Code generation plays a crucial role in various tasks, such as code auto-completion and mathematical reasoning. Previous work has proposed numerous methods to enhance code generation performance, including integrating feedback from the compiler. Inspired by this, we present ReflectionCoder, a novel approach that effectively leverages reflection sequences constructed by integrating compiler feedback to improve one-off code generation performance. Furthermore, we propose reflection self-distillation and dynamically masked distillation to effectively utilize these reflection sequences. Extensive experiments on three benchmarks, i.e., HumanEval (+), MBPP (+), and MultiPl-E, demonstrate that models fine-tuned with our method achieve state-of-the-art performance. Beyond the code domain, we believe this approach can benefit other domains that focus on final results and require long reasoning paths. Code and data are available at https://github.com/SenseLLM/ReflectionCoder.

Natural language image-caption datasets, widely used for training Large Multimodal Models, mainly focus on natural scenarios and overlook the intricate details of mathematical figures that are critical for problem-solving, hindering the advancement of current LMMs in multimodal mathematical reasoning. To this end, we propose leveraging code as supervision for cross-modal alignment, since code inherently encodes all information needed to generate corresponding figures, establishing a precise connection between the two modalities. Specifically, we co-develop our image-to-code model and dataset with model-in-the-loop approach, resulting in an image-to-code model, FigCodifier and ImgCode-8.6M dataset, the largest image-code dataset to date. Furthermore, we utilize FigCodifier to synthesize novel mathematical figures and then construct MM-MathInstruct-3M, a high-quality multimodal math instruction fine-tuning dataset. Finally, we present MathCoder-VL, trained with ImgCode-8.6M for cross-modal alignment and subsequently fine-tuned on MM-MathInstruct-3M for multimodal math problem solving. Our model achieves a new open-source SOTA across all six metrics. Notably, it surpasses GPT-4o and Claude 3.5 Sonnet in the geometry problem-solving subset of MathVista, achieving improvements of 8.9% and 9.2%.

Recent advances in preference optimization have demonstrated significant potential for improving mathematical reasoning capabilities in large language models (LLMs). While current approaches leverage high-quality pairwise preference data through outcome-based criteria like answer correctness or consistency, they fundamentally neglect the internal logical coherence of responses. To overcome this, we propose Probability-Consistent Preference Optimization (PCPO), a novel framework that establishes dual quantitative metrics for preference selection: (1) surface-level answer correctness and (2) intrinsic token-level probability consistency across responses. Extensive experiments show that our PCPO consistently outperforms existing outcome-only criterion approaches across a diverse range of LLMs and benchmarks. Our code is publicly available at https://github.com/YunqiaoYang/PCPO.

Large language models (LLMs) have exhibited great potential in mathematical reasoning. However, there remains a performance gap in this area between existing open-source models and closed-source models such as GPT-4. In this paper, we introduce MathGenie, a novel method for generating diverse and reliable math problems by leveraging the ground-truth solutions of the seed data. We augment these ground-truth solutions and use a specially finetuned model to translate these augmented solutions back into new questions. Subsequently, we generate code-integrated solutions for these questions. To ensure the correctness of the code-integrated solutions, we employ rationale-based verification for filtering. Then, we finetune various pretrained models, ranging from 7B to 70B, on the newly curated data, resulting in a family of models known as MathGenie. These models consistently outperform previous open-source models across five representative mathematical reasoning datasets, achieving state-of-the-art performance. In particular, MathGenie-InternLM2 achieves an accuracy of 87.7% on GSM8K and 55.7% on MATH, securing the best overall score.

A pivotal advancement in the progress of large language models (LLMs) is the emergence of the Mixture-of-Experts (MoE) LLMs. Compared to traditional LLMs, MoE LLMs can achieve higher performance with fewer active parameters, but it is still hard to deploy them due to their immense parameter sizes. Different from previous weight pruning methods that rely on specifically designed hardware, this paper mainly aims to enhance the deployment efficiency of MoE LLMs by introducing plug-and-play expert-level sparsification techniques. Specifically, we propose, for the first time to our best knowledge, post-training approaches for task-agnostic and task-specific expert pruning and skipping of MoE LLMs, tailored to improve deployment efficiency while maintaining model performance across a wide range of tasks. Extensive experiments show that our proposed methods can simultaneously reduce model sizes and increase the inference speed, while maintaining satisfactory performance. Code will be made available at https://github.com/Lucky-Lance/Expert_Sparsity.