Daily Papers

This paper explores the limits of the current generation of large language models for program synthesis in general purpose programming languages. We evaluate a collection of such models (with between 244M and 137B parameters) on two new benchmarks, MBPP and MathQA-Python, in both the few-shot and fine-tuning regimes. Our benchmarks are designed to measure the ability of these models to synthesize short Python programs from natural language descriptions. The Mostly Basic Programming Problems (MBPP) dataset contains 974 programming tasks, designed to be solvable by entry-level programmers. The MathQA-Python dataset, a Python version of the MathQA benchmark, contains 23914 problems that evaluate the ability of the models to synthesize code from more complex text. On both datasets, we find that synthesis performance scales log-linearly with model size. Our largest models, even without finetuning on a code dataset, can synthesize solutions to 59.6 percent of the problems from MBPP using few-shot learning with a well-designed prompt. Fine-tuning on a held-out portion of the dataset improves performance by about 10 percentage points across most model sizes. On the MathQA-Python dataset, the largest fine-tuned model achieves 83.8 percent accuracy. Going further, we study the model's ability to engage in dialog about code, incorporating human feedback to improve its solutions. We find that natural language feedback from a human halves the error rate compared to the model's initial prediction. Additionally, we conduct an error analysis to shed light on where these models fall short and what types of programs are most difficult to generate. Finally, we explore the semantic grounding of these models by fine-tuning them to predict the results of program execution. We find that even our best models are generally unable to predict the output of a program given a specific input.

We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either relatively small in scale or did not offer precise operational annotations over diverse problem types. We introduce a new representation language to model precise operation programs corresponding to each math problem that aim to improve both the performance and the interpretability of the learned models. Using this representation language, our new dataset, MathQA, significantly enhances the AQuA dataset with fully-specified operational programs. We additionally introduce a neural sequence-to-program model enhanced with automatic problem categorization. Our experiments show improvements over competitive baselines in our MathQA as well as the AQuA dataset. The results are still significantly lower than human performance indicating that the dataset poses new challenges for future research. Our dataset is available at: https://math-qa.github.io/math-QA/

The recent LLMs like GPT-4 and PaLM-2 have made tremendous progress in solving fundamental math problems like GSM8K by achieving over 90\% accuracy. However, their capabilities to solve more challenging math problems which require domain-specific knowledge (i.e. theorem) have yet to be investigated. In this paper, we introduce TheoremQA, the first theorem-driven question-answering dataset designed to evaluate AI models' capabilities to apply theorems to solve challenging science problems. \dataset is curated by domain experts containing 800 high-quality questions covering 350 theoremse.g. Taylor's theorem, Lagrange's theorem, Huffman coding, Quantum Theorem, Elasticity Theorem, etc from Math, Physics, EE\&CS, and Finance. We evaluate a wide spectrum of 16 large language and code models with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. We found that GPT-4's capabilities to solve these problems are unparalleled, achieving an accuracy of 51\% with Program-of-Thoughts Prompting. All the existing open-sourced models are below 15\%, barely surpassing the random-guess baseline. Given the diversity and broad coverage of \dataset, we believe it can be used as a better benchmark to evaluate LLMs' capabilities to solve challenging science problems. The data and code are released in https://github.com/wenhuchen/TheoremQA.

Large Language Models (LLMs) have recently achieved remarkable progress in mathematical reasoning. To enable such capabilities, many existing works distill strong reasoning models into long chains of thought or design algorithms to construct high-quality math QA data for training. However, these efforts primarily focus on generating correct reasoning paths and answers, while largely overlooking the validity of the questions themselves. In this work, we propose Math Question Verification (MathQ-Verify), a novel five-stage pipeline designed to rigorously filter ill-posed or under-specified math problems. MathQ-Verify first performs format-level validation to remove redundant instructions and ensure that each question is syntactically well-formed. It then formalizes each question, decomposes it into atomic conditions, and verifies them against mathematical definitions. Next, it detects logical contradictions among these conditions, followed by a goal-oriented completeness check to ensure the question provides sufficient information for solving. To evaluate this task, we use existing benchmarks along with an additional dataset we construct, containing 2,147 math questions with diverse error types, each manually double-validated. Experiments show that MathQ-Verify achieves state-of-the-art performance across multiple benchmarks, improving the F1 score by up to 25 percentage points over the direct verification baseline. It further attains approximately 90% precision and 63% recall through a lightweight model voting scheme. MathQ-Verify offers a scalable and accurate solution for curating reliable mathematical datasets, reducing label noise and avoiding unnecessary computation on invalid questions. Our code and data are available at https://github.com/scuuy/MathQ-Verify.

While question answering over knowledge bases (KBQA) has shown progress in addressing factoid questions, KBQA with numerical reasoning remains relatively unexplored. In this paper, we focus on the complex numerical reasoning in KBQA and propose a new task, NR-KBQA, which necessitates the ability to perform both multi-hop reasoning and numerical reasoning. We design a logic form in Python format called PyQL to represent the reasoning process of numerical reasoning questions. To facilitate the development of NR-KBQA, we present a large dataset called MarkQA, which is automatically constructed from a small set of seeds. Each question in MarkQA is equipped with its corresponding SPARQL query, alongside the step-by-step reasoning process in the QDMR format and PyQL program. Experimental results of some state-of-the-art QA methods on the MarkQA show that complex numerical reasoning in KBQA faces great challenges.

We investigate the mathematical capabilities of ChatGPT by testing it on publicly available datasets, as well as hand-crafted ones, and measuring its performance against other models trained on a mathematical corpus, such as Minerva. We also test whether ChatGPT can be a useful assistant to professional mathematicians by emulating various use cases that come up in the daily professional activities of mathematicians (question answering, theorem searching). In contrast to formal mathematics, where large databases of formal proofs are available (e.g., the Lean Mathematical Library), current datasets of natural-language mathematics, used to benchmark language models, only cover elementary mathematics. We address this issue by introducing a new dataset: GHOSTS. It is the first natural-language dataset made and curated by working researchers in mathematics that (1) aims to cover graduate-level mathematics and (2) provides a holistic overview of the mathematical capabilities of language models. We benchmark ChatGPT on GHOSTS and evaluate performance against fine-grained criteria. We make this new dataset publicly available to assist a community-driven comparison of ChatGPT with (future) large language models in terms of advanced mathematical comprehension. We conclude that contrary to many positive reports in the media (a potential case of selection bias), ChatGPT's mathematical abilities are significantly below those of an average mathematics graduate student. Our results show that ChatGPT often understands the question but fails to provide correct solutions. Hence, if your goal is to use it to pass a university exam, you would be better off copying from your average peer!

Code has been shown to be effective in enhancing the mathematical reasoning abilities of large language models due to its precision and accuracy. Previous works involving continued mathematical pretraining often include code that utilizes math-related packages, which are primarily designed for fields such as engineering, machine learning, signal processing, or module testing, rather than being directly focused on mathematical reasoning. In this paper, we introduce a novel method for generating mathematical code accompanied with corresponding reasoning steps for continued pretraining. Our approach begins with the construction of a high-quality mathematical continued pretraining dataset by incorporating math-related web data, code using mathematical packages, math textbooks, and synthetic data. Next, we construct reasoning steps by extracting LaTeX expressions, the conditions needed for the expressions, and the results of the expressions from the previously collected dataset. Based on this extracted information, we generate corresponding code to accurately capture the mathematical reasoning process. Appending the generated code to each reasoning step results in data consisting of paired natural language reasoning steps and their corresponding code. Combining this data with the original dataset results in a 19.2B-token high-performing mathematical pretraining corpus, which we name MathCode-Pile. Training several popular base models with this corpus significantly improves their mathematical abilities, leading to the creation of the MathCoder2 family of models. All of our data processing and training code is open-sourced, ensuring full transparency and easy reproducibility of the entire data collection and training pipeline. The code is released at https://github.com/mathllm/MathCoder2 .

We present lambeq, the first high-level Python library for Quantum Natural Language Processing (QNLP). The open-source toolkit offers a detailed hierarchy of modules and classes implementing all stages of a pipeline for converting sentences to string diagrams, tensor networks, and quantum circuits ready to be used on a quantum computer. lambeq supports syntactic parsing, rewriting and simplification of string diagrams, ansatz creation and manipulation, as well as a number of compositional models for preparing quantum-friendly representations of sentences, employing various degrees of syntax sensitivity. We present the generic architecture and describe the most important modules in detail, demonstrating the usage with illustrative examples. Further, we test the toolkit in practice by using it to perform a number of experiments on simple NLP tasks, implementing both classical and quantum pipelines.

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.

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a distinctive challenge, primarily due to its specialized structure and the precision it demands. In this study, we adopted a two-step approach for investigating the proficiency of LLMs in answering mathematical questions. First, we employ the most effective LLMs, as identified by their performance on math question-answer benchmarks, to generate answers to 78 questions from the Math Stack Exchange (MSE). Second, a case analysis is conducted on the LLM that showed the highest performance, focusing on the quality and accuracy of its answers through manual evaluation. We found that GPT-4 performs best (nDCG of 0.48 and P@10 of 0.37) amongst existing LLMs fine-tuned for answering mathematics questions and outperforms the current best approach on ArqMATH3 Task1, considering P@10. Our Case analysis indicates that while the GPT-4 can generate relevant responses in certain instances, it does not consistently answer all questions accurately. This paper explores the current limitations of LLMs in navigating complex mathematical problem-solving. Through case analysis, we shed light on the gaps in LLM capabilities within mathematics, thereby setting the stage for future research and advancements in AI-driven mathematical reasoning. We make our code and findings publicly available for research: https://github.com/gipplab/LLM-Investig-MathStackExchange

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

We publicly release a new large-scale dataset, called SearchQA, for machine comprehension, or question-answering. Unlike recently released datasets, such as DeepMind CNN/DailyMail and SQuAD, the proposed SearchQA was constructed to reflect a full pipeline of general question-answering. That is, we start not from an existing article and generate a question-answer pair, but start from an existing question-answer pair, crawled from J! Archive, and augment it with text snippets retrieved by Google. Following this approach, we built SearchQA, which consists of more than 140k question-answer pairs with each pair having 49.6 snippets on average. Each question-answer-context tuple of the SearchQA comes with additional meta-data such as the snippet's URL, which we believe will be valuable resources for future research. We conduct human evaluation as well as test two baseline methods, one simple word selection and the other deep learning based, on the SearchQA. We show that there is a meaningful gap between the human and machine performances. This suggests that the proposed dataset could well serve as a benchmark for question-answering.

We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH benchmark Llemma outperforms all known open base models, as well as the unreleased Minerva model suite on an equi-parameter basis. Moreover, Llemma is capable of tool use and formal theorem proving without any further finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

We demonstrate that a neural network pre-trained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates new questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a new dataset of questions from MIT's largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pre-trained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8% to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work is the first to automatically solve university-level mathematics course questions at a human level and the first work to explain and generate university-level mathematics course questions at scale, a milestone for higher education.

We present AlphaGeometry2, a significantly improved version of AlphaGeometry introduced in Trinh et al. (2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend the original AlphaGeometry language to tackle harder problems involving movements of objects, and problems containing linear equations of angles, ratios, and distances. This, together with other additions, has markedly improved the coverage rate of the AlphaGeometry language on International Math Olympiads (IMO) 2000-2024 geometry problems from 66% to 88%. The search process of AlphaGeometry2 has also been greatly improved through the use of Gemini architecture for better language modeling, and a novel knowledge-sharing mechanism that combines multiple search trees. Together with further enhancements to the symbolic engine and synthetic data generation, we have significantly boosted the overall solving rate of AlphaGeometry2 to 84% for all geometry problems over the last 25 years, compared to 54% previously. AlphaGeometry2 was also part of the system that achieved silver-medal standard at IMO 2024 https://dpmd.ai/imo-silver. Last but not least, we report progress towards using AlphaGeometry2 as a part of a fully automated system that reliably solves geometry problems directly from natural language input.

The tool-use Large Language Models (LLMs) that integrate with external Python interpreters have significantly enhanced mathematical reasoning capabilities for open-source LLMs, while tool-free methods chose another track: augmenting math reasoning data. However, a great method to integrate the above two research paths and combine their advantages remains to be explored. In this work, we firstly include new math questions via multi-perspective data augmenting methods and then synthesize code-nested solutions to them. The open LLMs (i.e., Llama-2) are finetuned on the augmented dataset to get the resulting models, MuMath-Code (mu-Math-Code). During the inference phase, our MuMath-Code generates code and interacts with the external python interpreter to get the execution results. Therefore, MuMath-Code leverages the advantages of both the external tool and data augmentation. To fully leverage the advantages of our augmented data, we propose a two-stage training strategy: In Stage-1, we finetune Llama-2 on pure CoT data to get an intermediate model, which then is trained on the code-nested data in Stage-2 to get the resulting MuMath-Code. Our MuMath-Code-7B achieves 83.8 on GSM8K and 52.4 on MATH, while MuMath-Code-70B model achieves new state-of-the-art performance among open methods -- achieving 90.7% on GSM8K and 55.1% on MATH. Extensive experiments validate the combination of tool use and data augmentation, as well as our two-stage training strategy. We release the proposed dataset along with the associated code for public use.

Mathematical reasoning is a cornerstone of human intelligence and a key benchmark for advanced capabilities in large language models (LLMs). However, the research community still lacks an open, large-scale, high-quality corpus tailored to the demands of math-centric LLM pre-training. We present MegaMath, an open dataset curated from diverse, math-focused sources through following practices: (1) Revisiting web data: We re-extracted mathematical documents from Common Crawl with math-oriented HTML optimizations, fasttext-based filtering and deduplication, all for acquiring higher-quality data on the Internet. (2) Recalling Math-related code data: We identified high quality math-related code from large code training corpus, Stack-V2, further enhancing data diversity. (3) Exploring Synthetic data: We synthesized QA-style text, math-related code, and interleaved text-code blocks from web data or code data. By integrating these strategies and validating their effectiveness through extensive ablations, MegaMath delivers 371B tokens with the largest quantity and top quality among existing open math pre-training datasets.

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (\eg, LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called {MetaMathQA}. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (\ie, GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, {MetaMath-70B} achieves an accuracy of 82.3% on {GSM8K}, slightly better than {GPT-3.5-Turbo}. We release the {MetaMathQA} dataset, the {MetaMath} models with different model sizes and the training code for public use.

A riddle is a question or statement with double or veiled meanings, followed by an unexpected answer. Solving riddle is a challenging task for both machine and human, testing the capability of understanding figurative, creative natural language and reasoning with commonsense knowledge. We introduce BiRdQA, a bilingual multiple-choice question answering dataset with 6614 English riddles and 8751 Chinese riddles. For each riddle-answer pair, we provide four distractors with additional information from Wikipedia. The distractors are automatically generated at scale with minimal bias. Existing monolingual and multilingual QA models fail to perform well on our dataset, indicating that there is a long way to go before machine can beat human on solving tricky riddles. The dataset has been released to the community.

We present a framework that formulates visual question answering as modular code generation. In contrast to prior work on modular approaches to VQA, our approach requires no additional training and relies on pre-trained language models (LMs), visual models pre-trained on image-caption pairs, and fifty VQA examples used for in-context learning. The generated Python programs invoke and compose the outputs of the visual models using arithmetic and conditional logic. Our approach improves accuracy on the COVR dataset by at least 3% and on the GQA dataset by roughly 2% compared to the few-shot baseline that does not employ code generation.

