Can scaling transform reasoning? In this work, we explore the untapped potential of scaling Long Chain-of-Thought (Long-CoT) data to 1000k samples, pioneering the development of a slow-thinking model, RedStar. Through extensive experiments with various LLMs and different sizes, we uncover the ingredients for specialization and scale for Long-CoT training. Surprisingly, even smaller models show significant performance gains with limited data, revealing the sample efficiency of Long-CoT and the critical role of sample difficulty in the learning process. Our findings demonstrate that Long-CoT reasoning can be effectively triggered with just a few thousand examples, while larger models achieve unparalleled improvements. We also introduce reinforcement learning (RL)-scale training as a promising direction for advancing slow-thinking systems. RedStar shines across domains: on the MATH-Hard benchmark, RedStar-code-math boosts performance from 66.2\% to 81.6\%, and on the USA Math Olympiad (AIME), it solves 46.7\% of problems using only 21k mixed-code-math datasets. In multimodal tasks like GeoQA and MathVista-GEO, RedStar-Geo achieves competitive results with minimal Long-CoT data, outperforming other slow-thinking systems like QvQ-Preview. Compared to QwQ, RedStar strikes the perfect balance between reasoning and generalizability. Our work highlights that, with careful tuning, scaling Long-CoT can unlock extraordinary reasoning capabilities-even with limited dataset and set a new standard for slow-thinking models across diverse challenges. Our data and models are released at https://huggingface.co/RedStar-Reasoning.
Large language models (LLMs) have recently demonstrated remarkable success in mathematical reasoning. Despite progress in methods like chain-of-thought prompting and self-consistency sampling, these advances often focus on final correctness without ensuring that the underlying reasoning process is coherent and reliable. This paper introduces Step-KTO, a training framework that combines process-level and outcome-level binary feedback to guide LLMs toward more trustworthy reasoning trajectories. By providing binary evaluations for both the intermediate reasoning steps and the final answer, Step-KTO encourages the model to adhere to logical progressions rather than relying on superficial shortcuts. Our experiments on challenging mathematical benchmarks show that Step-KTO significantly improves both final answer accuracy and the quality of intermediate reasoning steps. For example, on the MATH-500 dataset, Step-KTO achieves a notable improvement in Pass@1 accuracy over strong baselines. These results highlight the promise of integrating stepwise process feedback into LLM training, paving the way toward more interpretable and dependable reasoning capabilities.
In this paper, we present an investigative study on how Mental Sets influence the reasoning capabilities of LLMs. LLMs have excelled in diverse natural language processing (NLP) tasks, driven by advancements in parameter-efficient fine-tuning (PEFT) and emergent capabilities like in-context learning (ICL). For complex reasoning tasks, selecting the right model for PEFT or ICL is critical, often relying on scores on benchmarks such as MMLU, MATH, and GSM8K. However, current evaluation methods, based on metrics like F1 Score or reasoning chain assessments by larger models, overlook a key dimension: adaptability to unfamiliar situations and overcoming entrenched thinking patterns. In cognitive psychology, Mental Set refers to the tendency to persist with previously successful strategies, even when they become inefficient - a challenge for problem solving and reasoning. We compare the performance of LLM models like Llama-3.1-8B-Instruct, Llama-3.1-70B-Instruct and GPT-4o in the presence of mental sets. To the best of our knowledge, this is the first study to integrate cognitive psychology concepts into the evaluation of LLMs for complex reasoning tasks, providing deeper insights into their adaptability and problem-solving efficacy.
While Large Language Models (LLMs) have shown impressive capabilities in math problem-solving tasks, their robustness to noisy inputs is not well-studied. In this work, we propose ArithmAttack to examine how robust the LLMs are when they encounter noisy prompts that contain extra noise in the form of punctuation marks. While being easy to implement, ArithmAttack does not cause any information loss since words are not added or deleted from the context. We evaluate the robustness of seven LLMs, including LLama3, Mistral, and Mathstral, on noisy GSM8K and MultiArith datasets. Our experiments suggest that all the studied models show vulnerability to such noise, with more noise leading to poorer performances.
