The code generation capabilities of Large Language Models (LLMs) have advanced applications like tool invocation and problem-solving. However, improving performance in code-related tasks remains challenging due to limited training data that is verifiable with accurate test cases. While Direct Preference Optimization (DPO) has shown promise, existing methods for generating test cases still face limitations. In this paper, we propose a novel approach that splits code snippets into smaller, granular blocks, creating more diverse DPO pairs from the same test cases. Additionally, we introduce the Abstract Syntax Tree (AST) splitting and curriculum training method to enhance the DPO training. Our approach demonstrates significant improvements in code generation tasks, as validated by experiments on benchmark datasets such as HumanEval (+), MBPP (+), APPS, LiveCodeBench, and BigCodeBench. Code and data are available at https://github.com/SenseLLM/StructureCoder.

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.