Reinforcement Learning (RL) enhances LLM reasoning, yet a paradox emerges as models scale: strong base models saturate standard benchmarks (e.g., MATH), yielding correct but homogeneous solutions. In such environments, the lack of failure cases causes the advantage signal in group-relative algorithms (e.g., GRPO) to vanish, driving policies into mode collapse. To address this, we propose Constrained Uniform Top-K Sampling (CUTS), a parameter-free decoding strategy enforcing structure-preserving exploration. Unlike standard sampling that follows model biases, CUTS flattens the local optimization landscape by sampling uniformly from constrained high-confidence candidates. We integrate this into Mixed-CUTS, a training framework synergizing exploitative and exploratory rollouts to amplify intra-group advantage variance. Experiments on Qwen3 models demonstrate that our approach prevents policy degeneration and significantly boosts out-of-domain generalization. Notably, Mixed-CUTS improves Pass@1 accuracy on the challenging AIME25 benchmark by up to 15.1% over standard GRPO, validating that maintaining diversity within the semantic manifold is critical for rigorous reasoning.

Assessing the quality of Large Language Model (LLM) outputs becomes especially challenging in high-branching settings, where a single prompt yields many plausible candidates. Existing verifiers typically operate on the surface text (e.g., reward models, LLM judges, majority voting) or on confidence proxies derived from token probabilities, both of which can be brittle: the former can be influenced by stylistic artifacts, while the latter is often miscalibrated. In this paper, we study a third source of information—the model’s hidden states—for binary correctness verification in tasks with a reliable success/failure signal (e.g., deterministic checkers or reference-grounded answers). We find that correct and incorrect solutions exhibit measurable geometric differences in their hidden-state trajectories. To isolate this signal with minimal modeling assumptions, we introduce Clue (Clustering and Experience-based Verification), a training-free, non-parametric verifier. Clue summarizes each reasoning trace by an activation delta—the difference between hidden states at the start and end of the explicit reasoning span—and predicts correctness by comparing this delta to two class centroids computed from labeled experience. Across math (AIME 24/25), scientific QA (GPQA), and a multi-domain benchmark (WebInstruct-verified), Clue improves selection and reranking, with particularly strong gains on smaller or less-calibrated models. For example, on AIME 24 with a 1.5B model, Clue raises accuracy from 56.7% (majority@64) to 70.0% (top-maj@16).

Large Language Models (LLMs) have recently advanced the field of Automated Theorem Proving (ATP), attaining substantial performance gains through widely adopted test-time scaling strategies, notably reflective Chain-of-Thought (CoT) reasoning and increased sampling passes. However, they both introduce significant computational overhead for inference. Moreover, existing cost analyses typically regulate only the number of sampling passes, while neglecting the substantial disparities in sampling costs introduced by different scaling strategies. In this paper, we systematically compare the efficiency of different test-time scaling strategies for ATP models and demonstrate the inefficiency of the current state-of-the-art (SOTA) open-source approaches. We then investigate approaches to significantly reduce token usage and sample passes while maintaining the original performance. Specifically, we propose two complementary methods that can be integrated into a unified EconRL pipeline for amplified benefits: (1) a dynamic Chain-of-Thought (CoT) switching mechanism designed to mitigate unnecessary token consumption, and (2) Diverse parallel-scaled reinforcement learning (RL) with trainable prefixes to enhance pass rates under constrained sampling passes. Experiments on miniF2F and ProofNet demonstrate that our EconProver-GD achieves comparable performance to baseline methods with only 12% of the computational cost. This work provides actionable insights for deploying lightweight ATP models without sacrificing performance.

Multimodal Mathematical Reasoning (MMR) has recently attracted increasing attention for its capability to solve mathematical problems involving both textual and visual modalities. However, current models still face significant challenges in real-world visual math tasks, often misinterpreting diagrams, failing to align mathematical symbols with visual evidence, or producing inconsistent reasoning steps. Moreover, existing evaluations mainly focus on checking final answers rather than verifying the correctness or executability of each intermediate step. A growing body of recent research addresses these issues by integrating structured perception, explicit alignment, and verifiable reasoning within unified frameworks.To establish a clear roadmap for understanding and comparing different MMR approaches, we systematically review them around four fundamental questions: (1) What to extract from multimodal inputs, (2) How to represent and align textual and visual information, (3) How to perform the reasoning, and (4) How to evaluate the correctness of the overall reasoning process. Finally, we discuss open challenges and share our thoughts on future research directions.

Logical reasoning is a core capability for large language models (LLMs), yet existing benchmarks that rely solely on final-answer accuracy fail to capture the quality of the reasoning process. To address this, we introduce FineLogic, a fine-grained evaluation framework that assesses logical reasoning across three dimensions: overall accuracy, stepwise soundness, and representation-level probing. Leveraging this framework, we conduct a comprehensive study on how different supervision formats in fine-tuning shape reasoning abilities. We fine-tune LLMs on four supervision styles—one in natural language and three symbolic variants—and find a key trade-off: natural language supervision excels at generalization to out-of-distribution and long-chain problems, whereas symbolic supervision is superior at instilling structurally sound, atomic reasoning steps. Furthermore, our probing analysis indicates that fine-tuning primarily refines the model’s step-by-step generation process, rather than improving its ability to converge on an answer early. Together, our framework and analysis provide a more rigorous lens for evaluating and improving logical reasoning in LLMs. The code is available at https://github.com/YujunZhou/FineLogic.