The rapid advancements in Vision-Language Models (VLMs) have shown great potential in tackling mathematical reasoning tasks that involve visual context. Unlike humans who can reliably apply solution steps to similar problems with minor modifications, we found that SOTA VLMs like GPT-4o can consistently fail in these scenarios, revealing limitations in their mathematical reasoning capabilities. In this paper, we investigate the mathematical reasoning robustness in VLMs and evaluate how well these models perform under different variants of the same question, such as changes in visual numerical values or function graphs. While several vision-based math benchmarks have been developed to assess VLMs' problem-solving capabilities, these benchmarks contain only static sets of problems and cannot easily evaluate mathematical reasoning robustness. To fill this gap, we introduce DynaMath, a dynamic visual math benchmark designed for in-depth assessment of VLMs. DynaMath includes 501 high-quality, multi-topic seed questions, each represented as a Python program. Those programs are carefully designed and annotated to enable the automatic generation of a much larger set of concrete questions, including many different types of visual and textual variations. DynaMath allows us to evaluate the generalization ability of VLMs, by assessing their performance under varying input conditions of a seed question. We evaluated 14 SOTA VLMs with 5,010 generated concrete questions. Our results show that the worst-case model accuracy, defined as the percentage of correctly answered seed questions in all 10 variants, is significantly lower than the average-case accuracy. Our analysis emphasizes the need to study the robustness of VLMs' reasoning abilities, and DynaMath provides valuable insights to guide the development of more reliable models for mathematical reasoning.
Language model (LM) post-training relies on two stages of human supervision: task demonstrations for supervised finetuning (SFT), followed by preference comparisons for reinforcement learning from human feedback (RLHF). As LMs become more capable, the tasks they are given become harder to supervise. Will post-training remain effective under unreliable supervision? To test this, we simulate unreliable demonstrations and comparison feedback using small LMs and time-constrained humans. We find that in the presence of unreliable supervision, SFT still retains some effectiveness, but DPO (a common RLHF algorithm) fails to improve the model beyond SFT. To address this, we propose iterative label refinement (ILR) as an alternative to RLHF. ILR improves the SFT data by using comparison feedback to decide whether human demonstrations should be replaced by model-generated alternatives, then retrains the model via SFT on the updated data. SFT+ILR outperforms SFT+DPO on several tasks with unreliable supervision (math, coding, and safe instruction-following). Our findings suggest that as LMs are used for complex tasks where human supervision is unreliable, RLHF may no longer be the best use of human comparison feedback; instead, it is better to direct feedback towards improving the training data rather than continually training the model. Our code and data are available at https://github.com/helloelwin/iterative-label-refinement.
Current multimodal large language models (MLLMs) often underperform on mathematical problem-solving tasks that require fine-grained visual understanding. The limitation is largely attributable to inadequate perception of geometric primitives during image-level contrastive pre-training (e.g., CLIP). While recent efforts to improve math MLLMs have focused on scaling up mathematical visual instruction datasets and employing stronger LLM backbones, they often overlook persistent errors in visual recognition. In this paper, we systematically evaluate the visual grounding capabilities of state-of-the-art MLLMs and reveal a significant negative correlation between visual grounding accuracy and problem-solving performance, underscoring the critical role of fine-grained visual understanding. Notably, advanced models like GPT-4o exhibit a 70% error rate when identifying geometric entities, highlighting that this remains a key bottleneck in visual mathematical reasoning. To address this, we propose a novel approach, SVE-Math (Selective Vision-Enhanced Mathematical MLLM), featuring a geometric-grounded vision encoder and a feature router that dynamically adjusts the contribution of hierarchical visual feature maps. Our model recognizes accurate visual primitives and generates precise visual prompts tailored to the language model's reasoning needs. In experiments, SVE-Math-Qwen2.5-7B outperforms other 7B models by 15% on MathVerse and is compatible with GPT-4V on MathVista. Despite being trained on smaller datasets, SVE-Math-7B achieves competitive performance on GeoQA, rivaling models trained on significantly larger datasets. Our findings emphasize the importance of incorporating fine-grained visual understanding into MLLMs and provide a promising direction for future research.
Recent advancements in Vision-Language Models (VLMs) have opened new possibilities in automatic grading of handwritten student responses, particularly in mathematics. However, a comprehensive study to test the ability of VLMs to evaluate and reason over handwritten content remains absent. To address this gap, we introduce FERMAT, a benchmark designed to assess the ability of VLMs to detect, localize and correct errors in handwritten mathematical content. FERMAT spans four key error dimensions - computational, conceptual, notational, and presentation - and comprises over 2,200 handwritten math solutions derived from 609 manually curated problems from grades 7-12 with intentionally introduced perturbations. Using FERMAT we benchmark nine VLMs across three tasks: error detection, localization, and correction. Our results reveal significant shortcomings in current VLMs in reasoning over handwritten text, with Gemini-1.5-Pro achieving the highest error correction rate (77%). We also observed that some models struggle with processing handwritten content, as their accuracy improves when handwritten inputs are replaced with printed text or images. These findings highlight the limitations of current VLMs and reveal new avenues for improvement. We release FERMAT and all the associated resources in the open-source to drive further research.