Despite recent progress in improving the mathematical reasoning ability of large language models(LLMs), solving competition-level math problems without the use of external tools remains challenging for open-source LLMs. In this work, we introduce the MMIQC dataset, a mixture of processed web data and synthetic question-response pairs, to equip base models with better mathematical reasoning skills. Mistral-7B-MMIQC, the model obtained by fine-tuning Mistral-7B(arXiv:2310.06825) on MMIQC, achieves 36.0\% accuracy on MATH(arXiv:2103.03874), 5.8\% higher than the previous (model size sim7B) SOTA. Our experiments also show that a large part of the improvement attributes to our novel augmentation method IQC(Iterative Question Composing), where we iteratively ask an LLM to compose new questions from the given seed problems and do rejection sampling from another LLM. MMIQC has now been released on https://huggingface.co/datasets/Vivacem/MMIQC.

Large language models (LLMs) such as ChatGPT have received immense interest for their general-purpose language understanding and, in particular, their ability to generate high-quality text or computer code. For many professions, LLMs represent an invaluable tool that can speed up and improve the quality of work. In this note, we discuss to what extent they can aid professional mathematicians. We first provide a mathematical description of the transformer model used in all modern language models. Based on recent studies, we then outline best practices and potential issues and report on the mathematical abilities of language models. Finally, we shed light on the potential of LMMs to change how mathematicians work.

Large language models have demonstrated impressive capabilities across various natural language processing tasks, especially in solving mathematical problems. However, large language models are not good at math theorem proving using formal languages like Lean. A significant challenge in this area is the scarcity of training data available in these formal languages. To address this issue, we propose a novel pipeline that iteratively generates and filters synthetic data to translate natural language mathematical problems into Lean 4 statements, and vice versa. Our results indicate that the synthetic data pipeline can provide useful training data and improve the performance of LLMs in translating and understanding complex mathematical problems and proofs. Our final dataset contains about 57K formal-informal question pairs along with searched proof from the math contest forum and 21 new IMO questions. We open-source our code at https://github.com/InternLM/InternLM-Math and our data at https://huggingface.co/datasets/InternLM/Lean-Workbook.

This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the necessary math where needed. Note that you do not need to understand this material before you start learning to train and use deep learning in practice; rather, this material is for those who are already familiar with the basics of neural networks, and wish to deepen their understanding of the underlying math. Don't worry if you get stuck at some point along the way---just go back and reread the previous section, and try writing down and working through some examples. And if you're still stuck, we're happy to answer your questions in the Theory category at forums.fast.ai. Note: There is a reference section at the end of the paper summarizing all the key matrix calculus rules and terminology discussed here. See related articles at http://explained.ai

Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical reasoning skills. Existing approaches to address this challenge often rely on ensemble methods and suffer from the problem of data scarcity in target domains. In this work, we present a novel method to enhance LLMs' capabilities in mathematical reasoning tasks. Motivated by the need to bridge this gap, our approach incorporates a question paraphrase strategy, which aims at diversifying the linguistic forms of mathematical questions to improve generalization. Additionally, specialized training objectives are employed to guide the model's learning process, focusing on enhancing its understanding of mathematical concepts and reasoning processes. We conduct experiments on four datasets using different LLMs, and demonstrate the effectiveness of our approach in improving LLMs' performance on mathematical reasoning tasks. Our findings underscore the significance of our methodology in the advancement of large language models and its potential implications for real-world applications that require mathematical reasoning abilities.

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.

Advances in Large Language Models (LLMs) have sparked interest in their ability to solve Olympiad-level math problems. However, the training and evaluation of these models are constrained by the limited size and quality of available datasets, as creating large-scale data for such advanced problems requires extensive effort from human experts. In addition, current benchmarks are prone to contamination, leading to unreliable evaluations. In this paper, we present an automated pipeline that leverages the rich resources of the Art of Problem Solving (AoPS) forum, which predominantly features Olympiad-level problems and community-driven solutions. Using open-source LLMs, we develop a method to extract question-answer pairs from the forum, resulting in AoPS-Instruct, a dataset of more than 600,000 high-quality QA pairs. Our experiments demonstrate that fine-tuning LLMs on AoPS-Instruct improves their reasoning abilities across various benchmarks. Moreover, we build an automatic pipeline that introduces LiveAoPSBench, an evolving evaluation set with timestamps, derived from the latest forum data, providing a contamination-resistant benchmark for assessing LLM performance. Notably, we observe a significant decline in LLM performance over time, suggesting their success on older examples may stem from pre-training exposure rather than true reasoning ability. Our work presents a scalable approach to creating and maintaining large-scale, high-quality datasets for advanced math reasoning, offering valuable insights into the capabilities and limitations of LLMs in this domain. Our benchmark and code is available at https://github.com/DSL-Lab/aops

Automatic math word problem solving has attracted growing attention in recent years. The evaluation datasets used by previous works have serious limitations in terms of scale and diversity. In this paper, we release a new large-scale and template-rich math word problem dataset named Ape210K. It consists of 210K Chinese elementary school-level math problems, which is 9 times the size of the largest public dataset Math23K. Each problem contains both the gold answer and the equations needed to derive the answer. Ape210K is also of greater diversity with 56K templates, which is 25 times more than Math23K. Our analysis shows that solving Ape210K requires not only natural language understanding but also commonsense knowledge. We expect Ape210K to be a benchmark for math word problem solving systems. Experiments indicate that state-of-the-art models on the Math23K dataset perform poorly on Ape210K. We propose a copy-augmented and feature-enriched sequence to sequence (seq2seq) model, which outperforms existing models by 3.2% on the Math23K dataset and serves as a strong baseline of the Ape210K dataset. The gap is still significant between human and our baseline model, calling for further research efforts. We make Ape210K dataset publicly available at https://github.com/yuantiku/ape210k

The art of mathematical reasoning stands as a fundamental pillar of intellectual progress and is a central catalyst in cultivating human ingenuity. Researchers have recently published a plethora of works centered around the task of solving Math Word Problems (MWP) - a crucial stride towards general AI. These existing models are susceptible to dependency on shallow heuristics and spurious correlations to derive the solution expressions. In order to ameliorate this issue, in this paper, we propose a framework for MWP solvers based on the generation of linguistic variants of the problem text. The approach involves solving each of the variant problems and electing the predicted expression with the majority of the votes. We use DeBERTa (Decoding-enhanced BERT with disentangled attention) as the encoder to leverage its rich textual representations and enhanced mask decoder to construct the solution expressions. Furthermore, we introduce a challenging dataset, Psmall{ARAMAWPS}, consisting of paraphrased, adversarial, and inverse variants of selectively sampled MWPs from the benchmark Msmall{AWPS} dataset. We extensively experiment on this dataset along with other benchmark datasets using some baseline MWP solver models. We show that training on linguistic variants of problem statements and voting on candidate predictions improve the mathematical reasoning and robustness of the model. We make our code and data publicly available.

Mathematical questioning is crucial for assessing students problem-solving skills. Since manually creating such questions requires substantial effort, automatic methods have been explored. Existing state-of-the-art models rely on fine-tuning strategies and struggle to generate questions that heavily involve multiple steps of logical and arithmetic reasoning. Meanwhile, large language models(LLMs) such as ChatGPT have excelled in many NLP tasks involving logical and arithmetic reasoning. Nonetheless, their applications in generating educational questions are underutilized, especially in the field of mathematics. To bridge this gap, we take the first step to conduct an in-depth analysis of ChatGPT in generating pre-university math questions. Our analysis is categorized into two main settings: context-aware and context-unaware. In the context-aware setting, we evaluate ChatGPT on existing math question-answering benchmarks covering elementary, secondary, and ternary classes. In the context-unaware setting, we evaluate ChatGPT in generating math questions for each lesson from pre-university math curriculums that we crawl. Our crawling results in TopicMath, a comprehensive and novel collection of pre-university math curriculums collected from 121 math topics and 428 lessons from elementary, secondary, and tertiary classes. Through this analysis, we aim to provide insight into the potential of ChatGPT as a math questioner.

In this report, we present a series of math-specific large language models: Qwen2.5-Math and Qwen2.5-Math-Instruct-1.5B/7B/72B. The core innovation of the Qwen2.5 series lies in integrating the philosophy of self-improvement throughout the entire pipeline, from pre-training and post-training to inference: (1) During the pre-training phase, Qwen2-Math-Instruct is utilized to generate large-scale, high-quality mathematical data. (2) In the post-training phase, we develop a reward model (RM) by conducting massive sampling from Qwen2-Math-Instruct. This RM is then applied to the iterative evolution of data in supervised fine-tuning (SFT). With a stronger SFT model, it's possible to iteratively train and update the RM, which in turn guides the next round of SFT data iteration. On the final SFT model, we employ the ultimate RM for reinforcement learning, resulting in the Qwen2.5-Math-Instruct. (3) Furthermore, during the inference stage, the RM is used to guide sampling, optimizing the model's performance. Qwen2.5-Math-Instruct supports both Chinese and English, and possess advanced mathematical reasoning capabilities, including Chain-of-Thought (CoT) and Tool-Integrated Reasoning (TIR). We evaluate our models on 10 mathematics datasets in both English and Chinese, such as GSM8K, MATH, GaoKao, AMC23, and AIME24, covering a range of difficulties from grade school level to math competition problems.

Understanding sentences that contain mathematical expressions in text form poses significant challenges. To address this, the importance of converting these expressions into formula images has been highlighted. For instance, the expression ``x equals minus b plus or minus the square root of b squared minus four a c, all over two a'' is more readily comprehensible when displayed as an image x = -b pm sqrt{b^2 - 4ac}{2a}. To develop a text-to-image conversion system, we can break down the process into text-to-LaTeX and LaTeX-to-image conversions, with the latter being managed with by existing various LaTeX engines. However, the former approach has been notably hindered by the severe scarcity of text-to-LaTeX paired data, presenting a significant challenge in the field.In this context, we introduce MathBridge, the first extensive dataset for translating mathematical spoken English into LaTeX, which aims to establish a robust baseline for future research in text-to-LaTeX translation. MathBridge comprises approximately 23 million LaTeX formulas paired with corresponding spoken English expressions. Through comprehensive evaluations, including fine-tuning and testing with data, we discovered that MathBridge significantly enhances pre-trained language models' capabilities for text-to-LaTeX translation. Specifically, for the T5-large model, the sacreBLEU score increased from 4.77 to 46.8, demonstrating substantial enhancement. Our findings indicate the necessity for a new metric specifically for text-to-LaTeX conversion evaluation.

Premise selection is a crucial yet challenging step in mathematical formalization, especially for users with limited experience. Due to the lack of available formalization projects, existing approaches that leverage language models often suffer from data scarcity. In this work, we introduce an innovative method for training a premise retriever to support the formalization of mathematics. Our approach employs a BERT model to embed proof states and premises into a shared latent space. The retrieval model is trained within a contrastive learning framework and incorporates a domain-specific tokenizer along with a fine-grained similarity computation method. Experimental results show that our model is highly competitive compared to existing baselines, achieving strong performance while requiring fewer computational resources. Performance is further enhanced through the integration of a re-ranking module. To streamline the formalization process, we will release a search engine that enables users to query Mathlib theorems directly using proof states, significantly improving accessibility and efficiency. Codes are available at https://github.com/ruc-ai4math/Premise-Retrieval.

EasyMath is a compact benchmark for practical math reasoning in small language models. It covers thirteen categories, from basic arithmetic and order of operations to word problems, algebraic expressions, edge cases, and omits specialist topics. We tested 23 models (14M to 4B parameters) using exact, numerical, and symbolic checks on free-form answers in a zero-shot setting. Accuracy rises with size and training, chain-of-thought adds modest gains, and consistency improves at scale.

The increasing adoption of artificial intelligence in telecommunications has raised interest in the capability of Large Language Models (LLMs) to address domain-specific, mathematically intensive tasks. Although recent advancements have improved the performance of LLMs in general mathematical reasoning, their effectiveness within specialized domains, such as signal processing, network optimization, and performance analysis, remains largely unexplored. To address this gap, we introduce TeleMath, the first benchmark dataset specifically designed to evaluate LLM performance in solving mathematical problems with numerical solutions in the telecommunications domain. Comprising 500 question-answer (QnA) pairs, TeleMath covers a wide spectrum of topics in the telecommunications field. This paper outlines the proposed QnAs generation pipeline, starting from a selected seed of problems crafted by Subject Matter Experts. The evaluation of a wide range of open-source LLMs reveals that best performance on TeleMath is achieved by recent models explicitly designed for mathematical or logical reasoning. In contrast, general-purpose models, even those with a large number of parameters, often struggle with these challenges. We have released the dataset and the evaluation code to ease result reproducibility and support future research.

Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large language models (LLMs), offering insights beyond general mathematical problem-solving. Progress in this area is hampered by existing datasets that are often scarce, synthetic, or rigidly formal. We address this by proposing an informal yet verifiable task formulation, recasting inequality proving into two automatically checkable subtasks: bound estimation and relation prediction. Building on this, we release IneqMath, an expert-curated dataset of Olympiad-level inequalities, including a test set and training corpus enriched with step-wise solutions and theorem annotations. We also develop a novel LLM-as-judge evaluation framework, combining a final-answer judge with four step-wise judges designed to detect common reasoning flaws. A systematic evaluation of 29 leading LLMs on IneqMath reveals a surprising reality: even top models like o1 achieve less than 10% overall accuracy under step-wise scrutiny; this is a drop of up to 65.5% from their accuracy considering only final answer equivalence. This discrepancy exposes fragile deductive chains and a critical gap for current LLMs between merely finding an answer and constructing a rigorous proof. Scaling model size and increasing test-time computation yield limited gains in overall proof correctness. Instead, our findings highlight promising research directions such as theorem-guided reasoning and self-refinement. Code and data are available at https://ineqmath.github.io/.

Mathematics has long been conveyed through natural language, primarily for human understanding. With the rise of mechanized mathematics and proof assistants, there is a growing need to understand informal mathematical text, yet most existing benchmarks focus solely on English, overlooking other languages. This paper introduces RoMath, a Romanian mathematical reasoning benchmark suite comprising three datasets: RoMath-Baccalaureate, RoMath-Competitions and RoMath-Synthetic, which cover a range of mathematical domains and difficulty levels, aiming to improve non-English language models and promote multilingual AI development. By focusing on Romanian, a low-resource language with unique linguistic features, RoMath addresses the limitations of Anglo-centric models and emphasizes the need for dedicated resources beyond simple automatic translation. We benchmark several open-weight language models, highlighting the importance of creating resources for underrepresented languages. We make the code and dataset available.

Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short, particularly for proof-centric problems, as manual creation is unscalable and costly, leaving the true mathematical abilities of LLMs largely unassessed. To overcome these barriers, we propose Proof2Hybrid, the first fully automated framework that synthesizes high-quality, proof-centric benchmarks from natural language mathematical corpora. The key novelty of our solution is Proof2X, a roadmap of converting mathematical proofs into various kinds of questions that are easy to verify. Instructed by this roadmap, we propose a new type of hybrid-formatted questions, named ``m-out-of-n multiple judge questions'', specifically designed to enable robust, automatic evaluation while being resilient to guessing and superficial pattern matching inherent in traditional formats. As a demonstration of our framework, we introduce AlgGeoTest, a benchmark for algebraic geometry--a frontier domain of modern mathematics--comprising 456 challenging items. Our extensive evaluations on state-of-the-art LLMs using AlgGeoTest reveal profound deficits in their comprehension of algebraic geometry, providing a more precise measure of their true mathematical capabilities. Our framework and benchmark pave the way for a new wave of in-depth research into the mathematical intelligence of AI systems.

