open avenues for building agents that are both more effective and more aligned with human development practices.

Large language models (LLMs) use data to learn about the world in order to produce meaningful correlations and predictions. As such, the nature, scale, quality, and diversity of the datasets used to train these models, or to support their work at inference time, have a direct impact on their quality. The rapid development and adoption of LLMs of varying quality has brought into focus the scarcity of publicly available, high-quality training data and revealed an urgent need to ground the stewardship of these datasets in sustainable practices with clear provenance chains. To that end, this technical report introduces Institutional Books 1.0, a large collection of public domain books originally digitized through Harvard Library's participation in the Google Books project, beginning in 2006. Working with Harvard Library, we extracted, analyzed, and processed these volumes into an extensively-documented dataset of historic texts. This analysis covers the entirety of Harvard Library's collection scanned as part of that project, originally spanning 1,075,899 volumes written in over 250 different languages for a total of approximately 250 billion tokens. As part of this initial release, the OCR-extracted text (original and post-processed) as well as the metadata (bibliographic, source, and generated) of the 983,004 volumes, or 242B tokens, identified as being in the public domain have been made available. This report describes this project's goals and methods as well as the results of the analyses we performed, all in service of making this historical collection more accessible and easier for humans and machines alike to filter, read and use.

While existing benchmarks probe the reasoning abilities of large language models (LLMs) across diverse domains, they predominantly assess passive reasoning, providing models with all the information needed to reach a solution. By contrast, active reasoning-where an LLM must interact with external systems to acquire missing evidence or data-has received little systematic attention. To address this shortfall, we present AR-Bench, a novel benchmark designed explicitly to evaluate an LLM's active reasoning skills. AR-Bench comprises three task families-detective cases, situation puzzles, and guessing numbers-that together simulate real-world, agentic scenarios and measure performance across commonsense, logical, and symbolic reasoning challenges. Empirical evaluation on AR-Bench demonstrates that contemporary LLMs exhibit pronounced difficulties with active reasoning: they frequently fail to acquire or leverage the information needed to solve tasks. This gap highlights a stark divergence between their passive and active reasoning abilities. Moreover, ablation studies indicate that even advanced strategies, such as tree-based searching or post-training approaches, yield only modest gains and fall short of the levels required for real-world deployment. Collectively, these findings highlight the critical need to advance methodology for active reasoning, e.g., incorporating interactive learning, real-time feedback loops, and environment-aware objectives for training. The benchmark is publicly available at: https://github.com/tmlr-group/AR-Bench.

From professional filmmaking to user-generated content, creators and consumers have long recognized that the power of video depends on the harmonious integration of what we hear (the video's audio track) with what we see (the video's image sequence). Current approaches to video generation either ignore sound to focus on general-purpose but silent image sequence generation or address both visual and audio elements but focus on restricted application domains such as re-dubbing. We introduce Mirage, an audio-to-video foundation model that excels at generating realistic, expressive output imagery from scratch given an audio input. When integrated with existing methods for speech synthesis (text-to-speech, or TTS), Mirage results in compelling multimodal video. When trained on audio-video footage of people talking (A-roll) and conditioned on audio containing speech, Mirage generates video of people delivering a believable interpretation of the performance implicit in input audio. Our central technical contribution is a unified method for training self-attention-based audio-to-video generation models, either from scratch or given existing weights. This methodology allows Mirage to retain generality as an approach to audio-to-video generation while producing outputs of superior subjective quality to methods that incorporate audio-specific architectures or loss components specific to people, speech, or details of how images or audio are captured. We encourage readers to watch and listen to the results of Mirage for themselves (see paper and comments for links).