With the rapid development of deep learning, large language models have shown strong capabilities in complex reasoning tasks such as mathematical equation solving. However, their substantial computational and storage costs hinder practical deployment. This paper proposes a lightweight optimization method that integrates dynamic attention head pruning with knowledge distillation. The approach dynamically evaluates the importance of each attention head in the multi-head attention mechanism using a combination of weight norms and entropy, and prunes redundant heads in real time to reduce computational overhead. To mitigate performance degradation, knowledge distillation transfers information from the original model to the pruned student, enabling the smaller model to preserve reasoning ability. Experiments conducted on both Math23k and ASDiv-A verify the effectiveness of the proposed method. For example, on Math23k with a 30% pruning ratio, parameters are reduced by 18.7%, inference speed is improved by 27.5%, FLOPs are reduced by 19.3%, and accuracy drops only 0.7% (from 84.4% to 83.7%). These results demonstrate that the method achieves substantial efficiency gains while maintaining strong reasoning performance, providing a practical solution for efficient deployment of large language models in mathematical reasoning tasks.

Parameter-Efficient finetuning (PEFT) enhances model performance on downstream tasks by updating a minimal subset of parameters. Representation finetuning (ReFT) methods further improve efficiency by freezing model weights and optimizing internal representations with fewer parameters than PEFT, outperforming PEFT on several tasks. However, ReFT exhibits a significant performance decline on mathematical reasoning tasks. To address this problem, the paper demonstrates that ReFT's poor performance on mathematical tasks primarily stems from its struggle to generate effective reasoning prefixes during the early inference phase. Moreover, ReFT disturbs the numerical encoding and the error accumulats during the CoT stage. Based on these observations, this paper proposes Bias-REstrained Prefix Representation FineTuning (BREP ReFT), which enhances ReFT's mathematical reasoning capability by truncating training data to optimize the generation of initial reasoning prefixes, intervening on the early inference stage to prevent error accumulation, and constraining the intervention vectors' magnitude to avoid disturbing numerical encoding. Extensive experiments across diverse model architectures demonstrate BREP's superior effectiveness, efficiency, and robust generalization capability, outperforming both standard ReFT and weight-based PEFT methods on the task of mathematical reasoning. The source code is available at https://github.com/LiangThree/BREP.

LLMs demonstrate performance comparable to human abilities in complex tasks such as mathematical reasoning, but their robustness in mathematical reasoning under minor input perturbations still lacks systematic investigation. Existing methods generally suffer from limited scalability, weak semantic preservation, and high costs. Therefore, we propose MSCR, an automated adversarial attack method based on multi-source candidate replacement. By combining three information sources including cosine similarity in the embedding space of LLMs, the WordNet dictionary, and contextual predictions from a masked language model, we generate for each word in the input question a set of semantically similar candidates, which are then filtered and substituted one by one to carry out the attack. We conduct large-scale experiments on LLMs using the GSM8K and MATH500 benchmarks. The results show that even a slight perturbation involving only a single word can significantly reduce the accuracy of all models, with the maximum drop reaching 49.89% on GSM8K and 35.40% on MATH500, while preserving the high semantic consistency of the perturbed questions. Further analysis reveals that perturbations not only lead to incorrect outputs but also substantially increase the average response length, which results in more redundant reasoning paths and higher computational resource consumption.

Low-rank adaptation (LoRA) is a parameter-efficient fine-tuning (PEFT) method widely used in large language models (LLMs). LoRA essentially describes the projection of an input space into a low-dimensional output space, with the dimensionality determined by the LoRA rank. In standard LoRA, all input tokens share the same weights and undergo an identical input-output projection. This limits LoRA's ability to capture token-specific information due to the inherent semantic differences among tokens. To address this limitation, we propose Token-wise Projected Low-Rank Adaptation (TopLoRA), which dynamically adjusts LoRA weights according to the input token, thereby learning token-wise input-output projections in an end-to-end manner. Formally, the weights of TopLoRA can be expressed as $BΣ_X A$, where $A$ and $B$ are low-rank matrices (as in standard LoRA), and $Σ_X$ is a diagonal matrix generated from each input token $X$. Notably, TopLoRA does not increase the rank of LoRA weights but achieves more granular adaptation by learning token-wise LoRA weights (i.e., token-wise input-output projections). Extensive experiments across multiple models and datasets demonstrate that TopLoRA consistently outperforms LoRA and its variants. The code is available at https://github.com/Leopold1423/toplora-neurips25.