We introduce Confucius3-Math, an open-source large language model with 14B parameters that (1) runs efficiently on a single consumer-grade GPU; (2) achieves SOTA performances on a range of mathematical reasoning tasks, outperforming many models with significantly larger sizes. In particular, as part of our mission to enhancing education and knowledge dissemination with AI, Confucius3-Math is specifically committed to mathematics learning for Chinese K-12 students and educators. Built via post-training with large-scale reinforcement learning (RL), Confucius3-Math aligns with national curriculum and excels at solving main-stream Chinese K-12 mathematical problems with low cost. In this report we share our development recipe, the challenges we encounter and the techniques we develop to overcome them. In particular, we introduce three technical innovations: Targeted Entropy Regularization, Recent Sample Recovery and Policy-Specific Hardness Weighting. These innovations encompass a new entropy regularization, a novel data scheduling policy, and an improved group-relative advantage estimator. Collectively, they significantly stabilize the RL training, improve data efficiency, and boost performance. Our work demonstrates the feasibility of building strong reasoning models in a particular domain at low cost. We open-source our model and code at https://github.com/netease-youdao/Confucius3-Math.

Tool-augmented Large Language Models (TALM) are known to enhance the skillset of large language models (LLM), thereby, leading to their improved reasoning abilities across many tasks. While, TALMs have been successfully employed in different question-answering benchmarks, their efficacy on complex mathematical reasoning benchmarks, and the potential complimentary benefits offered by tools for knowledge retrieval and mathematical equation solving, are open research questions. In this work, we present MATHSENSEI, a tool-augmented large language model for mathematical reasoning. Augmented with tools for knowledge retrieval (Bing Web Search), program execution (Python), and symbolic equation solving (Wolfram-Alpha), we study the complimentary benefits of these tools through evaluations on mathematical reasoning datasets. We perform exhaustive ablations on MATH,a popular dataset for evaluating mathematical reasoning on diverse mathematical disciplines. We also conduct experiments involving well-known tool planners to study the impact of tool sequencing on the model performance. MATHSENSEI achieves 13.5% better accuracy over gpt-3.5-turbo with chain-of-thought on the MATH dataset. We further observe that TALMs are not as effective for simpler math word problems (in GSM-8k), and the benefit increases as the complexity and required knowledge increases (progressively over AQuA, MMLU-Math, and higher level complex questions in MATH). The code and data are available at https://github.com/Debrup-61/MathSensei.

To thoroughly assess the mathematical reasoning abilities of Large Language Models (LLMs), we need to carefully curate evaluation datasets covering diverse mathematical concepts and mathematical problems at different difficulty levels. In pursuit of this objective, we propose FineMath in this paper, a fine-grained mathematical evaluation benchmark dataset for assessing Chinese LLMs. FineMath is created to cover the major key mathematical concepts taught in elementary school math, which are further divided into 17 categories of math word problems, enabling in-depth analysis of mathematical reasoning abilities of LLMs. All the 17 categories of math word problems are manually annotated with their difficulty levels according to the number of reasoning steps required to solve these problems. We conduct extensive experiments on a wide range of LLMs on FineMath and find that there is still considerable room for improvements in terms of mathematical reasoning capability of Chinese LLMs. We also carry out an in-depth analysis on the evaluation process and methods that have been overlooked previously. These two factors significantly influence the model results and our understanding of their mathematical reasoning capabilities. The dataset will be publicly available soon.

This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a large-scale dataset comprising 540K unique high-quality math problems, including olympiad-level problems, and their 3.2M long-reasoning solutions. Second, we develop a novel method to integrate code execution with long reasoning models through iterative training, generation, and quality filtering, resulting in 1.7M high-quality Tool-Integrated Reasoning solutions. Third, we create a pipeline to train models to select the most promising solution from many candidates. We show that such generative solution selection (GenSelect) can significantly improve upon majority voting baseline. Combining these ideas, we train a series of models that achieve state-of-the-art results on mathematical reasoning benchmarks. To facilitate further research, we release our code, models, and the complete OpenMathReasoning dataset under a commercially permissive license.

Recent advancements in large language models (LLMs) have showcased significant improvements in mathematics. However, traditional math benchmarks like GSM8k offer a unidimensional perspective, falling short in providing a holistic assessment of the LLMs' math capabilities. To address this gap, we introduce MathBench, a new benchmark that rigorously assesses the mathematical capabilities of large language models. MathBench spans a wide range of mathematical disciplines, offering a detailed evaluation of both theoretical understanding and practical problem-solving skills. The benchmark progresses through five distinct stages, from basic arithmetic to college mathematics, and is structured to evaluate models at various depths of knowledge. Each stage includes theoretical questions and application problems, allowing us to measure a model's mathematical proficiency and its ability to apply concepts in practical scenarios. MathBench aims to enhance the evaluation of LLMs' mathematical abilities, providing a nuanced view of their knowledge understanding levels and problem solving skills in a bilingual context. The project is released at https://github.com/open-compass/MathBench .

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.

This paper introduces a novel benchmark, EGE-Math Solutions Assessment Benchmark, for evaluating Vision-Language Models (VLMs) on their ability to assess hand-written mathematical solutions. Unlike existing benchmarks that focus on problem solving, our approach centres on understanding student solutions, identifying mistakes, and assigning grades according to fixed criteria. We compile 122 scanned solutions from the Russian Unified State Exam (EGE) together with official expert grades, and evaluate seven modern VLMs from Google, OpenAI, Arcee AI, and Alibaba Cloud in three inference modes. The results reveal current limitations in mathematical reasoning and human-rubric alignment, opening new research avenues in AI-assisted assessment. You can find code in https://github.com/Karifannaa/Auto-check-EGE-math

Recent work has shown the immense potential of synthetically generated datasets for training large language models (LLMs), especially for acquiring targeted skills. Current large-scale math instruction tuning datasets such as MetaMathQA (Yu et al., 2024) and MAmmoTH (Yue et al., 2024) are constructed using outputs from closed-source LLMs with commercially restrictive licenses. A key reason limiting the use of open-source LLMs in these data generation pipelines has been the wide gap between the mathematical skills of the best closed-source LLMs, such as GPT-4, and the best open-source LLMs. Building on the recent progress in open-source LLMs, our proposed prompting novelty, and some brute-force scaling, we construct OpenMathInstruct-1, a math instruction tuning dataset with 1.8M problem-solution pairs. The dataset is constructed by synthesizing code-interpreter solutions for GSM8K and MATH, two popular math reasoning benchmarks, using the recently released and permissively licensed Mixtral model. Our best model, OpenMath-CodeLlama-70B, trained on a subset of OpenMathInstruct-1, achieves a score of 84.6% on GSM8K and 50.7% on MATH, which is competitive with the best gpt-distilled models. We release our code, models, and the OpenMathInstruct-1 dataset under a commercially permissive license.

Quantitative reasoning is a higher-order reasoning skill that any intelligent natural language understanding system can reasonably be expected to handle. We present EQUATE (Evaluating Quantitative Understanding Aptitude in Textual Entailment), a new framework for quantitative reasoning in textual entailment. We benchmark the performance of 9 published NLI models on EQUATE, and find that on average, state-of-the-art methods do not achieve an absolute improvement over a majority-class baseline, suggesting that they do not implicitly learn to reason with quantities. We establish a new baseline Q-REAS that manipulates quantities symbolically. In comparison to the best performing NLI model, it achieves success on numerical reasoning tests (+24.2%), but has limited verbal reasoning capabilities (-8.1%). We hope our evaluation framework will support the development of models of quantitative reasoning in language understanding.

High-quality, large-scale corpora are the cornerstone of building foundation models. In this work, we introduce MathPile, a diverse and high-quality math-centric corpus comprising about 9.5 billion tokens. Throughout its creation, we adhered to the principle of ``less is more'', firmly believing in the supremacy of data quality over quantity, even in the pre-training phase. Our meticulous data collection and processing efforts included a complex suite of preprocessing, prefiltering, language identification, cleaning, filtering, and deduplication, ensuring the high quality of our corpus. Furthermore, we performed data contamination detection on downstream benchmark test sets to eliminate duplicates. We hope our MathPile can help to enhance the mathematical reasoning abilities of language models. We plan to open-source different versions of \mathpile with the scripts used for processing, to facilitate future developments in this field.

Large language models (LLMs) have seen considerable advancements in natural language understanding tasks, yet there remains a gap to bridge before attaining true artificial general intelligence, especially concerning shortcomings in mathematical reasoning capabilities. We postulate that the inherent nature of LLM training, which focuses on predicting probabilities of next token, presents challenges in effectively modeling mathematical reasoning that demands exact calculations, both from data-driven and theoretical standpoints. In this paper, we address this challenge by enriching the data landscape and introducing a novel math dataset, enhanced with a capability to utilize a Python code interpreter. This dataset is derived from GSM8K and MATH and has been further refined through a combination of GPT-4 annotations, human review, and self-training processes, where the errors in the original GSM8K training set have been fixed. Additionally, we propose a tentative, easily replicable protocol for the fine-tuning of math-specific LLMs, which has led to a significant improvement in the performance of a 7B-parameter LLM on the GSM8K and MATH datasets. We are committed to advancing the field of mathematical reasoning in LLMs and, to that end, we have made the model checkpoints and will make the dataset publicly available. We hope this will facilitate further research and development within the community.

This paper introduces MedMCQA, a new large-scale, Multiple-Choice Question Answering (MCQA) dataset designed to address real-world medical entrance exam questions. More than 194k high-quality AIIMS \& NEET PG entrance exam MCQs covering 2.4k healthcare topics and 21 medical subjects are collected with an average token length of 12.77 and high topical diversity. Each sample contains a question, correct answer(s), and other options which requires a deeper language understanding as it tests the 10+ reasoning abilities of a model across a wide range of medical subjects \& topics. A detailed explanation of the solution, along with the above information, is provided in this study.

Large language models (LLMs) have demonstrated remarkable capabilities in problem-solving. However, their proficiency in solving mathematical problems remains inadequate. We propose MathScale, a simple and scalable method to create high-quality mathematical reasoning data using frontier LLMs (e.g., {\tt GPT-3.5}). Inspired by the cognitive mechanism in human mathematical learning, it first extracts topics and knowledge points from seed math questions and then build a concept graph, which is subsequently used to generate new math questions. MathScale exhibits effective scalability along the size axis of the math dataset that we generate. As a result, we create a mathematical reasoning dataset (MathScaleQA) containing two million math question-answer pairs. To evaluate mathematical reasoning abilities of LLMs comprehensively, we construct {\sc MwpBench}, a benchmark of Math Word Problems, which is a collection of ten datasets (including GSM8K and MATH) covering K-12, college, and competition level math problems. We apply MathScaleQA to fine-tune open-source LLMs (e.g., LLaMA-2 and Mistral), resulting in significantly improved capabilities in mathematical reasoning. Evaluated on {\sc MwpBench}, MathScale-7B achieves state-of-the-art performance across all datasets, surpassing its best peers of equivalent size by 42.9\% in micro average accuracy and 43.7\% in macro average accuracy, respectively.

We introduce MathWriting, the largest online handwritten mathematical expression dataset to date. It consists of 230k human-written samples and an additional 400k synthetic ones. MathWriting can also be used for offline HME recognition and is larger than all existing offline HME datasets like IM2LATEX-100K. We introduce a benchmark based on MathWriting data in order to advance research on both online and offline HME recognition.

Increasing interest in reasoning models has led math to become a prominent testing ground for algorithmic and methodological improvements. However, existing open math datasets either contain a small collection of high-quality, human-written problems or a large corpus of machine-generated problems of uncertain quality, forcing researchers to choose between quality and quantity. In this work, we present Big-Math, a dataset of over 250,000 high-quality math questions with verifiable answers, purposefully made for reinforcement learning (RL). To create Big-Math, we rigorously filter, clean, and curate openly available datasets, extracting questions that satisfy our three desiderata: (1) problems with uniquely verifiable solutions, (2) problems that are open-ended, (3) and problems with a closed-form solution. To ensure the quality of Big-Math, we manually verify each step in our filtering process. Based on the findings from our filtering process, we introduce 47,000 new questions with verified answers, Big-Math-Reformulated: closed-ended questions (i.e. multiple choice questions) that have been reformulated as open-ended questions through a systematic reformulation algorithm. Compared to the most commonly used existing open-source datasets for math reasoning, GSM8k and MATH, Big-Math is an order of magnitude larger, while our rigorous filtering ensures that we maintain the questions most suitable for RL. We also provide a rigorous analysis of the dataset, finding that Big-Math contains a high degree of diversity across problem domains, and incorporates a wide range of problem difficulties, enabling a wide range of downstream uses for models of varying capabilities and training requirements. By bridging the gap between data quality and quantity, Big-Math establish a robust foundation for advancing reasoning in LLMs.

In this paper, we introduce AceMath, a suite of frontier math models that excel in solving complex math problems, along with highly effective reward models capable of evaluating generated solutions and reliably identifying the correct ones. To develop the instruction-tuned math models, we propose a supervised fine-tuning (SFT) process that first achieves competitive performance across general domains, followed by targeted fine-tuning for the math domain using a carefully curated set of prompts and synthetically generated responses. The resulting model, AceMath-72B-Instruct greatly outperforms Qwen2.5-Math-72B-Instruct, GPT-4o and Claude-3.5 Sonnet. To develop math-specialized reward model, we first construct AceMath-RewardBench, a comprehensive and robust benchmark for evaluating math reward models across diverse problems and difficulty levels. After that, we present a systematic approach to build our math reward models. The resulting model, AceMath-72B-RM, consistently outperforms state-of-the-art reward models. Furthermore, when combining AceMath-72B-Instruct with AceMath-72B-RM, we achieve the highest average rm@8 score across the math reasoning benchmarks. We will release model weights, training data, and evaluation benchmarks at: https://research.nvidia.com/labs/adlr/acemath

The remarkable progress of Multi-modal Large Language Models (MLLMs) has garnered unparalleled attention, due to their superior performance in visual contexts. However, their capabilities in visual math problem-solving remain insufficiently evaluated and understood. We investigate current benchmarks to incorporate excessive visual content within textual questions, which potentially assist MLLMs in deducing answers without truly interpreting the input diagrams. To this end, we introduce MathVerse, an all-around visual math benchmark designed for an equitable and in-depth evaluation of MLLMs. We meticulously collect 2,612 high-quality, multi-subject math problems with diagrams from publicly available sources. Each problem is then transformed by human annotators into six distinct versions, each offering varying degrees of information content in multi-modality, contributing to 15K test samples in total. This approach allows MathVerse to comprehensively assess whether and how much MLLMs can truly understand the visual diagrams for mathematical reasoning. In addition, we propose a Chain-of-Thought (CoT) evaluation strategy for a fine-grained assessment of the output answers. Rather than naively judging True or False, we employ GPT-4(V) to adaptively extract crucial reasoning steps, and then score each step with detailed error analysis, which can reveal the intermediate CoT reasoning quality by MLLMs. We hope the MathVerse benchmark may provide unique insights to guide the future development of MLLMs. Project page: https://mathverse-cuhk.github.io

With the rapid development of large language models (LLMs), the quality of training data has become crucial. Among the various types of training data, mathematical data plays a key role in enabling LLMs to acquire strong reasoning abilities. While high-quality open-source data is important, it is often insufficient for pre-training, necessitating the addition of synthetic math problems. However, synthetic math questions and answers can introduce inaccuracies, which may degrade both the training data and web data. Therefore, an effective method for cleaning synthetic math data is essential. In this paper, we propose the MathClean benchmark to evaluate the effectiveness of math data cleaning models. The MathClean benchmark consists of 2,000 correct questions and 2,000 erroneous questions with additional 2,000 correct and erroneous answers sourced from augmented data based on GSM8K and MATH. Moreover, we also annotate error types for each question or answer, since it can assess whether models can correctly identify the error categories for future improvements. Finally, we present comprehensive evaluations using state-of-the-art (SOTA) models. Our results demonstrate that even strong models like GPT-o1 and DeepSeek-R1 perform poorly on this benchmark, highlighting the utility of MathClean. Our code and data is available at https://github.com/YuYingLi0/MathClean.

