Zimu Lu

Ke Wang, Houxing Ren, Aojun Zhou et al.

The recently released GPT-4 Code Interpreter has demonstrated remarkable proficiency in solving challenging math problems, primarily attributed to its ability to seamlessly reason with natural language, generate code, execute code, and continue reasoning based on the execution output. In this paper, we present a method to fine-tune open-source language models, enabling them to use code for modeling and deriving math equations and, consequently, enhancing their mathematical reasoning abilities. We propose a method of generating novel and high-quality datasets with math problems and their code-based solutions, referred to as MathCodeInstruct. Each solution interleaves natural language, code, and execution results. We also introduce a customized supervised fine-tuning and inference approach. This approach yields the MathCoder models, a family of models capable of generating code-based solutions for solving challenging math problems. Impressively, the MathCoder models achieve state-of-the-art scores among open-source LLMs on the MATH (45.2%) and GSM8K (83.9%) datasets, substantially outperforming other open-source alternatives. Notably, the MathCoder model not only surpasses ChatGPT-3.5 and PaLM-2 on GSM8K and MATH but also outperforms GPT-4 on the competition-level MATH dataset. The dataset and models will be released at https://github.com/mathllm/MathCoder.

Aojun Zhou, Ke Wang, Zimu Lu et al.

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the \textit{Code Usage Frequency} of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit \uline{c}ode-based \uline{s}elf-\uline{v}erification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset \textbf{(53.9\% $\to$ 84.3\%)}.

Yunqiao Yang, Wenbo Li, Houxing Ren et al.

The rapid evolution of Large Language Models (LLMs) has fostered diverse paradigms for automated slide generation, ranging from code-driven layouts to image-centric synthesis. However, evaluating these heterogeneous systems remains challenging, as existing protocols often struggle to provide comparable scores across architectures or rely on uncalibrated judgments. In this paper, we introduce SlidesGen-Bench, a benchmark designed to evaluate slide generation through a lens of three core principles: universality, quantification, and reliability. First, to establish a unified evaluation framework, we ground our analysis in the visual domain, treating terminal outputs as renderings to remain agnostic to the underlying generation method. Second, we propose a computational approach that quantitatively assesses slides across three distinct dimensions - Content, Aesthetics, and Editability - offering reproducible metrics where prior works relied on subjective or reference-dependent proxies. Finally, to ensure high correlation with human preference, we construct the Slides-Align1.5k dataset, a human preference aligned dataset covering slides from nine mainstream generation systems across seven scenarios. Our experiments demonstrate that SlidesGen-Bench achieves a higher degree of alignment with human judgment than existing evaluation pipelines. Our code and data are available at https://github.com/YunqiaoYang/SlidesGen-Bench.

Houxing Ren, Mingjie Zhan, Zimu Lu et al.

Masked diffusion language models enable parallel token generation and offer improved decoding efficiency over autoregressive models. However, their performance degrades significantly when generating multiple tokens simultaneously, due to a mismatch between token-level training objectives and joint sequence consistency. In this paper, we propose ME-DLM, an edit-based refinement framework that augments diffusion generation with lightweight post-editing steps. After producing an initial complete response, the model refines it through minimal edit operations, including replacement, deletion, and insertion, conditioned on the full sequence. Training supervision is derived from edit distance, providing a deterministic signal under a fixed canonicalization scheme for learning minimal corrections. This approach encourages sequence-level consistency through globally conditioned edits while preserving the efficiency benefits of parallel diffusion decoding. Extensive experiments demonstrate that ME-DLM improves the quality and robustness of multi-token parallel generation. In particular, when built upon LLaDA, our method achieves consistent gains of 11.6 points on HumanEval and 33.6 points on GSM8K while using one-eighth of the total diffusion steps. Code is available at https://github.com/renhouxing/ME-DLM.

Zimu Lu, Aojun Zhou, Houxing Ren et al.

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 from a small-scale problem-solution dataset (denoted as seed data). We augment the ground-truth solutions of our seed data and train a back-translation model to translate the augmented solutions back into new questions. Subsequently, we generate code-integrated solutions for the new questions. To ensure the correctness of the code-integrated solutions, we employ rationale-based strategy for solution verification. Various pretrained models, ranging from 7B to 70B, are trained on the newly curated data to test the effectiveness of the proposed augmentation technique, resulting in a family of models known as MathGenieLM. These models consistently outperform previous open-source models across five representative mathematical reasoning datasets, achieving state-of-the-art performance. In particular, MathGenieLM-InternLM2 achieves an accuracy of 87.7% on GSM8K and 55.7% on MATH, securing the best overall score among open-source language models.

Ke Wang, Junting Pan, Linda Wei et al.