Reinforcement Learning (RL) has become a compelling way to strengthen the multi step reasoning ability of Large Language Models (LLMs). However, prevalent RL paradigms still lean on sparse outcome-based rewards and limited exploration, which often drives LLMs toward repetitive and suboptimal reasoning patterns. In this paper, we study the central question of how to design exploration for LLM reasoning and introduce MERCI (Motivating Exploration in LLM Reasoning with Count-based Intrinsic Rewards), a novel RL algorithm that augments policy optimization with a principled intrinsic reward. Building on the idea of count-based exploration, MERCI leverages a lightweight Coin Flipping Network (CFN) to estimate the pseudo count and further epistemic uncertainty over reasoning trajectories, and converts them into an intrinsic reward that values novelty while preserving the learning signal from task rewards. We integrate MERCI into some advanced RL frameworks like Group Relative Policy Optimization (GRPO). Experiments on complex reasoning benchmarks demonstrate that MERCI encourages richer and more varied chains of thought, significantly improves performance over strong baselines, and helps the policy escape local routines to discover better solutions. It indicates that our targeted intrinsic motivation can make exploration reliable for language model reasoning.

The growing disparity between the exponential scaling of computational resources and the finite growth of high-quality text data now constrains conventional scaling approaches for large language models (LLMs). To address this challenge, we introduce Reinforcement Learning on Pre-Training data (RLPT), a new training-time scaling paradigm for optimizing LLMs. In contrast to prior approaches that scale training primarily through supervised learning, RLPT enables the policy to autonomously explore meaningful trajectories to learn from pre-training data and improve its capability through reinforcement learning (RL). While existing RL strategies such as reinforcement learning from human feedback (RLHF) and reinforcement learning with verifiable rewards (RLVR) rely on human annotation for reward construction, RLPT eliminates this dependency by deriving reward signals directly from pre-training data. Specifically, it adopts a next-segment reasoning objective, rewarding the policy for accurately predicting subsequent text segments conditioned on the preceding context. This formulation allows RL to be scaled on pre-training data, encouraging the exploration of richer trajectories across broader contexts and thereby fostering more generalizable reasoning skills. Extensive experiments on both general-domain and mathematical reasoning benchmarks across multiple models validate the effectiveness of RLPT. For example, when applied to Qwen3-4B-Base, RLPT yields absolute improvements of $3.0$, $5.1$, $8.1$, $6.0$, $6.6$, and $5.3$ on MMLU, MMLU-Pro, GPQA-Diamond, KOR-Bench, AIME24, and AIME25, respectively. The results further demonstrate favorable scaling behavior, suggesting strong potential for continued gains with more compute. In addition, RLPT provides a solid foundation, extending the reasoning boundaries of LLMs and enhancing RLVR performance.

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) have empowered large language models (LLMs) to tackle challenging reasoning tasks such as mathematics and programming. RLVR leverages verifiable outcome rewards to guide policy optimization, enabling LLMs to progressively improve output quality in a grounded and reliable manner. Despite its promise, the RLVR paradigm poses significant challenges, as existing methods often suffer from sparse reward signals and unstable policy gradient updates, particularly in RL-based approaches. To address the challenges, we propose $\textbf{PACS}$, a novel RLVR framework that achieves im$\textbf{P}$licit $\textbf{A}$ctor $\textbf{C}$ritic coupling via a $\textbf{S}$upervised learning framework. By treating the outcome reward as a predictable label, we reformulate the RLVR problem into a supervised learning task over a score function parameterized by the policy model and optimized using cross-entropy loss. A detailed gradient analysis shows that this supervised formulation inherently recovers the classical policy gradient update while implicitly coupling actor and critic roles, yielding more stable and efficient training. Benchmarking on challenging mathematical reasoning tasks, PACS outperforms strong RLVR baselines, such as PPO and GRPO, achieving superior reasoning performance. For instance, PACS achieves 59.78\% at pass@256 on AIME 2025, representing improvements of 13.32 and 14.36 points over PPO and GRPO. This simple yet powerful framework offers a promising avenue for LLMs post-training with verifiable rewards. Our code and data are available as open source at https://github.com/ritzz-ai/PACS.