Math reasoning is becoming an ever increasing area of focus as we scale large language models. However, even the previously-toughest evals like MATH are now close to saturated by frontier models (90.0% for o1-mini and 86.5% for Gemini 1.5 Pro). We introduce HARP, Human Annotated Reasoning Problems (for Math), consisting of 5,409 problems from the US national math competitions (A(J)HSME, AMC, AIME, USA(J)MO). Of these, 4,780 have answers that are automatically check-able (with libraries such as SymPy). These problems range six difficulty levels, with frontier models performing relatively poorly on the hardest bracket of 197 problems (average accuracy 41.1% for o1-mini, and 9.6% for Gemini 1.5 Pro). Our dataset also features multiple choices (for 4,110 problems) and an average of two human-written, ground-truth solutions per problem, offering new avenues of research that we explore briefly. We report evaluations for many frontier models and share some interesting analyses, such as demonstrating that frontier models across families intrinsically scale their inference-time compute for more difficult problems. Finally, we open source all code used for dataset construction (including scraping) and all code for evaluation (including answer checking) to enable future research at: https://github.com/aadityasingh/HARP.

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.

Large language models (LLMs) have shown great potential to solve varieties of natural language processing (NLP) tasks, including mathematical reasoning. In this work, we present SkyMath, a large language model for mathematics with 13 billion parameters. By applying self-compare fine-tuning, we have enhanced mathematical reasoning abilities of Skywork-13B-Base remarkably. On GSM8K, SkyMath outperforms all known open-source models of similar size and has established a new SOTA performance.

Conversion of spoken mathematical expressions is a challenging task that involves transcribing speech into a strictly structured symbolic representation while addressing the ambiguity inherent in the pronunciation of equations. Although significant progress has been achieved in automatic speech recognition (ASR) and language models (LM), the problem of converting spoken mathematics into LaTeX remains underexplored. This task directly applies to educational and research domains, such as lecture transcription or note creation. Based on ASR post-correction, prior work requires 2 transcriptions, focuses only on isolated equations, has a limited test set, and provides neither training data nor multilingual coverage. To address these issues, we present the first fully open-source large-scale dataset, comprising over 66,000 human-annotated audio samples of mathematical equations and sentences in both English and Russian, drawn from diverse scientific domains. In addition to the ASR post-correction models and few-shot prompting, we apply audio language models, demonstrating comparable character error rate (CER) results on the MathSpeech benchmark (28% vs. 30%) for the equations conversion. In contrast, on the proposed S2L-equations benchmark, our models outperform the MathSpeech model by a substantial margin of more than 40 percentage points, even after accounting for LaTeX formatting artifacts (27% vs. 64%). We establish the first benchmark for mathematical sentence recognition (S2L-sentences) and achieve an equation CER of 40%. This work lays the groundwork for future advances in multimodal AI, with a particular focus on mathematical content recognition.

Although Large Language Models (LLMs) and Large Multimodal Models (LMMs) exhibit impressive skills in various domains, their ability for mathematical reasoning within visual contexts has not been formally examined. Equipping LLMs and LMMs with this capability is vital for general-purpose AI assistants and showcases promising potential in education, data analysis, and scientific discovery. To bridge this gap, we present MathVista, a benchmark designed to amalgamate challenges from diverse mathematical and visual tasks. We first taxonomize the key task types, reasoning skills, and visual contexts from the literature to guide our selection from 28 existing math-focused and visual question answering datasets. Then, we construct three new datasets, IQTest, FunctionQA, and PaperQA, to accommodate for missing types of visual contexts. The problems featured often require deep visual understanding beyond OCR or image captioning, and compositional reasoning with rich domain-specific tools, thus posing a notable challenge to existing models. We conduct a comprehensive evaluation of 11 prominent open-source and proprietary foundation models (LLMs, LLMs augmented with tools, and LMMs), and early experiments with GPT-4V. The best-performing model, Multimodal Bard, achieves only 58% of human performance (34.8% vs 60.3%), indicating ample room for further improvement. Given this significant gap, MathVista fuels future research in the development of general-purpose AI agents capable of tackling mathematically intensive and visually rich real-world tasks. Preliminary tests show that MathVista also presents challenges to GPT-4V, underscoring the benchmark's importance. The project is available at https://mathvista.github.io/.

Large Language Models (LLMs) have limited performance when solving arithmetic reasoning tasks and often provide incorrect answers. Unlike natural language understanding, math problems typically have a single correct answer, making the task of generating accurate solutions more challenging for LLMs. To the best of our knowledge, we are not aware of any LLMs that indicate their level of confidence in their responses which fuels a trust deficit in these models impeding their adoption. To address this deficiency, we propose `MathPrompter', a technique that improves performance of LLMs on arithmetic problems along with increased reliance in the predictions. MathPrompter uses the Zero-shot chain-of-thought prompting technique to generate multiple Algebraic expressions or Python functions to solve the same math problem in different ways and thereby raise the confidence level in the output results. This is in contrast to other prompt based CoT methods, where there is no check on the validity of the intermediate steps followed. Our technique improves over state-of-the-art on the MultiArith dataset (78.7%rightarrow92.5%) evaluated using 175B parameter GPT-based LLM.

Recent advances in large language models (LLMs) and multimodal LLMs (MLLMs) have led to strong reasoning ability across a wide range of tasks. However, their ability to perform mathematical reasoning from spoken input remains underexplored. Prior studies on speech modality have mostly focused on factual speech understanding or simple audio reasoning tasks, providing limited insight into logical step-by-step reasoning, such as that required for mathematical problem solving. To address this gap, we introduce Spoken Math Question Answering (Spoken-MQA), a new benchmark designed to evaluate the mathematical reasoning capabilities of speech-based models, including both cascade models (ASR + LLMs) and end-to-end speech LLMs. Spoken-MQA covers a diverse set of math problems, including pure arithmetic, single-step and multi-step contextual reasoning, and knowledge-oriented reasoning problems, all presented in unambiguous natural spoken language. Through extensive experiments, we find that: (1) while some speech LLMs perform competitively on contextual reasoning tasks involving basic arithmetic, they still struggle with direct arithmetic problems; (2) current LLMs exhibit a strong bias toward symbolic mathematical expressions written in LaTex and have difficulty interpreting verbalized mathematical expressions; and (3) mathematical knowledge reasoning abilities are significantly degraded in current speech LLMs.

Pretrained language models have shown superior performance on many natural language processing tasks, yet they still struggle at multi-step formal reasoning tasks like grade school math problems. One key challenge of finetuning them to solve such math reasoning problems is that many existing datasets only contain one reference solution for each problem, despite the fact that there are often alternative solutions resembling different reasoning paths to the final answer. This way, the finetuned models are biased towards the limited reference solutions, which limits their generalization to unseen examples. To mitigate this issue, we propose to let the model perform sampling during training and learn from both self-sampled fully-correct solutions, which yield the correct answer upon execution, and partially-correct solutions, whose intermediate state matches an intermediate state of a known correct solution. We show that our use of self-sampled correct and partially-correct solutions can benefit learning and help guide the sampling process, leading to more efficient exploration of the solution space. Additionally, we explore various training objectives to support learning from multiple solutions per example and find they greatly affect the performance. Experiments on two math reasoning datasets show the effectiveness of our method compared to learning from a single reference solution with MLE, where we improve PASS@100 from 35.5% to 44.5% for GSM8K, and 27.6% to 36.2% PASS@80 for MathQA. Such improvements are also consistent across different model sizes. Our code is available at https://github.com/microsoft/TraceCodegen.

Formulas involving fundamental mathematical constants had a great impact on various fields of science and mathematics, for example aiding in proofs of irrationality of constants. However, the discovery of such formulas has historically remained scarce, often perceived as an act of mathematical genius by great mathematicians such as Ramanujan, Euler, and Gauss. Recent efforts to automate the discovery of formulas for mathematical constants, such as the Ramanujan Machine project, relied on exhaustive search. Despite several successful discoveries, exhaustive search remains limited by the space of options that can be covered and by the need for vast amounts of computational resources. Here we propose a fundamentally different method to search for conjectures on mathematical constants: through analysis of integer sequences. We introduce the Enumerated Signed-continued-fraction Massey Approve (ESMA) algorithm, which builds on the Berlekamp-Massey algorithm to identify patterns in integer sequences that represent mathematical constants. The ESMA algorithm found various known formulas for e, e^2, tan(1), and ratios of values of Bessel functions. The algorithm further discovered a large number of new conjectures for these constants, some providing simpler representations and some providing faster numerical convergence than the corresponding simple continued fractions. Along with the algorithm, we present mathematical tools for manipulating continued fractions. These connections enable us to characterize what space of constants can be found by ESMA and quantify its algorithmic advantage in certain scenarios. Altogether, this work continues in the development of augmenting mathematical intuition by computer algorithms, to help reveal mathematical structures and accelerate mathematical research.

Large language models (LLMs) have achieved impressive performance across various mathematical reasoning benchmarks. However, there are increasing debates regarding whether these models truly understand and apply mathematical knowledge or merely rely on shortcuts for mathematical reasoning. One essential and frequently occurring evidence is that when the math questions are slightly changed, LLMs can behave incorrectly. This motivates us to evaluate the robustness of LLMs' math reasoning capability by testing a wide range of question variations. We introduce the adversarial grade school math (\datasetname) dataset, an extension of GSM8K augmented with various mathematical perturbations. Our experiments on 25 LLMs and 4 prompting techniques show that while LLMs exhibit different levels of math reasoning abilities, their performances are far from robust. In particular, even for problems that have been solved in GSM8K, LLMs can make mistakes when new statements are added or the question targets are altered. We also explore whether more robust performance can be achieved by composing existing prompting methods, in which we try an iterative method that generates and verifies each intermediate thought based on its reasoning goal and calculation result. Code and data are available at https://github.com/qtli/GSM-Plus.

FinanceQA is a testing suite that evaluates LLMs' performance on complex numerical financial analysis tasks that mirror real-world investment work. Despite recent advances, current LLMs fail to meet the strict accuracy requirements of financial institutions, with models failing approximately 60% of realistic tasks that mimic on-the-job analyses at hedge funds, private equity firms, investment banks, and other financial institutions. The primary challenges include hand-spreading metrics, adhering to standard accounting and corporate valuation conventions, and performing analysis under incomplete information - particularly in multi-step tasks requiring assumption generation. This performance gap highlights the disconnect between existing LLM capabilities and the demands of professional financial analysis that are inadequately tested by current testing architectures. Results show that higher-quality training data is needed to support such tasks, which we experiment with using OpenAI's fine-tuning API. FinanceQA is publicly released at [this https URL](https://huggingface.co/datasets/AfterQuery/FinanceQA).

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet demand for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core "skills" from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an "out of distribution" task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH^2 - a dataset of higher-quality math questions, as evidenced by: (a) Lower performance of all models on MATH^2 than on MATH (b) Higher performance on MATH when using MATH^2 questions as in-context examples. Although focused on mathematics, our methodology seems applicable to other domains requiring structured reasoning, and potentially as a component of scalable oversight. Also of interest is a striking relationship observed between models' performance on the new dataset: the success rate on MATH^2 is the square on MATH, suggesting that successfully solving the question in MATH^2 requires a nontrivial combination of two distinct math skills.

We introduce KnowledgeMath, a novel benchmark designed to evaluate LLMs' capabilities in applying financial knowledge to solve complex math word problems. Compared to prior works, this study features three core advancements. First, KnowledgeMath includes 1,259 problems with a hybrid of textual and tabular content and require college-level knowledge in the finance domain for effective resolution. Second, we provide expert-annotated, detailed solution references in Python program format, ensuring a high-quality benchmark for LLM assessment. Finally, we evaluate a wide spectrum of 14 LLMs with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. The current best-performing system (i.e., GPT-4 with Program-of-Thoughts) achieves only 45.4% accuracy, leaving substantial room for improvement. While knowledge-augmented LLMs can improve the performance (e.g., from 23.9% to 32.0% for GPT-3.5), it is still significantly lower the estimated human expert performance of 94%. We believe that KnowledgeMath can facilitate future research on domain-specific knowledge retrieval and augmentation into the math word problem-solving process. We will release the benchmark and code at https://github.com/yale-nlp/KnowledgeMath.

We present the Chinese Elementary School Math Word Problems (CMATH) dataset, comprising 1.7k elementary school-level math word problems with detailed annotations, source from actual Chinese workbooks and exams. This dataset aims to provide a benchmark tool for assessing the following question: to what grade level of elementary school math do the abilities of popular large language models (LLMs) correspond? We evaluate a variety of popular LLMs, including both commercial and open-source options, and discover that only GPT-4 achieves success (accuracy geq 60\%) across all six elementary school grades, while other models falter at different grade levels. Furthermore, we assess the robustness of several top-performing LLMs by augmenting the original problems in the CMATH dataset with distracting information. Our findings reveal that GPT-4 is able to maintains robustness, while other model fail. We anticipate that our study will expose limitations in LLMs' arithmetic and reasoning capabilities, and promote their ongoing development and advancement.

How can we perform computations over natural language representations to solve tasks that require symbolic and numeric reasoning? We propose natural language embedded programs (NLEP) as a unifying framework for addressing math/symbolic reasoning, natural language understanding, and instruction following tasks. Our approach prompts a language model to generate full Python programs that define functions over data structures which contain natural language representations of structured knowledge. A Python interpreter then executes the generated code and prints the output. Despite using a task-general prompt, we find that this approach can improve upon strong baselines across a range of different tasks including math and symbolic reasoning, text classification, question answering, and instruction following. We further find the generated programs are often interpretable and enable post-hoc verification of the intermediate reasoning steps.

In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the specialized nature of Coq syntax and semantics poses unique challenges for Large Language Models (LLMs). Addressing this gap, we present a comprehensive dataset specifically designed to enhance LLMs' proficiency in interpreting and generating Coq code. This dataset, derived from a collection of over 10,000 Coq source files, encompasses a wide array of propositions, proofs, and definitions, enriched with metadata including source references and licensing information. Our primary aim is to facilitate the development of LLMs capable of generating syntactically correct and semantically meaningful Coq constructs, thereby advancing the frontier of automated theorem proving. Initial experiments with this dataset have showcased its significant potential; models trained on this data exhibited enhanced accuracy in Coq code generation. Notably, a particular experiment revealed that a fine-tuned LLM was capable of generating 141 valid proofs for a basic lemma, highlighting the dataset's utility in facilitating the discovery of diverse and valid proof strategies. This paper discusses the dataset's composition, the methodology behind its creation, and the implications of our findings for the future of machine learning in formal verification. The dataset is accessible for further research and exploration: https://huggingface.co/datasets/florath/coq-facts-props-proofs-gen0-v1

We present SimpleQA, a benchmark that evaluates the ability of language models to answer short, fact-seeking questions. We prioritized two properties in designing this eval. First, SimpleQA is challenging, as it is adversarially collected against GPT-4 responses. Second, responses are easy to grade, because questions are created such that there exists only a single, indisputable answer. Each answer in SimpleQA is graded as either correct, incorrect, or not attempted. A model with ideal behavior would get as many questions correct as possible while not attempting the questions for which it is not confident it knows the correct answer. SimpleQA is a simple, targeted evaluation for whether models "know what they know," and our hope is that this benchmark will remain relevant for the next few generations of frontier models. SimpleQA can be found at https://github.com/openai/simple-evals.

The availability of high-quality data is one of the most important factors in improving the reasoning capability of LLMs. Existing works have demonstrated the effectiveness of creating more instruction data from seed questions or knowledge bases. Recent research indicates that continually scaling up data synthesis from strong models (e.g., GPT-4) can further elicit reasoning performance. Though promising, the open-sourced community still lacks high-quality data at scale and scalable data synthesis methods with affordable costs. To address this, we introduce ScaleQuest, a scalable and novel data synthesis method that utilizes "small-size" (e.g., 7B) open-source models to generate questions from scratch without the need for seed data with complex augmentation constraints. With the efficient ScaleQuest, we automatically constructed a mathematical reasoning dataset consisting of 1 million problem-solution pairs, which are more effective than existing open-sourced datasets. It can universally increase the performance of mainstream open-source models (i.e., Mistral, Llama3, DeepSeekMath, and Qwen2-Math) by achieving 29.2% to 46.4% gains on MATH. Notably, simply fine-tuning the Qwen2-Math-7B-Base model with our dataset can even surpass Qwen2-Math-7B-Instruct, a strong and well-aligned model on closed-source data, and proprietary models such as GPT-4-Turbo and Claude-3.5 Sonnet.