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%. The dataset and models will be released at https://github.com/mathllm/MathCoder.

Weikang Shi, Houxing Ren, Junting Pan et al.

Large Language Models (LLMs) show significant potential in AI mathematical tutoring, yet current evaluations often rely on simplistic metrics or narrow pedagogical scenarios, failing to assess comprehensive, multi-turn teaching effectiveness. In this paper, we introduce KMP-Bench, a comprehensive K-8 Mathematical Pedagogical Benchmark designed to assess LLMs from two complementary perspectives. The first module, KMP-Dialogue, evaluates holistic pedagogical capabilities against six core principles (e.g., Challenge, Explanation, Feedback), leveraging a novel multi-turn dialogue dataset constructed by weaving together diverse pedagogical components. The second module, KMP-Skills, provides a granular assessment of foundational tutoring abilities, including multi-turn problem-solving, error detection and correction, and problem generation. Our evaluations on KMP-Bench reveal a key disparity: while leading LLMs excel at tasks with verifiable solutions, they struggle with the nuanced application of pedagogical principles. Additionally, we present KMP-Pile, a large-scale (150K) dialogue dataset. Models fine-tuned on KMP-Pile show substantial improvement on KMP-Bench, underscoring the value of pedagogically-rich training data for developing more effective AI math tutors.

Han Xiao, Guozhi Wang, Yuxiang Chai et al.

In this paper, we introduce UI-Genie, a self-improving framework addressing two key challenges in GUI agents: verification of trajectory outcome is challenging and high-quality training data are not scalable. These challenges are addressed by a reward model and a self-improving pipeline, respectively. The reward model, UI-Genie-RM, features an image-text interleaved architecture that efficiently pro- cesses historical context and unifies action-level and task-level rewards. To sup- port the training of UI-Genie-RM, we develop deliberately-designed data genera- tion strategies including rule-based verification, controlled trajectory corruption, and hard negative mining. To address the second challenge, a self-improvement pipeline progressively expands solvable complex GUI tasks by enhancing both the agent and reward models through reward-guided exploration and outcome verification in dynamic environments. For training the model, we generate UI- Genie-RM-517k and UI-Genie-Agent-16k, establishing the first reward-specific dataset for GUI agents while demonstrating high-quality synthetic trajectory gen- eration without manual annotation. Experimental results show that UI-Genie achieves state-of-the-art performance across multiple GUI agent benchmarks with three generations of data-model self-improvement. We open-source our complete framework implementation and generated datasets to facilitate further research in https://github.com/Euphoria16/UI-Genie.

Ke Wang, Junting Pan, Weikang Shi et al.

Recent advancements in Large Multimodal Models (LMMs) have shown promising results in mathematical reasoning within visual contexts, with models approaching human-level performance on existing benchmarks such as MathVista. However, we observe significant limitations in the diversity of questions and breadth of subjects covered by these benchmarks. To address this issue, we present the MATH-Vision (MATH-V) dataset, a meticulously curated collection of 3,040 high-quality mathematical problems with visual contexts sourced from real math competitions. Spanning 16 distinct mathematical disciplines and graded across 5 levels of difficulty, our dataset provides a comprehensive and diverse set of challenges for evaluating the mathematical reasoning abilities of LMMs. Through extensive experimentation, we unveil a notable performance gap between current LMMs and human performance on MATH-V, underscoring the imperative for further advancements in LMMs. Moreover, our detailed categorization allows for a thorough error analysis of LMMs, offering valuable insights to guide future research and development. The project is available at https://mathvision-cuhk.github.io

Yunqiao Yang, Houxing Ren, Zimu Lu et al.

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.

Zimu Lu, Aojun Zhou, Ke Wang et al.

Direct Preference Optimization (DPO) has proven effective at improving the performance of large language models (LLMs) on downstream tasks such as reasoning and alignment. In this work, we propose Step-Controlled DPO (SCDPO), a method for automatically providing stepwise error supervision by creating negative samples of mathematical reasoning rationales that start making errors at a specified step. By applying these samples in DPO training, SCDPO can better align the model to understand reasoning errors and output accurate reasoning steps. We apply SCDPO to both code-integrated and chain-of-thought solutions, empirically showing that it consistently improves the performance compared to naive DPO on three different SFT models, including one existing SFT model and two models we finetuned. Qualitative analysis of the credit assignment of SCDPO and DPO demonstrates the effectiveness of SCDPO at identifying errors in mathematical solutions. We then apply SCDPO to an InternLM2-20B model, resulting in a 20B model that achieves high scores of 88.5% on GSM8K and 58.1% on MATH, rivaling all other open-source LLMs, showing the great potential of our method.