As the usage of large language models for problems outside of simple text understanding or generation increases, assessing their abilities and limitations becomes crucial. While significant progress has been made in this area over the last few years, most research has focused on benchmarking English, leaving other languages underexplored. This makes evaluating the reasoning and robustness level of language models in Ukrainian particularly challenging. The purpose of this work is to establish a comprehensive benchmark for the reasoning capabilities evaluation of large language models in the Ukrainian language. This paper presents the ZNO-Eval benchmark based on real exam tasks from Ukraine's standardized educational testing system: the External Independent Evaluation and the National Multi-subject Test. With single-answer options, multiple-choice, matching, and open-ended questions from diverse subjects, including Ukrainian language, mathematics, history, and geography, this dataset paves the way toward a thorough analysis of reasoning capabilities across different domains and complexities. Evaluation of several well-known language models, such as GPT-3.5-Turbo, GPT-4o, GPT-4-Turbo, Mistral Large, Claude 3 Opus, and Gemini-1.5 Pro on this benchmark demonstrated the superiority of GPT-4o in both common knowledge reasoning and intricate language tasks. At the same time, Gemini Pro and GPT-4 Turbo excelled in the arithmetic domain, leading in single-answer and open-ended math problems. While all models were close to max performance in text-only common knowledge tasks like history and geography, there still is a gap for Ukrainian language and math, thus highlighting the importance of developing specialized language benchmarks for more accurate assessments of model capabilities and limitations across different languages and contexts.
Efficient Multimodal Large Language Models (EMLLMs) have rapidly advanced recently. Incorporating Chain-of-Thought (CoT) reasoning and step-by-step self-evaluation has improved their performance. However, limited parameters often hinder EMLLMs from effectively using self-evaluation during inference. Key challenges include synthesizing evaluation data, determining its quantity, optimizing training and inference strategies, and selecting appropriate prompts. To address these issues, we introduce Self-Evaluation Augmented Training (SEAT). SEAT uses more powerful EMLLMs for CoT reasoning, data selection, and evaluation generation, then trains EMLLMs with the synthesized data. However, handling long prompts and maintaining CoT reasoning quality are problematic. Therefore, we propose Cascaded Self-Evaluation Augmented Training (Cas-SEAT), which breaks down lengthy prompts into shorter, task-specific cascaded prompts and reduces costs for resource-limited settings. During data synthesis, we employ open-source 7B-parameter EMLLMs and annotate a small dataset with short prompts. Experiments demonstrate that Cas-SEAT significantly boosts EMLLMs' self-evaluation abilities, improving performance by 19.68%, 55.57%, and 46.79% on the MathVista, Math-V, and We-Math datasets, respectively. Additionally, our Cas-SEAT Dataset serves as a valuable resource for future research in enhancing EMLLM self-evaluation.
The rapid advancement of large language models (LLMs) has led to significant improvements in their capabilities, but also to increased concerns about their alignment with human values and intentions. Current alignment strategies, including adaptive training and inference-time methods, have demonstrated potential in this area. However, these approaches still struggle to balance deployment complexity and capability across various tasks and difficulties. In this work, we introduce the Streaming Distribution Induce Aligner (Stream Aligner), a novel alignment paradigm that combines efficiency with enhanced performance in various tasks throughout the generation process. Stream Aligner achieves dynamic sentence-level correction by using a small model to learn the preferences of the suffix sentence, iteratively correcting the suffix sentence output by the upstream model, and then using the corrected sentence to replace the suffix sentence in subsequent generations. Compared to Aligner, our experiments demonstrate that Stream Aligner reduces reliance on the capabilities of additional models, enhances the reasoning abilities of LLMs, and decreases latency during user interaction. Specifically, Stream Aligner-2B model has achieved an improvement of 76.1% in helpfulness, 36.0% in harmlessness on the tested Llama2-70B-chat model, and Stream Aligner-8B has achieved an improvement of 3.5% on the math ability of the tested Llama3-70B-Instruct model.