Large language models (LLMs) have made impressive progress in handling simple math problems, yet they still struggle with more challenging and complex mathematical tasks. In this paper, we introduce a series of LLMs that employs the Decomposition of thought with code assistance and self-correction for mathematical reasoning, dubbed as DotaMath. DotaMath models tackle complex mathematical tasks by decomposing them into simpler logical subtasks, leveraging code to solve these subtasks, obtaining fine-grained feedback from the code interpreter, and engaging in self-reflection and correction. By annotating diverse interactive tool-use trajectories and employing query evolution on GSM8K and MATH datasets, we generate an instruction fine-tuning dataset called DotaMathQA with 574K query-response pairs. We train a series of base LLMs using imitation learning on DotaMathQA, resulting in DotaMath models that achieve remarkable performance compared to open-source LLMs across various in-domain and out-of-domain benchmarks. Notably, DotaMath-deepseek-7B showcases an outstanding performance of 64.8% on the competitive MATH dataset and 86.7% on GSM8K. Besides, DotaMath-deepseek-7B maintains strong competitiveness on a series of in-domain and out-of-domain benchmarks (Avg. 80.1%). Looking forward, we anticipate that the DotaMath paradigm will open new pathways for addressing intricate mathematical problems. Our code is publicly available at https://github.com/ChengpengLi1003/DotaMath.

Our work presents a novel angle for evaluating language models' (LMs) mathematical abilities, by investigating whether they can discern skills and concepts enabled by math content. We contribute two datasets: one consisting of 385 fine-grained descriptions of K-12 math skills and concepts, or standards, from Achieve the Core (ATC), and another of 9.9K problems labeled with these standards (MathFish). Working with experienced teachers, we find that LMs struggle to tag and verify standards linked to problems, and instead predict labels that are close to ground truth, but differ in subtle ways. We also show that LMs often generate problems that do not fully align with standards described in prompts. Finally, we categorize problems in GSM8k using math standards, allowing us to better understand why some problems are more difficult to solve for models than others.

Recent advances in the field of language modeling have improved state-of-the-art results on many Natural Language Processing tasks. Among them, Reading Comprehension has made significant progress over the past few years. However, most results are reported in English since labeled resources available in other languages, such as French, remain scarce. In the present work, we introduce the French Question Answering Dataset (FQuAD). FQuAD is a French Native Reading Comprehension dataset of questions and answers on a set of Wikipedia articles that consists of 25,000+ samples for the 1.0 version and 60,000+ samples for the 1.1 version. We train a baseline model which achieves an F1 score of 92.2 and an exact match ratio of 82.1 on the test set. In order to track the progress of French Question Answering models we propose a leader-board and we have made the 1.0 version of our dataset freely available at https://illuin-tech.github.io/FQuAD-explorer/.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

We introduce BM25S, an efficient Python-based implementation of BM25 that only depends on Numpy and Scipy. BM25S achieves up to a 500x speedup compared to the most popular Python-based framework by eagerly computing BM25 scores during indexing and storing them into sparse matrices. It also achieves considerable speedups compared to highly optimized Java-based implementations, which are used by popular commercial products. Finally, BM25S reproduces the exact implementation of five BM25 variants based on Kamphuis et al. (2020) by extending eager scoring to non-sparse variants using a novel score shifting method. The code can be found at https://github.com/xhluca/bm25s

Existing synthetic datasets (FigureQA, DVQA) for reasoning over plots do not contain variability in data labels, real-valued data, or complex reasoning questions. Consequently, proposed models for these datasets do not fully address the challenge of reasoning over plots. In particular, they assume that the answer comes either from a small fixed size vocabulary or from a bounding box within the image. However, in practice, this is an unrealistic assumption because many questions require reasoning and thus have real-valued answers which appear neither in a small fixed size vocabulary nor in the image. In this work, we aim to bridge this gap between existing datasets and real-world plots. Specifically, we propose PlotQA with 28.9 million question-answer pairs over 224,377 plots on data from real-world sources and questions based on crowd-sourced question templates. Further, 80.76% of the out-of-vocabulary (OOV) questions in PlotQA have answers that are not in a fixed vocabulary. Analysis of existing models on PlotQA reveals that they cannot deal with OOV questions: their overall accuracy on our dataset is in single digits. This is not surprising given that these models were not designed for such questions. As a step towards a more holistic model which can address fixed vocabulary as well as OOV questions, we propose a hybrid approach: Specific questions are answered by choosing the answer from a fixed vocabulary or by extracting it from a predicted bounding box in the plot, while other questions are answered with a table question-answering engine which is fed with a structured table generated by detecting visual elements from the image. On the existing DVQA dataset, our model has an accuracy of 58%, significantly improving on the highest reported accuracy of 46%. On PlotQA, our model has an accuracy of 22.52%, which is significantly better than state of the art models.

In this paper, we investigate the underlying factors that potentially enhance the mathematical reasoning capabilities of large language models (LLMs). We argue that the data scaling law for math reasoning capabilities in modern LLMs is far from being saturated, highlighting how the model's quality improves with increases in data quantity. To support this claim, we introduce the Skywork-Math model series, supervised fine-tuned (SFT) on common 7B LLMs using our proposed 2.5M-instance Skywork-MathQA dataset. Skywork-Math 7B has achieved impressive accuracies of 51.2% on the competition-level MATH benchmark and 83.9% on the GSM8K benchmark using only SFT data, outperforming an early version of GPT-4 on MATH. The superior performance of Skywork-Math models contributes to our novel two-stage data synthesis and model SFT pipelines, which include three different augmentation methods and a diverse seed problem set, ensuring both the quantity and quality of Skywork-MathQA dataset across varying difficulty levels. Most importantly, we provide several practical takeaways to enhance math reasoning abilities in LLMs for both research and industry applications.

We present NewsQA, a challenging machine comprehension dataset of over 100,000 human-generated question-answer pairs. Crowdworkers supply questions and answers based on a set of over 10,000 news articles from CNN, with answers consisting of spans of text from the corresponding articles. We collect this dataset through a four-stage process designed to solicit exploratory questions that require reasoning. A thorough analysis confirms that NewsQA demands abilities beyond simple word matching and recognizing textual entailment. We measure human performance on the dataset and compare it to several strong neural models. The performance gap between humans and machines (0.198 in F1) indicates that significant progress can be made on NewsQA through future research. The dataset is freely available at https://datasets.maluuba.com/NewsQA.

Large language models (LLMs) have significantly advanced natural language understanding and demonstrated strong problem-solving abilities. Despite these successes, most LLMs still struggle with solving mathematical problems due to the intricate reasoning required. This paper investigates the mathematical problem-solving capabilities of LLMs using the newly developed "MathOdyssey" dataset. The dataset includes diverse mathematical problems at high school and university levels, created by experts from notable institutions to rigorously test LLMs in advanced problem-solving scenarios and cover a wider range of subject areas. By providing the MathOdyssey dataset as a resource to the AI community, we aim to contribute to the understanding and improvement of AI capabilities in complex mathematical problem-solving. We conduct benchmarking on open-source models, such as Llama-3 and DBRX-Instruct, and closed-source models from the GPT series and Gemini models. Our results indicate that while LLMs perform well on routine and moderately difficult tasks, they face significant challenges with Olympiad-level problems and complex university-level questions. Our analysis shows a narrowing performance gap between open-source and closed-source models, yet substantial challenges remain, particularly with the most demanding problems. This study highlights the ongoing need for research to enhance the mathematical reasoning of LLMs. The dataset, results, and code are publicly available.

Recent advancements in large language models (LLMs) have led to significant breakthroughs in mathematical reasoning capabilities. However, existing benchmarks like GSM8K or MATH are now being solved with high accuracy (e.g., OpenAI o1 achieves 94.8% on MATH dataset), indicating their inadequacy for truly challenging these models. To bridge this gap, we propose a comprehensive and challenging benchmark specifically designed to assess LLMs' mathematical reasoning at the Olympiad level. Unlike existing Olympiad-related benchmarks, our dataset focuses exclusively on mathematics and comprises a vast collection of 4428 competition-level problems with rigorous human annotation. These problems are meticulously categorized into over 33 sub-domains and span more than 10 distinct difficulty levels, enabling a holistic assessment of model performance in Olympiad-mathematical reasoning. Furthermore, we conducted an in-depth analysis based on this benchmark. Our experimental results show that even the most advanced models, OpenAI o1-mini and OpenAI o1-preview, struggle with highly challenging Olympiad-level problems, with 60.54% and 52.55% accuracy, highlighting significant challenges in Olympiad-level mathematical reasoning.

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

The African continent lacks enough qualified teachers which hampers the provision of adequate learning support. An AI could potentially augment the efforts of the limited number of teachers, leading to better learning outcomes. Towards that end, this work describes and evaluates the first key output for the NSMQ AI Grand Challenge, which proposes a robust, real-world benchmark for such an AI: "Build an AI to compete live in Ghana's National Science and Maths Quiz (NSMQ) competition and win - performing better than the best contestants in all rounds and stages of the competition". The NSMQ is an annual live science and mathematics competition for senior secondary school students in Ghana in which 3 teams of 2 students compete by answering questions across biology, chemistry, physics, and math in 5 rounds over 5 progressive stages until a winning team is crowned for that year. In this work, we built Brilla AI, an AI contestant that we deployed to unofficially compete remotely and live in the Riddles round of the 2023 NSMQ Grand Finale, the first of its kind in the 30-year history of the competition. Brilla AI is currently available as a web app that livestreams the Riddles round of the contest, and runs 4 machine learning systems: (1) speech to text (2) question extraction (3) question answering and (4) text to speech that work together in real-time to quickly and accurately provide an answer, and then say it with a Ghanaian accent. In its debut, our AI answered one of the 4 riddles ahead of the 3 human contesting teams, unofficially placing second (tied). Improvements and extensions of this AI could potentially be deployed to offer science tutoring to students and eventually enable millions across Africa to have one-on-one learning interactions, democratizing science education.

We present SpaceQA, to the best of our knowledge the first open-domain QA system in Space mission design. SpaceQA is part of an initiative by the European Space Agency (ESA) to facilitate the access, sharing and reuse of information about Space mission design within the agency and with the public. We adopt a state-of-the-art architecture consisting of a dense retriever and a neural reader and opt for an approach based on transfer learning rather than fine-tuning due to the lack of domain-specific annotated data. Our evaluation on a test set produced by ESA is largely consistent with the results originally reported by the evaluated retrievers and confirms the need of fine tuning for reading comprehension. As of writing this paper, ESA is piloting SpaceQA internally.

The paper introduces SceMQA, a novel benchmark for scientific multimodal question answering at the college entrance level. It addresses a critical educational phase often overlooked in existing benchmarks, spanning high school to pre-college levels. SceMQA focuses on core science subjects including Mathematics, Physics, Chemistry, and Biology. It features a blend of multiple-choice and free-response formats, ensuring a comprehensive evaluation of AI models' abilities. Additionally, our benchmark provides specific knowledge points for each problem and detailed explanations for each answer. SceMQA also uniquely presents problems with identical contexts but varied questions to facilitate a more thorough and accurate assessment of reasoning capabilities. In the experiment, we evaluate both open-source and close-source state-of-the-art Multimodal Large Language Models (MLLMs), across various experimental settings. The results show that further research and development are needed in developing more capable MLLM, as highlighted by only 50% to 60% accuracy achieved by the strongest models. Our benchmark and analysis will be available at https://scemqa.github.io/

Employing Large Language Models (LLMs) to address mathematical problems is an intriguing research endeavor, considering the abundance of math problems expressed in natural language across numerous science and engineering fields. While several prior works have investigated solving elementary mathematics using LLMs, this work explores the frontier of using GPT-4 for solving more complex and challenging math problems. We evaluate various ways of using GPT-4. Some of them are adapted from existing work, and one is \MathChat, a conversational problem-solving framework newly proposed in this work. We perform the evaluation on difficult high school competition problems from the MATH dataset, which shows the advantage of the proposed conversational approach.

Pretraining large language models (LLMs) on high-quality, structured data such as mathematics and code substantially enhances reasoning capabilities. However, existing math-focused datasets built from Common Crawl suffer from degraded quality due to brittle extraction heuristics, lossy HTML-to-text conversion, and the failure to reliably preserve mathematical structure. In this work, we introduce Nemotron-CC-Math, a large-scale, high-quality mathematical corpus constructed from Common Crawl using a novel, domain-agnostic pipeline specifically designed for robust scientific text extraction. Unlike previous efforts, our pipeline recovers math across various formats (e.g., MathJax, KaTeX, MathML) by leveraging layout-aware rendering with lynx and a targeted LLM-based cleaning stage. This approach preserves the structural integrity of equations and code blocks while removing boilerplate, standardizing notation into LaTeX representation, and correcting inconsistencies. We collected a large, high-quality math corpus, namely Nemotron-CC-Math-3+ (133B tokens) and Nemotron-CC-Math-4+ (52B tokens). Notably, Nemotron-CC-Math-4+ not only surpasses all prior open math datasets-including MegaMath, FineMath, and OpenWebMath-but also contains 5.5 times more tokens than FineMath-4+, which was previously the highest-quality math pretraining dataset. When used to pretrain a Nemotron-T 8B model, our corpus yields +4.8 to +12.6 gains on MATH and +4.6 to +14.3 gains on MBPP+ over strong baselines, while also improving general-domain performance on MMLU and MMLU-Stem. We present the first pipeline to reliably extract scientific content--including math--from noisy web-scale data, yielding measurable gains in math, code, and general reasoning, and setting a new state of the art among open math pretraining corpora. To support open-source efforts, we release our code and datasets.

Question answering systems provide short, precise, and specific answers to questions. So far, many robust question answering systems have been developed for English, while some languages with fewer resources, like Persian, have few numbers of standard dataset. In this study, a comprehensive open-domain dataset is presented for Persian. This dataset is called NextQuAD and has 7,515 contexts, including 23,918 questions and answers. Then, a BERT-based question answering model has been applied to this dataset using two pre-trained language models, including ParsBERT and XLM-RoBERTa. The results of these two models have been ensembled using mean logits. Evaluation on the development set shows 0.95 Exact Match (EM) and 0.97 Fl_score. Also, to compare the NextQuAD with other Persian datasets, our trained model on the NextQuAD, is evaluated on two other datasets named PersianQA and ParSQuAD. Comparisons show that the proposed model increased EM by 0.39 and 0.14 respectively in PersianQA and ParSQuAD-manual, while a slight EM decline of 0.007 happened in ParSQuAD-automatic.

We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised learning. Additionally, unsupervised methods can provide insight into the structure of such geometrical data. At the heart of this programme is the question of how geometry can be machine learned, and indeed how AI helps one to do mathematics. This is a chapter contribution to the book Machine learning and Algebraic Geometry, edited by A. Kasprzyk et al.