Reasoning in mathematical domains remains a significant challenge for relatively small language models (LMs). Many current methods focus on specializing LMs in mathematical reasoning and rely heavily on distilling knowledge from powerful yet inefficient large LMs (LLMs). In this work, we explore a new direction that avoids over-reliance on LLM teachers, introducing a multi-view fine-tuning method that efficiently exploits existing mathematical problem datasets with diverse annotation styles. Our approach uniquely considers the various annotation formats as different “views” that may help each other and leverage them in training the model. By postpending distinct instructions to input questions, models can learn to generate solutions in diverse formats in a flexible manner. Experimental results show that our strategy enables relatively small LMs to outperform prior approaches that heavily rely on knowledge distillation, as well as carefully established baselines. Additionally, the proposed method grants the models promising generalization ability across various views and datasets, and the capability to learn from inaccurate or incomplete noisy data. We hope our multi-view training paradigm could inspire future studies in other machine reasoning domains.

Audio-Visual Question Answering (AVQA) is a challenging task that involves answering questions based on both auditory and visual information in videos. A significant challenge is interpreting complex multi-modal scenes, which include both visual objects and sound sources, and connecting them to the given question. In this paper, we introduce the Source-aware Semantic Representation Network (SaSR-Net), a novel model designed for AVQA. SaSR-Net utilizes source-wise learnable tokens to efficiently capture and align audio-visual elements with the corresponding question. It streamlines the fusion of audio and visual information using spatial and temporal attention mechanisms to identify answers in multi-modal scenes. Extensive experiments on the Music-AVQA and AVQA-Yang datasets show that SaSR-Net outperforms state-of-the-art AVQA methods. We will release our source code and pre-trained models.

Supervised fine-tuning enhances the problem-solving abilities of language models across various mathematical reasoning tasks. To maximize such benefits, existing research focuses on *broadening* the training set with various data augmentation techniques, which is effective for standard single-round question-answering settings. Our work introduces a novel technique aimed at cultivating a *deeper* understanding of the training problems at hand, enhancing performance not only in standard settings but also in more complex scenarios that require reflective thinking. Specifically, we propose **reflective augmentation**, a method that embeds problem reflection into each training instance. It trains the model to consider alternative perspectives and engage with abstractions and analogies, thereby fostering a thorough comprehension through reflective reasoning. Extensive experiments validate the achievement of our aim, underscoring the unique advantages of our method and its complementary nature relative to existing augmentation techniques.

Large Language Models (LLMs) demonstrate remarkable capabilities across diverse applications. However, concerns regarding their security, particularly the vulnerability to jailbreak attacks, persist. Drawing inspiration from adversarial training in deep learning and LLM agent learning processes, we introduce the In-Context Adversarial Game (ICAG) for defending against jailbreaks without the need for fine-tuning. ICAG leverages agent learning to conduct an adversarial game, aiming to dynamically extend knowledge to defend against jailbreaks. Unlike traditional methods that rely on static datasets, ICAG employs an iterative process to enhance both the defense and attack agents. This continuous improvement process strengthens defenses against newly generated jailbreak prompts. Our empirical studies affirm ICAG’s efficacy, where LLMs safeguarded by ICAG exhibit significantly reduced jailbreak success rates across various attack scenarios. Moreover, ICAG demonstrates remarkable transferability to other LLMs, indicating its potential as a versatile defense mechanism. The code is available at https://github.com/YujunZhou/In-Context-Adversarial-Game.

The paper introduces SceMQA, a novel benchmark for scientific multimodal question answering at the college entrance level. It addresses a critical educational phase often overlooked in existing benchmarks, spanning high school to pre-college levels. SceMQA focuses on core science subjects including Mathematics, Physics, Chemistry, and Biology. It features a blend of multiple-choice and free-response formats, ensuring a comprehensive evaluation of AI models’ abilities. Additionally, our benchmark provides specific knowledge points for each problem and detailed explanations for each answer. SceMQA also uniquely presents problems with identical contexts but varied questions to facilitate a more thorough and accurate assessment of reasoning capabilities. In the experiment, we evaluate both open-source and close-source state-of-the-art Multimodal Large Language Models (MLLMs), across various experimental settings. The results show that further research and development are needed in developing more capable MLLM, as highlighted by only 50% to 60% accuracy achieved by the strongest models.

Solving math word problem (MWP) remains a challenging task, as it requires to understand both the semantic meanings of the text and the mathematical logic among quantities, i.e., for both semantics modal and quantity modal learning. Current MWP encoders work in a uni-modal setting and map the given problem description to a latent representation, then for decoding. The generalizability of these MWP encoders is thus limited because some problems are semantics-demanding and others are quantity-demanding. To address this problem, we propose a Compositional Math Word Problem Solver (C-MWP) which works in a bi-modal setting encoding in an interactive way. Extensive experiments validate the effectiveness of C-MWP and show its superiority over state-of-the-art models on public benchmarks.