Case-based reasoning (CBR) is an experience-based approach to problem solving, where a repository of solved cases is adapted to solve new cases. Recent research shows that Large Language Models (LLMs) with Retrieval-Augmented Generation (RAG) can support the Retrieve and Reuse stages of the CBR pipeline by retrieving similar cases and using them as additional context to an LLM query. Most studies have focused on text-only applications, however, in many real-world problems the components of a case are multimodal. In this paper we present MCBR-RAG, a general RAG framework for multimodal CBR applications. The MCBR-RAG framework converts non-text case components into text-based representations, allowing it to: 1) learn application-specific latent representations that can be indexed for retrieval, and 2) enrich the query provided to the LLM by incorporating all case components for better context. We demonstrate MCBR-RAG's effectiveness through experiments conducted on a simplified Math-24 application and a more complex Backgammon application. Our empirical results show that MCBR-RAG improves generation quality compared to a baseline LLM with no contextual information provided.
We present rStar-Math to demonstrate that small language models (SLMs) can rival or even surpass the math reasoning capability of OpenAI o1, without distillation from superior models. rStar-Math achieves this by exercising "deep thinking" through Monte Carlo Tree Search (MCTS), where a math policy SLM performs test-time search guided by an SLM-based process reward model. rStar-Math introduces three innovations to tackle the challenges in training the two SLMs: (1) a novel code-augmented CoT data sythesis method, which performs extensive MCTS rollouts to generate step-by-step verified reasoning trajectories used to train the policy SLM; (2) a novel process reward model training method that avoids na\"ive step-level score annotation, yielding a more effective process preference model (PPM); (3) a self-evolution recipe in which the policy SLM and PPM are built from scratch and iteratively evolved to improve reasoning capabilities. Through 4 rounds of self-evolution with millions of synthesized solutions for 747k math problems, rStar-Math boosts SLMs' math reasoning to state-of-the-art levels. On the MATH benchmark, it improves Qwen2.5-Math-7B from 58.8% to 90.0% and Phi3-mini-3.8B from 41.4% to 86.4%, surpassing o1-preview by +4.5% and +0.9%. On the USA Math Olympiad (AIME), rStar-Math solves an average of 53.3% (8/15) of problems, ranking among the top 20% the brightest high school math students. Code and data will be available at https://github.com/microsoft/rStar.
This work introduces systematic approach for enhancing large language models (LLMs) to address Bangla AI mathematical challenges. Through the assessment of diverse LLM configurations, fine-tuning with specific datasets, and the implementation of Retrieval-Augmented Generation (RAG), we enhanced the model's reasoning precision in a multilingual setting. Crucial discoveries indicate that customized prompting, dataset augmentation, and iterative reasoning improve the model's efficiency regarding Olympiad-level mathematical challenges.
Chain-of-Thought (CoT) reasoning is widely used to enhance the mathematical reasoning capabilities of large language models (LLMs). The introduction of process supervision for CoT trajectories has sparked discussions on improving test-time scaling, thereby unlocking the System 2-style thinking capabilities of these models. However, in multimodal mathematical reasoning, the scarcity of high-quality CoT training data has hindered existing models from achieving both deliberate reasoning and fine-grained verification. In this work, we propose a novel framework that introduces System 2-style thinking to multimodal mathematical reasoning. We introduce a three-module CoT data synthesis process that integrates CoT distillation, trajectory-format rewriting, and format unification. This process generates MMathCoT-1M, a high-quality CoT reasoning instruction fine-tuning dataset. Furthermore, we implement a dual-view trajectory labeling automation that targets both visual grounding fidelity and deductive chain validity, resulting in the DualMath-1.1M dataset. The URSA-8B model, trained on MMathCoT-1M, achieves new state-of-the-art (SOTA) performance among similarly sized multimodal LLMs on six popular reasoning benchmarks. Training URSA-8B further on the DualMath-1.1M dataset yields URSA-RM-8B, a verifier that enhances URSA-8B's test-time performance and surpasses strong closed-source multimodal MLLMs like GPT-4o. The model weights, training data, and code have been open-sourced: https://github.com/URSA-MATH/URSA-MATH.