Recently, large language models have presented promising results in aiding formal mathematical reasoning. However, their performance is restricted due to the scarcity of formal theorem-proving data, which requires additional effort to be extracted from raw formal language corpora. Meanwhile, a significant amount of human-written formal language corpora remains underutilized. To address this issue, we propose LEAN-GitHub, a dataset consisting of large-scale formal data extracted from almost all Lean 4 repositories on GitHub. After fine-tuning InternLM-math-plus on this dataset, our model achieved accuracies of 48.8% with a single pass and 54.5% with 64 passes on the Lean 4 miniF2F test, surpassing state-of-the-art method at 52%. And it also achieves state-of-the-art on two other Lean 4 benchmarks (ProofNet and Putnam) targeting different fields/levels of math. These results demonstrate that our proposed dataset is beneficial for formal reasoning on a wide range of math topics. We open-source our model at https://GitHub. com/InternLM/InternLM-Math and our data at https://huggingface.co/ datasets/InternLM/Lean-GitHub

Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, o3-mini, achieving scores comparable to top human competitors. However, these benchmarks evaluate models solely based on final numerical answers, neglecting rigorous reasoning and proof generation which are essential for real-world mathematical tasks. To address this, we introduce the first comprehensive evaluation of full-solution reasoning for challenging mathematical problems. Using expert human annotators, we evaluated several state-of-the-art reasoning models on the six problems from the 2025 USAMO within hours of their release. Our results reveal that all tested models struggled significantly, achieving less than 5% on average. Through detailed analysis of reasoning traces, we identify the most common failure modes and find several unwanted artifacts arising from the optimization strategies employed during model training. Overall, our results suggest that current LLMs are inadequate for rigorous mathematical reasoning tasks, highlighting the need for substantial improvements in reasoning and proof generation capabilities.

Large Language Models (LLMs) have made significant strides in mathematical reasoning, underscoring the need for a comprehensive and fair evaluation of their capabilities. However, existing benchmarks often fall short, either lacking extensive coverage of undergraduate-level mathematical problems or probably suffering from test-set contamination. To address these issues, we introduce UGMathBench, a diverse and dynamic benchmark specifically designed for evaluating undergraduate-level mathematical reasoning with LLMs. UGMathBench comprises 5,062 problems across 16 subjects and 111 topics, featuring 10 distinct answer types. Each problem includes three randomized versions, with additional versions planned for release as leading open-source LLMs become saturated in UGMathBench. Furthermore, we propose two key metrics: effective accuracy (EAcc), which measures the percentage of correctly solved problems across all three versions, and reasoning gap (Delta), which assesses reasoning robustness by calculating the difference between the average accuracy across all versions and EAcc. Our extensive evaluation of 23 leading LLMs reveals that the highest EAcc achieved is 56.3\% by OpenAI-o1-mini, with large Delta values observed across different models. This highlights the need for future research aimed at developing "large reasoning models" with high EAcc and Delta = 0. We anticipate that the release of UGMathBench, along with its detailed evaluation codes, will serve as a valuable resource to advance the development of LLMs in solving mathematical problems.

We present PyThaiNLP, a free and open-source natural language processing (NLP) library for Thai language implemented in Python. It provides a wide range of software, models, and datasets for Thai language. We first provide a brief historical context of tools for Thai language prior to the development of PyThaiNLP. We then outline the functionalities it provided as well as datasets and pre-trained language models. We later summarize its development milestones and discuss our experience during its development. We conclude by demonstrating how industrial and research communities utilize PyThaiNLP in their work. The library is freely available at https://github.com/pythainlp/pythainlp.

We introduce Goedel-Prover, an open-source large language model (LLM) that achieves the state-of-the-art (SOTA) performance in automated formal proof generation for mathematical problems. The key challenge in this field is the scarcity of formalized math statements and proofs, which we tackle in the following ways. We train statement formalizers to translate the natural language math problems from Numina into formal language (Lean 4), creating a dataset of 1.64 million formal statements. LLMs are used to check that the formal statements accurately preserve the content of the original natural language problems. We then iteratively build a large dataset of formal proofs by training a series of provers. Each prover succeeds in proving many statements that the previous ones could not, and these new proofs are added to the training set for the next prover. The final prover outperforms all existing open-source models in whole-proof generation. On the miniF2F benchmark, it achieves a 57.6% success rate (Pass@32), exceeding the previous best open-source model by 7.6%. On PutnamBench, Goedel-Prover successfully solves 7 problems (Pass@512), ranking first on the leaderboard. Furthermore, it generates 29.7K formal proofs for Lean Workbook problems, nearly doubling the 15.7K produced by earlier works.

Recent advances in large language models (LLMs), such as OpenAI-o1 and DeepSeek-R1, have demonstrated the effectiveness of test-time scaling, where extended reasoning processes substantially enhance model performance. Despite this, current models are constrained by limitations in handling long texts and reinforcement learning (RL) training efficiency. To address these issues, we propose a simple yet effective test-time scaling approach Multi-round Thinking. This method iteratively refines model reasoning by leveraging previous answers as prompts for subsequent rounds. Extensive experiments across multiple models, including QwQ-32B and DeepSeek-R1, consistently show performance improvements on various benchmarks such as AIME 2024, MATH-500, GPQA-diamond, and LiveCodeBench. For instance, the accuracy of QwQ-32B improved from 80.3% (Round 1) to 82.1% (Round 2) on the AIME 2024 dataset, while DeepSeek-R1 showed a similar increase from 79.7% to 82.0%. These results confirm that Multi-round Thinking is a broadly applicable, straightforward approach to achieving stable enhancements in model performance, underscoring its potential for future developments in test-time scaling techniques. The key prompt: {Original question prompt} The assistant's previous answer is: <answer> {last round answer} </answer>, and please re-answer.

We analyzed effectiveness of three generative pre-trained transformer (GPT) models in answering multiple-choice question (MCQ) assessments, often involving short snippets of code, from introductory and intermediate programming courses at the postsecondary level. This emerging technology stirs countless discussions of its potential uses (e.g., exercise generation, code explanation) as well as misuses in programming education (e.g., cheating). However, the capabilities of GPT models and their limitations to reason about and/or analyze code in educational settings have been under-explored. We evaluated several OpenAI's GPT models on formative and summative MCQ assessments from three Python courses (530 questions). We found that MCQs containing code snippets are not answered as successfully as those that only contain natural language. While questions requiring to fill-in a blank in the code or completing a natural language statement about the snippet are handled rather successfully, MCQs that require analysis and/or reasoning about the code (e.g., what is true/false about the snippet, or what is its output) appear to be the most challenging. These findings can be leveraged by educators to adapt their instructional practices and assessments in programming courses, so that GPT becomes a valuable assistant for a learner as opposed to a source of confusion and/or potential hindrance in the learning process.

We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we develop a Prolog solution that includes problem-specific predicates and intermediate predicates derived from these background operators, ensuring that each solution adheres to the defined operator set. We introduce the MATH-Prolog corpus, which is derived from the counting and probability categories of the MATH corpus. For efficient data augmentation, we apply K-fold cross-validated self-training. This method incrementally generates new Prolog solutions for each fold, incorporating those verified as correct into the training set throughout the model training process. Our experimental results demonstrate that 5-fold crossvalidated self-training effectively identifies new, accurate Prolog solutions, achieving an accuracy of 84.6% on the cross-validated set, and 84.8% on the test set during fine-tuning the Meta-Llama-3.1-8B-Instruct model. This approach successfully uncovers new solutions with fully computable inference steps for previously unseen problems. Additionally, incorporating the background mathematical predicates into the prompt enhances solution coverage.

Financial reports offer critical insights into a company's operations, yet their extensive length typically spanning 30 40 pages poses challenges for swift decision making in dynamic markets. To address this, we leveraged finetuned Large Language Models (LLMs) to distill key indicators and operational metrics from these reports basis questions from the user. We devised a method to locate critical data, and leverage the FinQA dataset to fine-tune both Llama-2 7B and T5 models for customized question answering. We achieved results comparable to baseline on the final numerical answer, a competitive accuracy in numerical reasoning and calculation.

Large Language Models (LLMs) exhibit impressive performance across various domains but still struggle with arithmetic reasoning tasks. Recent work shows the effectiveness of prompt design methods in enhancing reasoning capabilities. However, these approaches overlook crucial requirements for prior knowledge of specific concepts, theorems, and tricks to tackle most arithmetic reasoning problems successfully. To address this issue, we propose a novel and effective Teaching-Inspired Integrated Framework, which emulates the instructional process of a teacher guiding students. This method equips LLMs with essential concepts, relevant theorems, and similar problems with analogous solution approaches, facilitating the enhancement of reasoning abilities. Additionally, we introduce two new Chinese datasets, MathMC and MathToF, both with detailed explanations and answers. Experiments are conducted on nine benchmarks which demonstrates that our approach improves the reasoning accuracy of LLMs. With GPT-4 and our framework, we achieve new state-of-the-art performance on four math benchmarks (AddSub, SVAMP, Math23K and AQuA) with accuracies of 98.2% (+3.3%), 93.9% (+0.2%), 94.3% (+7.2%) and 81.1% (+1.2%). Our data and code are available at https://github.com/SallyTan13/Teaching-Inspired-Prompting.

Mathematical understanding and reasoning are crucial tasks for assessing the capabilities of artificial intelligence (AI). However, existing benchmarks either require just a few steps of reasoning, or only contain a small amount of data in one specific topic, making it hard to analyse AI's behaviour with reference to different problems within a specific topic in detail. In this work, we propose Conic10K, a challenging math problem dataset on conic sections in Chinese senior high school education. Our dataset contains various problems with different reasoning depths, while only the knowledge from conic sections is required. Since the dataset only involves a narrow range of knowledge, it is easy to separately analyse the knowledge a model possesses and the reasoning ability it has. For each problem, we provide a high-quality formal representation, the reasoning steps, and the final solution. Experiments show that existing large language models, including GPT-4, exhibit weak performance on complex reasoning. We hope that our findings could inspire more advanced techniques for precise natural language understanding and reasoning. Our dataset and codes are available at https://github.com/whyNLP/Conic10K.

We introduce TechQA, a domain-adaptation question answering dataset for the technical support domain. The TechQA corpus highlights two real-world issues from the automated customer support domain. First, it contains actual questions posed by users on a technical forum, rather than questions generated specifically for a competition or a task. Second, it has a real-world size -- 600 training, 310 dev, and 490 evaluation question/answer pairs -- thus reflecting the cost of creating large labeled datasets with actual data. Consequently, TechQA is meant to stimulate research in domain adaptation rather than being a resource to build QA systems from scratch. The dataset was obtained by crawling the IBM Developer and IBM DeveloperWorks forums for questions with accepted answers that appear in a published IBM Technote---a technical document that addresses a specific technical issue. We also release a collection of the 801,998 publicly available Technotes as of April 4, 2019 as a companion resource that might be used for pretraining, to learn representations of the IT domain language.

In math reasoning with large language models (LLMs), fine-tuning data augmentation by query evolution and diverse reasoning paths is empirically verified effective, profoundly narrowing the gap between open-sourced LLMs and cutting-edge proprietary LLMs. In this paper, we conduct an investigation for such data augmentation in math reasoning and are intended to answer: (1) What strategies of data augmentation are more effective; (2) What is the scaling relationship between the amount of augmented data and model performance; and (3) Can data augmentation incentivize generalization to out-of-domain mathematical reasoning tasks? To this end, we create a new dataset, AugGSM8K, by complicating and diversifying the queries from GSM8K and sampling multiple reasoning paths. We obtained a series of LLMs called MuggleMath by fine-tuning on subsets of AugGSM8K. MuggleMath substantially achieves new state-of-the-art on GSM8K (from 54% to 68.4% at the scale of 7B, and from 63.9% to 74.0% at the scale of 13B). A log-linear relationship is presented between MuggleMath's performance and the amount of augmented data. We also find that MuggleMath is weak in out-of-domain math reasoning generalization to MATH. This is attributed to the differences in query distribution between AugGSM8K and MATH which suggest that augmentation on a single benchmark could not help with overall math reasoning performance. Codes and AugGSM8K will be uploaded to https://github.com/OFA-Sys/gsm8k-ScRel.

We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO level, FIMO is currently tailored for the Lean formal language. It comprises 149 formal problem statements, accompanied by both informal problem descriptions and their corresponding LaTeX-based informal proofs. Through initial experiments involving GPT-4, our findings underscore the existing limitations in current methodologies, indicating a substantial journey ahead before achieving satisfactory IMO-level automated theorem proving outcomes.

Geometry problem solving is a key area of mathematical reasoning, which is widely involved in many important fields such as education, mathematical ability assessment of artificial intelligence, and multimodal ability assessment. In recent years, the rapid development of deep learning technology, especially the rise of multimodal large language models, has triggered a widespread research boom. This paper provides a survey of the applications of deep learning in geometry problem solving, including (i) a comprehensive summary of the relevant tasks in geometry problem solving; (ii) a thorough review of related deep learning methods; (iii) a detailed analysis of evaluation metrics and methods; and (iv) a critical discussion of the current challenges and future directions that can be explored. Our goal is to provide a comprehensive and practical reference of deep learning for geometry problem solving to promote further developments in this field. We create a continuously updated list of papers on GitHub: https://github.com/majianz/dl4gps.

Question Answering, including Reading Comprehension, is one of the NLP research areas that has seen significant scientific breakthroughs over the past few years, thanks to the concomitant advances in Language Modeling. Most of these breakthroughs, however, are centered on the English language. In 2020, as a first strong initiative to bridge the gap to the French language, Illuin Technology introduced FQuAD1.1, a French Native Reading Comprehension dataset composed of 60,000+ questions and answers samples extracted from Wikipedia articles. Nonetheless, Question Answering models trained on this dataset have a major drawback: they are not able to predict when a given question has no answer in the paragraph of interest, therefore making unreliable predictions in various industrial use-cases. In the present work, we introduce FQuAD2.0, which extends FQuAD with 17,000+ unanswerable questions, annotated adversarially, in order to be similar to answerable ones. This new dataset, comprising a total of almost 80,000 questions, makes it possible to train French Question Answering models with the ability of distinguishing unanswerable questions from answerable ones. We benchmark several models with this dataset: our best model, a fine-tuned CamemBERT-large, achieves a F1 score of 82.3% on this classification task, and a F1 score of 83% on the Reading Comprehension task.

We extract mathematical concepts from mathematical text using generative large language models (LLMs) like ChatGPT, contributing to the field of automatic term extraction (ATE) and mathematical text processing, and also to the study of LLMs themselves. Our work builds on that of others in that we aim for automatic extraction of terms (keywords) in one mathematical field, category theory, using as a corpus the 755 abstracts from a snapshot of the online journal "Theory and Applications of Categories", circa 2020. Where our study diverges from previous work is in (1) providing a more thorough analysis of what makes mathematical term extraction a difficult problem to begin with; (2) paying close attention to inter-annotator disagreements; (3) providing a set of guidelines which both human and machine annotators could use to standardize the extraction process; (4) introducing a new annotation tool to help humans with ATE, applicable to any mathematical field and even beyond mathematics; (5) using prompts to ChatGPT as part of the extraction process, and proposing best practices for such prompts; and (6) raising the question of whether ChatGPT could be used as an annotator on the same level as human experts. Our overall findings are that the matter of mathematical ATE is an interesting field which can benefit from participation by LLMs, but LLMs themselves cannot at this time surpass human performance on it.

We present miniF2F, a dataset of formal Olympiad-level mathematics problems statements intended to provide a unified cross-system benchmark for neural theorem proving. The miniF2F benchmark currently targets Metamath, Lean, Isabelle (partially) and HOL Light (partially) and consists of 488 problem statements drawn from the AIME, AMC, and the International Mathematical Olympiad (IMO), as well as material from high-school and undergraduate mathematics courses. We report baseline results using GPT-f, a neural theorem prover based on GPT-3 and provide an analysis of its performance. We intend for miniF2F to be a community-driven effort and hope that our benchmark will help spur advances in neural theorem proving.