Large language models (LLMs) achieve strong performance across many domains but are difficult to deploy in resource-constrained settings due to their size. Low-rank weight matrix compression is a popular strategy for reducing model size, typically by minimizing weight reconstruction error under the assumption that weights are low-rank. However, this assumption often does not hold in LLMs. Instead, LLM activations exhibit stronger low-rank structure-prompting a shift toward minimizing activation reconstruction error. We show that this shift alone is insufficient: activation dimensions contribute unequally to model performance, and uniform reconstruction can harm performance. We propose IMPACT, a principled framework for importance-aware activation reconstruction that links model compression decisions to their impact on model behavior. IMPACT formulates an optimization problem that considers both activation structure and gradient sensitivity, and derives a closed-form solution where the optimal reconstruction bases are the eigenvectors of an importance-weighted activation covariance matrix. This enables low-rank approximations explicitly optimized to preserve accuracy. Experiments across diverse models and tasks show that IMPACT achieves up to 48.6% greater model size reduction with accuracy comparable to state-of-the-art baselines.

Reasoning Large Language Models (RLLMs) have demonstrated impressive performance on complex tasks, largely due to the adoption of Long Chain-of-Thought (Long CoT) reasoning. However, they often exhibit overthinking -- performing unnecessary reasoning steps even after arriving at the correct answer. Prior work has largely focused on qualitative analyses of overthinking through sample-based observations of long CoTs. In contrast, we present a quantitative analysis of overthinking from the perspective of self-doubt, characterized by excessive token usage devoted to re-verifying already-correct answer. We find that self-doubt significantly contributes to overthinking. In response, we introduce a simple and effective prompting method to reduce the model's over-reliance on input questions, thereby avoiding self-doubt. Specifically, we first prompt the model to question the validity of the input question, and then respond concisely based on the outcome of that evaluation. Experiments on three mathematical reasoning tasks and four datasets with missing premises demonstrate that our method substantially reduces answer length and yields significant improvements across nearly all datasets upon 4 widely-used RLLMs. Further analysis demonstrates that our method effectively minimizes the number of reasoning steps and reduces self-doubt.

Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning tasks. However, the complete technical details remain unrevealed, and the techniques that are believed certainly to be adopted are only reinforcement learning (RL) and the long chain of thoughts. This paper proposes a new RL framework, termed OREAL, to pursue the performance limit that can be achieved through \textbf{O}utcome \textbf{RE}w\textbf{A}rd-based reinforcement \textbf{L}earning for mathematical reasoning tasks, where only binary outcome rewards are easily accessible. We theoretically prove that behavior cloning on positive trajectories from best-of-N (BoN) sampling is sufficient to learn the KL-regularized optimal policy in binary feedback environments. This formulation further implies that the rewards of negative samples should be reshaped to ensure the gradient consistency between positive and negative samples. To alleviate the long-existing difficulties brought by sparse rewards in RL, which are even exacerbated by the partial correctness of the long chain of thought for reasoning tasks, we further apply a token-level reward model to sample important tokens in reasoning trajectories for learning. With OREAL, for the first time, a 7B model can obtain 94.0 pass@1 accuracy on MATH-500 through RL, being on par with 32B models. OREAL-32B also surpasses previous 32B models trained by distillation with 95.0 pass@1 accuracy on MATH-500. Our investigation also indicates the importance of initial policy models and training queries for RL. Code, models, and data will be released to benefit future research\footnote{https://github.com/InternLM/OREAL}.