Math Word Problem (MWP) solving is a critical task in natural language processing, has garnered significant research interest in recent years. Various recent studies heavily rely on Seq2Seq models and their extensions (e.g., Seq2Tree and Graph2Tree) to generate mathematical equations. While effective, these models struggle to generate diverse but counterpart solution equations, limiting their generalization across various math problem scenarios. In this paper, we introduce a novel Diversity-enhanced Knowledge Distillation (DivKD) model for practical MWP solving. Our approach proposes an adaptive diversity distillation method, in which a student model learns diverse equations by selectively transferring high-quality knowledge from a teacher model. Additionally, we design a diversity prior-enhanced student model to better capture the diversity distribution of equations by incorporating a conditional variational auto-encoder. Extensive experiments on {four} MWP benchmark datasets demonstrate that our approach achieves higher answer accuracy than strong baselines while maintaining high efficiency for practical applications.
Large language models (LLMs) demonstrate exceptional performance on complex reasoning tasks. However, despite their strong reasoning capabilities in high-resource languages (e.g., English and Chinese), a significant performance gap persists in other languages. To investigate this gap in Korean, we introduce HRM8K, a benchmark comprising 8,011 English-Korean parallel bilingual math problems. Through systematic analysis of model behaviors, we identify a key finding: these performance disparities stem primarily from difficulties in comprehending non-English inputs, rather than limitations in reasoning capabilities. Based on these findings, we propose UST (Understand, Solve, and Translate), a method that strategically uses English as an anchor for reasoning and solution generation. By fine-tuning the model on 130k synthetically generated data points, UST achieves a 10.91% improvement on the HRM8K benchmark and reduces the multilingual performance gap from 11.6% to 0.7%. Additionally, we show that improvements from UST generalize effectively to different Korean domains, demonstrating that capabilities acquired from machine-verifiable content can be generalized to other areas. We publicly release the benchmark, training dataset, and models.
With the rapid scaling of large language models (LLMs), structured pruning has become a widely used technique to learn efficient, smaller models from larger ones, delivering superior performance compared to training similarly sized models from scratch. In this paper, we move beyond the traditional static pruning approach of determining a fixed pruning mask for a model, and propose a dynamic approach to structured pruning. In our method, the pruning mask is input-dependent and adapts dynamically based on the information described in a user instruction. Our approach, termed "instruction-following pruning", introduces a sparse mask predictor that takes the user instruction as input and dynamically selects the most relevant model parameters for the given task. To identify and activate effective parameters, we jointly optimize the sparse mask predictor and the LLM, leveraging both instruction-following data and the pre-training corpus. Experimental results demonstrate the effectiveness of our approach on a wide range of evaluation benchmarks. For example, our 3B activated model improves over the 3B dense model by 5-8 points of absolute margin on domains such as math and coding, and rivals the performance of a 9B model.
Due to the rapid advancements in multimodal large language models, evaluating their multimodal mathematical capabilities continues to receive wide attention. Despite the datasets like MathVista proposed benchmarks for assessing mathematical capabilities in multimodal scenarios, there is still a lack of corresponding evaluation tools and datasets for fine-grained assessment in the context of K12 education in Chinese language. To systematically evaluate the capability of multimodal large models in solving Chinese multimodal mathematical problems, we propose a Chinese Multi-modal Math Skill Evaluation Benchmark, named CMMaTH, contraining 23k multimodal K12 math related questions, forming the largest Chinese multimodal mathematical problem benchmark to date. CMMaTH questions from elementary to high school levels, provide increased diversity in problem types, solution objectives, visual elements, detailed knowledge points, and standard solution annotations. We have constructed an open-source tool GradeGPT integrated with the CMMaTH dataset, facilitating stable, rapid, and cost-free model evaluation. Our data and code are available.
Large Language Models (LLMs) have demonstrated strong performance across various reasoning tasks, yet building a single model that consistently excels across all domains remains challenging. This paper addresses this problem by exploring strategies to integrate multiple domain-specialized models into an efficient pivot model.We propose two fusion strategies to combine the strengths of multiple LLMs: (1) a pairwise, multi-step fusion approach that sequentially distills each source model into the pivot model, followed by a weight merging step to integrate the distilled models into the final model. This method achieves strong performance but requires substantial training effort; and (2) a unified fusion approach that aggregates all source models' outputs simultaneously.To improve the fusion process, we introduce a novel Rate-Skewness Adaptive Fusion (RSAF) technique, which dynamically adjusts top-K ratios during parameter merging for enhanced flexibility and stability.Furthermore, we propose an uncertainty-based weighting method for the unified approach, which dynamically balances the contributions of source models and outperforms other logits/distribution ensemble methods.We achieved accuracy improvements of 9.27%, 8.80%, and 8.89% on the GSM8K, MATH, and HumanEval tasks, respectively.