In this paper, we present a novel approach for distilling math word problem solving capabilities from large language models (LLMs) into smaller, more efficient student models. Our approach is designed to consider the student model’s weaknesses and foster a tailored learning experience by generating targeted exercises aligned with educational science principles, such as knowledge tracing and personalized learning. Concretely, we let GPT-3 be a math tutor and run two steps iteratively: 1) assessing the student model’s current learning status on a GPT-generated exercise book, and 2) improving the student model by training it with tailored exercise samples generated by GPT-3. Experimental results reveal that our approach outperforms LLMs (e.g., GPT-3 and PaLM) in accuracy across three distinct benchmarks while employing significantly fewer parameters. Furthermore, we provide a comprehensive analysis of the various components within our methodology to substantiate their efficacy.

While significant progress has been made in natural language processing (NLP), existing methods exhibit limitations in effectively interpreting and processing diverse mathematical modalities. Therefore, we introduce UniMath, a versatile and unified system designed for multimodal mathematical reasoning tasks. Tackling complex problem-solving in arithmetic, geometry, and table-based math, UniMath utilizes a fine-tuned T5 model augmented with a variational autoencoder (VAE)-based image tokenizer. By jointly training and evaluating the model on three diverse datasets - SVAMP, GeoQA, and TableMWP, UniMath achieves state-of-the-art performance. The model’s generalization ability is further demonstrated via fine-tuning on two additional datasets, MathQA and Geo-Proving. Through comprehensive evaluations, we showcase that joint training across diverse math tasks improves overall model performance and enhances its ability to generalize across different mathematical reasoning tasks. This pioneering approach provides a blueprint and inspires further efforts on unified mathematical reasoning with deep learning systems.

This paper studies solving Arabic Math Word Problems by deep learning. A Math Word Problem (MWP) is a text description of a mathematical problem that can be solved by deriving a math equation to reach the answer. Effective models have been developed for solving MWPs in English and Chinese. However, Arabic MWPs are rarely studied. This paper contributes the first large-scale dataset for Arabic MWPs, which contains 6,000 samples of primary-school math problems, written in Modern Standard Arabic (MSA). Arabic MWP solvers are then built with deep learning models and evaluated on this dataset. In addition, a transfer learning model is built to let the high-resource Chinese MWP solver promote the performance of the low-resource Arabic MWP solver. This work is the first to use deep learning methods to solve Arabic MWP and the first to use transfer learning to solve MWP across different languages. The transfer learning enhanced solver has an accuracy of 74.15%, which is 3% higher than the solver without using transfer learning. We make the dataset and solvers available in public for encouraging more research of Arabic MWPs: https://github.com/reem-codes/ArMATH

Math word problem (MWP) solving faces a dilemma in number representation learning. In order to avoid the number representation issue and reduce the search space of feasible solutions, existing works striving for MWP solving usually replace real numbers with symbolic placeholders to focus on logic reasoning. However, different from common symbolic reasoning tasks like program synthesis and knowledge graph reasoning, MWP solving has extra requirements in numerical reasoning. In other words, instead of the number value itself, it is the reusable numerical property that matters more in numerical reasoning. Therefore, we argue that injecting numerical properties into symbolic placeholders with contextualized representation learning schema can provide a way out of the dilemma in the number representation issue here. In this work, we introduce this idea to the popular pre-training language model (PLM) techniques and build MWP-BERT, an effective contextual number representation PLM. We demonstrate the effectiveness of our MWP-BERT on MWP solving and several MWP-specific understanding tasks on both English and Chinese benchmarks.

Math word problem (MWP) solving is an important task in question answering which requires human-like reasoning ability. Analogical reasoning has long been used in mathematical education, as it enables students to apply common relational structures of mathematical situations to solve new problems. In this paper, we propose to build a novel MWP solver by leveraging analogical MWPs, which advance the solver’s generalization ability across different kinds of MWPs. The key idea, named analogy identification, is to associate the analogical MWP pairs in a latent space, i.e., encoding an MWP close to another analogical MWP, while leaving away from the non-analogical ones. Moreover, a solution discriminator is integrated into the MWP solver to enhance the association between an MWP and its true solution. The evaluation results verify that our proposed analogical learning strategy promotes the performance of MWP-BERT on Math23k over the state-of-the-art model Generate2Rank, with 5 times fewer parameters in the encoder. We also find that our model has a stronger generalization ability in solving difficult MWPs due to the analogical learning from easy MWPs.

Many existing works have demonstrated that language is a helpful guider for image understanding by neural networks. We focus on a language-shaped learning problem in a few-shot setting, i.e., using language to improve few-shot image classification when language descriptions are only available during training. We propose a data-efficient method that can make the best usage of the few-shot images and the language available only in training. Experimental results on dataset ShapeWorld and Birds show that our method outperforms other state-of-the-art baselines in language-shaped few-shot learning area, especially when training data is more severely limited. Therefore, we call our approach data-efficient language-shaped learning (DF-LSL).