We introduce Sabi\'a-2, a family of large language models trained on Portuguese texts. The models are evaluated on a diverse range of exams, including entry-level tests for Brazilian universities, professional certification exams, and graduate-level exams for various disciplines such as accounting, economics, engineering, law and medicine. Our results reveal that our best model so far, Sabi\'a-2 Medium, matches or surpasses GPT-4's performance in 23 out of 64 exams and outperforms GPT-3.5 in 58 out of 64 exams. Notably, specialization has a significant impact on a model's performance without the need to increase its size, allowing us to offer Sabi\'a-2 Medium at a price per token that is 10 times cheaper than GPT-4. Finally, we identified that math and coding are key abilities that need improvement.

We introduce the Formally Verified Automated Programming Progress Standards, or FVAPPS, a benchmark of 4715 samples for writing programs and proving their correctness, the largest formal verification benchmark, including 1083 curated and quality controlled samples. Previously, APPS provided a benchmark and dataset for programming puzzles to be completed in Python and checked against unit tests, of the kind seen in technical assessments in the software engineering industry. Building upon recent approaches for benchmarks in interactive theorem proving, we generalize the unit tests to Lean 4 theorems given without proof (i.e., using Lean's "sorry" keyword). On the 406 theorems of 100 randomly selected samples, Sonnet correctly proves 30% and Gemini correctly proves 18%. We challenge the machine learning and program synthesis communities to solve both each general purpose programming problem and its associated correctness specifications. The benchmark is available at https://huggingface.co/datasets/quinn-dougherty/fvapps.

Mathematical reasoning continues to be a critical challenge in large language model (LLM) development with significant interest. However, most of the cutting-edge progress in mathematical reasoning with LLMs has become closed-source due to lack of access to training data. This lack of data access limits researchers from understanding the impact of different choices for synthesizing and utilizing the data. With the goal of creating a high-quality finetuning (SFT) dataset for math reasoning, we conduct careful ablation experiments on data synthesis using the recently released Llama3.1 family of models. Our experiments show that: (a) solution format matters, with excessively verbose solutions proving detrimental to SFT performance, (b) data generated by a strong teacher outperforms on-policy data generated by a weak student model, (c) SFT is robust to low-quality solutions, allowing for imprecise data filtering, and (d) question diversity is crucial for achieving data scaling gains. Based on these insights, we create the OpenMathInstruct-2 dataset, which consists of 14M question-solution pairs (approx 600K unique questions), making it nearly eight times larger than the previous largest open-source math reasoning dataset. Finetuning the Llama-3.1-8B-Base using OpenMathInstruct-2 outperforms Llama3.1-8B-Instruct on MATH by an absolute 15.9\% (51.9\% rightarrow 67.8\%). Finally, to accelerate the open-source efforts, we release the code, the finetuned models, and the OpenMathInstruct-2 dataset under a commercially permissive license.

We propose Step-by-Step Coding (SBSC): a multi-turn math reasoning framework that enables Large Language Models (LLMs) to generate sequence of programs for solving Olympiad level math problems. At each step/turn, by leveraging the code execution outputs and programs of previous steps, the model generates the next sub-task and the corresponding program to solve it. This way, SBSC, sequentially navigates to reach the final answer. SBSC allows more granular, flexible and precise approach to problem-solving compared to existing methods. Extensive experiments highlight the effectiveness of SBSC in tackling competition and Olympiad-level math problems. For Claude-3.5-Sonnet, we observe SBSC (greedy decoding) surpasses existing state-of-the-art (SOTA) program generation based reasoning strategies by absolute 10.7% on AMC12, 8% on AIME and 12.6% on MathOdyssey. Given SBSC is multi-turn in nature, we also benchmark SBSC's greedy decoding against self-consistency decoding results of existing SOTA math reasoning strategies and observe performance gain by absolute 6.2% on AMC, 6.7% on AIME and 7.4% on MathOdyssey.

Large language models (LLMs) have obtained promising results in mathematical reasoning, which is a foundational skill for human intelligence. Most previous studies focus on improving and measuring the performance of LLMs based on textual math reasoning datasets (e.g., MATH, GSM8K). Recently, a few researchers have released English multimodal math datasets (e.g., MATHVISTA and MATH-V) to evaluate the effectiveness of large multimodal models (LMMs). In this paper, we release a Chinese multimodal math (CMM-Math) dataset, including benchmark and training parts, to evaluate and enhance the mathematical reasoning of LMMs. CMM-Math contains over 28,000 high-quality samples, featuring a variety of problem types (e.g., multiple-choice, fill-in-the-blank, and so on) with detailed solutions across 12 grade levels from elementary to high school in China. Specifically, the visual context may be present in the questions or opinions, which makes this dataset more challenging. Through comprehensive analysis, we discover that state-of-the-art LMMs on the CMM-Math dataset face challenges, emphasizing the necessity for further improvements in LMM development. We also propose a Multimodal Mathematical LMM (Math-LMM) to handle the problems with mixed input of multiple images and text segments. We train our model using three stages, including foundational pre-training, foundational fine-tuning, and mathematical fine-tuning. The extensive experiments indicate that our model effectively improves math reasoning performance by comparing it with the SOTA LMMs over three multimodal mathematical datasets.

We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original mathematical terms -- might be addressable via generation from language models. We present an automated prover and proof assistant, GPT-f, for the Metamath formalization language, and analyze its performance. GPT-f found new short proofs that were accepted into the main Metamath library, which is to our knowledge, the first time a deep-learning based system has contributed proofs that were adopted by a formal mathematics community.

Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmarks like GSM8K. In this paper, we formally study how language models solve these problems. We design a series of controlled experiments to address several fundamental questions: (1) Can language models truly develop reasoning skills, or do they simply memorize templates? (2) What is the model's hidden (mental) reasoning process? (3) Do models solve math questions using skills similar to or different from humans? (4) Do models trained on GSM8K-like datasets develop reasoning skills beyond those necessary for solving GSM8K problems? (5) What mental process causes models to make reasoning mistakes? (6) How large or deep must a model be to effectively solve GSM8K-level math questions? Our study uncovers many hidden mechanisms by which language models solve mathematical questions, providing insights that extend beyond current understandings of LLMs.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

While closed-source Large Language Models (LLMs) demonstrate strong mathematical problem-solving abilities, open-source models continue to struggle with such tasks. To bridge this gap, we propose a data augmentation approach and introduce PersonaMathQA, a dataset derived from MATH and GSM8K, on which we train the PersonaMath models. Our approach consists of two stages: the first stage is learning from Persona Diversification, and the second stage is learning from Reflection. In the first stage, we regenerate detailed chain-of-thought (CoT) solutions as instructions using a closed-source LLM and introduce a novel persona-driven data augmentation technique to enhance the dataset's quantity and diversity. In the second stage, we incorporate reflection to fully leverage more challenging and valuable questions. Evaluation of our PersonaMath models on MATH and GSM8K reveals that the PersonaMath-7B model (based on LLaMA-2-7B) achieves an accuracy of 24.2% on MATH and 68.7% on GSM8K, surpassing all baseline methods and achieving state-of-the-art performance. Notably, our dataset contains only 70.3K data points-merely 17.8% of MetaMathQA and 27% of MathInstruct-yet our model outperforms these baselines, demonstrating the high quality and diversity of our dataset, which enables more efficient model training. We open-source the PersonaMathQA dataset, PersonaMath models, and our code for public usage.

Preference optimization techniques, such as Direct Preference Optimization (DPO), are frequently employed to enhance the reasoning capabilities of large language models (LLMs) in domains like mathematical reasoning and coding, typically following supervised fine-tuning. These methods rely on high-quality labels for reasoning tasks to generate preference pairs; however, the availability of reasoning datasets with human-verified labels is limited. In this study, we introduce a novel approach to generate pseudo feedback for reasoning tasks by framing the labeling of solutions to reason problems as an evaluation against associated test cases. We explore two forms of pseudo feedback based on test cases: one generated by frontier LLMs and the other by extending self-consistency to multi-test-case. We conduct experiments on both mathematical reasoning and coding tasks using pseudo feedback for preference optimization, and observe improvements across both tasks. Specifically, using Mathstral-7B as our base model, we improve MATH results from 58.3 to 68.6, surpassing both NuminaMath-72B and GPT-4-Turbo-1106-preview. In GSM8K and College Math, our scores increase from 85.6 to 90.3 and from 34.3 to 42.3, respectively. Building on Deepseek-coder-7B-v1.5, we achieve a score of 24.6 on LiveCodeBench (from 21.1), surpassing Claude-3-Haiku.

Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 4,998 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research. Our benchmark and code are released at https://github.com/chen-judge/GeoQA .

Large Language Models (LLMs) exhibit strong potential in mathematical reasoning, yet their effectiveness is often limited by a shortage of high-quality queries. This limitation necessitates scaling up computational responses through self-generated data, yet current methods struggle due to spurious correlated data caused by ineffective exploration across all reasoning stages. To address such challenge, we introduce MARGE: Improving Math Reasoning with Guided Exploration, a novel method to address this issue and enhance mathematical reasoning through hit-guided exploration. MARGE systematically explores intermediate reasoning states derived from self-generated solutions, enabling adequate exploration and improved credit assignment throughout the reasoning process. Through extensive experiments across multiple backbone models and benchmarks, we demonstrate that MARGE significantly improves reasoning capabilities without requiring external annotations or training additional value models. Notably, MARGE improves both single-shot accuracy and exploration diversity, mitigating a common trade-off in alignment methods. These results demonstrate MARGE's effectiveness in enhancing mathematical reasoning capabilities and unlocking the potential of scaling self-generated training data. Our code and models are available at https://github.com/georgao35/MARGE{this link}.

We present EXAONE Deep series, which exhibits superior capabilities in various reasoning tasks, including math and coding benchmarks. We train our models mainly on the reasoning-specialized dataset that incorporates long streams of thought processes. Evaluation results show that our smaller models, EXAONE Deep 2.4B and 7.8B, outperform other models of comparable size, while the largest model, EXAONE Deep 32B, demonstrates competitive performance against leading open-weight models. All EXAONE Deep models are openly available for research purposes and can be downloaded from https://huggingface.co/LGAI-EXAONE

Question answering over source code provides software engineers and project managers with helpful information about the implemented features of a software product. This paper presents a work devoted to using large language models for question answering over source code in Python. The proposed method for implementing a source code question answering system involves fine-tuning a large language model on a unified dataset of questions and answers for Python code. To achieve the highest quality answers, we tested various models trained on datasets preprocessed in different ways: a dataset without grammar correction, a dataset with grammar correction, and a dataset augmented with the generated summaries. The model answers were also analyzed for errors manually. We report BLEU-4, BERTScore F1, BLEURT, and Exact Match metric values, along with the conclusions from the manual error analysis. The obtained experimental results highlight the current problems of the research area, such as poor quality of the public genuine question-answering datasets. In addition, the findings include the positive effect of the grammar correction of the training data on the testing metric values. The addressed findings and issues could be important for other researchers who attempt to improve the quality of source code question answering solutions. The training and evaluation code is publicly available at https://github.com/IU-AES-AI4Code/CodeQuestionAnswering.

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.

Large language models (LLMs) now achieve near-human performance on standard math word problem benchmarks (e.g., GSM8K), yet their true reasoning ability remains disputed. A key concern is that models often produce confident, yet unfounded, answers to unanswerable problems. We introduce TreeCut, a synthetic dataset that systematically generates infinite unanswerable math word problems and their answerable counterparts, by representing each question as a tree and removing chosen necessary conditions. Experiments show TreeCut effectively induce hallucinations in large language models, including GPT-4o and o3-mini, with rates of 64% and 44% in their respective worst-case scenarios under zero-shot setting. Further analysis highlights that deeper or more complex trees, composite item names, and removing necessary condition near the middle of a path all increase the likelihood of hallucinations, underscoring the persistent challenges LLMs face in identifying unanswerable math problems. The dataset generation code and sample data are available at https://github.com/j-bagel/treecut-math.

The recent progress in large language models (LLMs), especially the invention of chain-of-thoughts (CoT) prompting, makes it possible to solve reasoning problems. However, even the strongest LLMs are still struggling with more complicated problems that require non-linear thinking and multi-step reasoning. In this work, we explore whether LLMs have the ability to recognize their own errors, without resorting to external resources. In particular, we investigate whether they can be used to identify individual errors within a step-by-step reasoning. To this end, we propose a zero-shot verification scheme to recognize such errors. We then use this verification scheme to improve question-answering performance, by using it to perform weighted voting on different generated answers. We test the method on three math datasets-GSM8K, MathQA, and MATH-and find that it successfully recognizes errors and, in turn, increases final predictive performance.

Large language models (LLMs) have demonstrated impressive reasoning capabilities, particularly in textual mathematical problem-solving. However, existing open-source image instruction fine-tuning datasets, containing limited question-answer pairs per image, do not fully exploit visual information to enhance the multimodal mathematical reasoning capabilities of Multimodal LLMs (MLLMs). To bridge this gap, we address the lack of high-quality, diverse multimodal mathematical datasets by collecting 40K high-quality images with question-answer pairs from 24 existing datasets and synthesizing 320K new pairs, creating the MathV360K dataset, which enhances both the breadth and depth of multimodal mathematical questions. We introduce Math-LLaVA, a LLaVA-1.5-based model fine-tuned with MathV360K. This novel approach significantly improves the multimodal mathematical reasoning capabilities of LLaVA-1.5, achieving a 19-point increase and comparable performance to GPT-4V on MathVista's minitest split. Furthermore, Math-LLaVA demonstrates enhanced generalizability, showing substantial improvements on the MMMU benchmark. Our research highlights the importance of dataset diversity and synthesis in advancing MLLMs' mathematical reasoning abilities. The code and data are available at: https://github.com/HZQ950419/Math-LLaVA.

Recent large language models (LLMs) have demonstrated versatile capabilities in long-context scenarios. Although some recent benchmarks have been developed to evaluate the long-context capabilities of LLMs, there is a lack of benchmarks evaluating the mathematical reasoning abilities of LLMs over long contexts, which is crucial for LLMs' application in real-world scenarios. In this paper, we introduce MathHay, an automated benchmark designed to assess the long-context mathematical reasoning capabilities of LLMs. Unlike previous benchmarks like Needle in a Haystack, which focus primarily on information retrieval within long texts, MathHay demands models with both information-seeking and complex mathematical reasoning abilities. We conduct extensive experiments on MathHay to assess the long-context mathematical reasoning abilities of eight top-performing LLMs. Even the best-performing model, Gemini-1.5-Pro-002, still struggles with mathematical reasoning over long contexts, achieving only 51.26% accuracy at 128K tokens. This highlights the significant room for improvement on the MathHay benchmark.

In this paper we look at the ability of recent large language models (LLMs) at solving mathematical problems in combinatorics. We compare models LLaMA-2, LLaMA-3.1, GPT-4, and Mixtral against each other and against human pupils and undergraduates with prior experience in mathematical olympiads. To facilitate these comparisons we introduce the Combi-Puzzles dataset, which contains 125 problem variants based on 25 combinatorial reasoning problems. Each problem is presented in one of five distinct forms, created by systematically manipulating the problem statements through adversarial additions, numeric parameter changes, and linguistic obfuscation. Our variations preserve the mathematical core and are designed to measure the generalisability of LLM problem-solving abilities, while also increasing confidence that problems are submitted to LLMs in forms that have not been seen as training instances. We found that a model based on GPT-4 outperformed all other models in producing correct responses, and performed significantly better in the mathematical variation of the problems than humans. We also found that modifications to problem statements significantly impact the LLM's performance, while human performance remains unaffected.

This paper presents our system for SemEval-2025 Task 8: DataBench, Question-Answering over Tabular Data. The primary objective of this task is to perform question answering on given tabular datasets from diverse domains under two subtasks: DataBench QA (Subtask I) and DataBench Lite QA (Subtask II). To tackle both subtasks, we developed a zero-shot solution with a particular emphasis on leveraging Large Language Model (LLM)-based code generation. Specifically, we propose a Python code generation framework utilizing state-of-the-art open-source LLMs to generate executable Pandas code via optimized prompting strategies. Our experiments reveal that different LLMs exhibit varying levels of effectiveness in Python code generation. Additionally, results show that Python code generation achieves superior performance in tabular question answering compared to alternative approaches. Although our ranking among zero-shot systems is unknown at the time of this paper's submission, our system achieved eighth place in Subtask I and sixth place in Subtask~II among the 30 systems that outperformed the baseline in the open-source models category.

We propose a framework for robust evaluation of reasoning capabilities of language models, using functional variants of benchmarks. Models that solve a reasoning test should exhibit no difference in performance over the static version of a problem compared to a snapshot of the functional variant. We have rewritten the relevant fragment of the MATH benchmark into its functional variant MATH(), with functionalization of other benchmarks to follow. When evaluating current state-of-the-art models over snapshots of MATH(), we find a reasoning gap -- the percentage difference between the static and functional accuracies. We find reasoning gaps from 58.35% to 80.31% among the state-of-the-art closed and open weights models that perform well on static benchmarks, with the caveat that the gaps are likely to be smaller with more sophisticated prompting strategies. Here we show that models which anecdotally have good reasoning performance over real-world tasks, have quantifiable lower gaps, motivating the open problem of building "gap 0" models. Code for evaluation and new evaluation datasets, three MATH() snapshots, are publicly available at https://github.com/consequentai/fneval/.

Mathematical word problem-solving has long been recognized as a complex task for small language models (SLMs). A recent study hypothesized that the smallest model size, needed to achieve over 80% accuracy on the GSM8K benchmark, is 34 billion parameters. To reach this level of performance with smaller models, researcher often train SLMs to generate Python code or use tools to help avoid calculation errors. Additionally, they employ ensembling, where outputs of up to 100 model runs are combined to arrive at a more accurate result. Result selection is done using consensus, majority vote or a separate a verifier model used in conjunction with the SLM. Ensembling provides a substantial boost in accuracy but at a significant cost increase with multiple calls to the model (e.g., Phi-GSM uses top-48 to boost the performance from 68.2 to 81.5). In this work, we present Orca-Math, a 7-billion-parameter SLM based on the Mistral-7B, which achieves 86.81% on GSM8k without the need for multiple model calls or the use of verifiers, code execution or any other external tools. Our approach has the following key elements: (1) A high quality synthetic dataset of 200K math problems created using a multi-agent setup where agents collaborate to create the data, (2) An iterative learning techniques that enables the SLM to practice solving problems, receive feedback on its solutions and learn from preference pairs incorporating the SLM solutions and the feedback. When trained with Supervised Fine-Tuning alone, Orca-Math achieves 81.50% on GSM8k pass@1 metric. With iterative preference learning, Orca-Math achieves 86.81% pass@1. Orca-Math surpasses the performance of significantly larger models such as LLAMA-2-70B, WizardMath-70B, Gemini-Pro, ChatGPT-3.5. It also significantly outperforms other smaller models while using much smaller data (hundreds of thousands vs. millions of problems).

To bridge the gap between the capabilities of the state-of-the-art in factoid question answering (QA) and what users ask, we need large datasets of real user questions that capture the various question phenomena users are interested in, and the diverse ways in which these questions are formulated. We introduce ComQA, a large dataset of real user questions that exhibit different challenging aspects such as compositionality, temporal reasoning, and comparisons. ComQA questions come from the WikiAnswers community QA platform, which typically contains questions that are not satisfactorily answerable by existing search engine technology. Through a large crowdsourcing effort, we clean the question dataset, group questions into paraphrase clusters, and annotate clusters with their answers. ComQA contains 11,214 questions grouped into 4,834 paraphrase clusters. We detail the process of constructing ComQA, including the measures taken to ensure its high quality while making effective use of crowdsourcing. We also present an extensive analysis of the dataset and the results achieved by state-of-the-art systems on ComQA, demonstrating that our dataset can be a driver of future research on QA.

Designing high-quality educational questions is a challenging and time-consuming task. In this work, we propose a novel approach that utilizes prompt-based techniques to generate descriptive and reasoning-based questions. However, current question-answering (QA) datasets are inadequate for conducting our experiments on prompt-based question generation (QG) in an educational setting. Therefore, we curate a new QG dataset called EduProbe for school-level subjects, by leveraging the rich content of NCERT textbooks. We carefully annotate this dataset as quadruples of 1) Context: a segment upon which the question is formed; 2) Long Prompt: a long textual cue for the question (i.e., a longer sequence of words or phrases, covering the main theme of the context); 3) Short Prompt: a short textual cue for the question (i.e., a condensed representation of the key information or focus of the context); 4) Question: a deep question that aligns with the context and is coherent with the prompts. We investigate several prompt-based QG methods by fine-tuning pre-trained transformer-based large language models (LLMs), namely PEGASUS, T5, MBART, and BART. Moreover, we explore the performance of two general-purpose pre-trained LLMs such as Text-Davinci-003 and GPT-3.5-Turbo without any further training. By performing automatic evaluation, we show that T5 (with long prompt) outperforms all other models, but still falls short of the human baseline. Under human evaluation criteria, TextDavinci-003 usually shows better results than other models under various prompt settings. Even in the case of human evaluation criteria, QG models mostly fall short of the human baseline. Our code and dataset are available at: https://github.com/my625/PromptQG

Large Language Models (LLMs) excel at complex reasoning through search algorithms, yet current strategies often suffer from massive token consumption due to redundant exploration of semantically equivalent steps. Existing semantic similarity methods struggle to accurately identify such equivalence in domain-specific contexts like mathematical reasoning. To address this, we propose EquivPruner, a simple yet effective approach that identifies and prunes semantically equivalent actions during LLM reasoning search. We also introduce MathEquiv, the first dataset we created for mathematical statement equivalence, which enables the training of a lightweight equivalence detector. Extensive experiments across various models and tasks demonstrate that EquivPruner significantly reduces token consumption, improving searching efficiency and often bolstering reasoning accuracy. For instance, when applied to Qwen2.5-Math-7B-Instruct on GSM8K, EquivPruner reduced token consumption by 48.1\% while also improving accuracy. Our code is available at https://github.com/Lolo1222/EquivPruner.

Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.

Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.

The evaluation of mathematical reasoning capabilities is essential for advancing Artificial General Intelligence (AGI). While Large Language Models (LLMs) have shown impressive performance in solving mathematical problems, existing benchmarks such as GSM8K and MATH present limitations, including narrow problem definitions with specific numbers and reliance on predetermined rules that hinder accurate assessments of reasoning and adaptability. This paper introduces the UTMath Benchmark, which robustly evaluates the models through extensive unit tests. It consists of 1,053 problems across 9 mathematical domains, with over 68 test cases per problem. We propose an innovative evaluation framework inspired by unit testing in software development, focusing on both accuracy and reliability of results. Furthermore, we introduce the Reasoning-to-Coding of Thoughts (RCoT) approach, which encourages LLMs to perform explicit reasoning before generating code, leading to generating more advanced solution and improved performance. Furthermore, we are releasing not only the UTMath benchmark but also the UTMath-Train training dataset (more than 70k samples), to support the community in further exploring mathematical reasoning.

We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra puzzles. Each puzzle is associated with the entire set of atomic questions that can be generated based on the relations and individuals occurring in the text. For each question we provide the correct answer: entailment, contradiction or ambiguity. The answer's correctness is verified against theorem provers. Good puzzles have two properties: (i) each piece of information is necessary and (ii) no unnecessary information is provided. These properties make puzzles interesting candidates for machine comprehension tasks.

In this paper, we introduce and apply Operations Research Question Answering (ORQA), a new benchmark designed to assess the generalization capabilities of Large Language Models (LLMs) in the specialized technical domain of Operations Research (OR). This benchmark evaluates whether LLMs can emulate the knowledge and reasoning skills of OR experts when confronted with diverse and complex optimization problems. The dataset, developed by OR experts, features real-world optimization problems that demand multistep reasoning to construct their mathematical models. Our evaluations of various open source LLMs, such as LLaMA 3.1, DeepSeek, and Mixtral, reveal their modest performance, highlighting a gap in their ability to generalize to specialized technical domains. This work contributes to the ongoing discourse on LLMs generalization capabilities, offering valuable insights for future research in this area. The dataset and evaluation code are publicly available.

Theano is a Python library that allows to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Since its introduction, it has been one of the most used CPU and GPU mathematical compilers - especially in the machine learning community - and has shown steady performance improvements. Theano is being actively and continuously developed since 2008, multiple frameworks have been built on top of it and it has been used to produce many state-of-the-art machine learning models. The present article is structured as follows. Section I provides an overview of the Theano software and its community. Section II presents the principal features of Theano and how to use them, and compares them with other similar projects. Section III focuses on recently-introduced functionalities and improvements. Section IV compares the performance of Theano against Torch7 and TensorFlow on several machine learning models. Section V discusses current limitations of Theano and potential ways of improving it.

In recent years, the rapid development of large reasoning models has resulted in the saturation of existing benchmarks for evaluating mathematical reasoning, highlighting the urgent need for more challenging and rigorous evaluation frameworks. To address this gap, we introduce OlymMATH, a novel Olympiad-level mathematical benchmark, designed to rigorously test the complex reasoning capabilities of LLMs. OlymMATH features 200 meticulously curated problems, each manually verified and available in parallel English and Chinese versions. The problems are systematically organized into two distinct difficulty tiers: (1) AIME-level problems (easy) that establish a baseline for mathematical reasoning assessment, and (2) significantly more challenging problems (hard) designed to push the boundaries of current state-of-the-art models. In our benchmark, these problems span four core mathematical fields, each including a verifiable numerical solution to enable objective, rule-based evaluation. Empirical results underscore the significant challenge presented by OlymMATH, with state-of-the-art models including DeepSeek-R1 and OpenAI's o3-mini demonstrating notably limited accuracy on the hard subset. Furthermore, the benchmark facilitates comprehensive bilingual assessment of mathematical reasoning abilities-a critical dimension that remains largely unaddressed in mainstream mathematical reasoning benchmarks. We release the OlymMATH benchmark at the STILL project: https://github.com/RUCAIBox/Slow_Thinking_with_LLMs.

In current NLP research, large-scale language models and their abilities are widely being discussed. Some recent works have also found notable failures of these models. Often these failure examples involve complex reasoning abilities. This work focuses on a simple commonsense ability, reasoning about when an action (or its effect) is feasible. To this end, we introduce FeasibilityQA, a question-answering dataset involving binary classification (BCQ) and multi-choice multi-correct questions (MCQ) that test understanding of feasibility. We show that even state-of-the-art models such as GPT-3, GPT-2, and T5 struggle to answer the feasibility questions correctly. Specifically, on MCQ and BCQ questions, GPT-3 achieves an accuracy of just (19%, 62%) and (25%, 64%) in zero-shot and few-shot settings, respectively. We also evaluate models by providing relevant knowledge statements required to answer the question. We find that the additional knowledge leads to a 7% gain in performance, but the overall performance still remains low. These results make one wonder how much commonsense knowledge about action feasibility is encoded in state-of-the-art models and how well they can reason about it.

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

Test set contamination, wherein test data from a benchmark ends up in a newer model's training set, is a well-documented obstacle for fair LLM evaluation and can quickly render benchmarks obsolete. To mitigate this, many recent benchmarks crowdsource new prompts and evaluations from human or LLM judges; however, these can introduce significant biases, and break down when scoring hard questions. In this work, we introduce a new benchmark for LLMs designed to be immune to both test set contamination and the pitfalls of LLM judging and human crowdsourcing. We release LiveBench, the first benchmark that (1) contains frequently-updated questions from recent information sources, (2) scores answers automatically according to objective ground-truth values, and (3) contains a wide variety of challenging tasks, spanning math, coding, reasoning, language, instruction following, and data analysis. To achieve this, LiveBench contains questions that are based on recently-released math competitions, arXiv papers, news articles, and datasets, and it contains harder, contamination-free versions of tasks from previous benchmarks such as Big-Bench Hard, AMPS, and IFEval. We evaluate many prominent closed-source models, as well as dozens of open-source models ranging from 0.5B to 110B in size. LiveBench is difficult, with top models achieving below 65% accuracy. We release all questions, code, and model answers. Questions will be added and updated on a monthly basis, and we will release new tasks and harder versions of tasks over time so that LiveBench can distinguish between the capabilities of LLMs as they improve in the future. We welcome community engagement and collaboration for expanding the benchmark tasks and models.

The math abilities of large language models can represent their abstract reasoning ability. In this paper, we introduce and open-source our math reasoning LLMs InternLM-Math which is continue pre-trained from InternLM2. We unify chain-of-thought reasoning, reward modeling, formal reasoning, data augmentation, and code interpreter in a unified seq2seq format and supervise our model to be a versatile math reasoner, verifier, prover, and augmenter. These abilities can be used to develop the next math LLMs or self-iteration. InternLM-Math obtains open-sourced state-of-the-art performance under the setting of in-context learning, supervised fine-tuning, and code-assisted reasoning in various informal and formal benchmarks including GSM8K, MATH, Hungary math exam, MathBench-ZH, and MiniF2F. Our pre-trained model achieves 30.3 on the MiniF2F test set without fine-tuning. We further explore how to use LEAN to solve math problems and study its performance under the setting of multi-task learning which shows the possibility of using LEAN as a unified platform for solving and proving in math. Our models, codes, and data are released at https://github.com/InternLM/InternLM-Math.

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstats and Giotto-TDA. The challenge attracted 16 teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

Recent advancements in Large Language Models (LLMs) have sparked interest in their formal reasoning capabilities, particularly in mathematics. The GSM8K benchmark is widely used to assess the mathematical reasoning of models on grade-school-level questions. While the performance of LLMs on GSM8K has significantly improved in recent years, it remains unclear whether their mathematical reasoning capabilities have genuinely advanced, raising questions about the reliability of the reported metrics. To address these concerns, we conduct a large-scale study on several SOTA open and closed models. To overcome the limitations of existing evaluations, we introduce GSM-Symbolic, an improved benchmark created from symbolic templates that allow for the generation of a diverse set of questions. GSM-Symbolic enables more controllable evaluations, providing key insights and more reliable metrics for measuring the reasoning capabilities of models.Our findings reveal that LLMs exhibit noticeable variance when responding to different instantiations of the same question. Specifically, the performance of all models declines when only the numerical values in the question are altered in the GSM-Symbolic benchmark. Furthermore, we investigate the fragility of mathematical reasoning in these models and show that their performance significantly deteriorates as the number of clauses in a question increases. We hypothesize that this decline is because current LLMs cannot perform genuine logical reasoning; they replicate reasoning steps from their training data. Adding a single clause that seems relevant to the question causes significant performance drops (up to 65%) across all state-of-the-art models, even though the clause doesn't contribute to the reasoning chain needed for the final answer. Overall, our work offers a more nuanced understanding of LLMs' capabilities and limitations in mathematical reasoning.

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.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in visual mathematical reasoning across various existing benchmarks. However, these benchmarks are predominantly based on clean or processed multimodal inputs, without incorporating the images provided by real-world Kindergarten through 12th grade (K-12) educational users. To address this gap, we introduce MathReal, a meticulously curated dataset comprising 2,000 mathematical questions with images captured by handheld mobile devices in authentic scenarios. Each question is an image, containing the question text and visual element. We systematically classify the real images into three primary categories: image quality degradation, perspective variation, and irrelevant content interference, which are further delineated into 14 subcategories. Additionally, MathReal spans five core knowledge and ability categories, which encompass three question types and are divided into three difficulty levels. To comprehensively evaluate the multimodal mathematical reasoning abilities of state-of-the-art MLLMs in real-world scenarios, we design six experimental settings that enable a systematic analysis of their performance. Through extensive experimentation, we find that the problem-solving abilities of existing MLLMs are significantly challenged in realistic educational contexts. Based on this, we conduct a thorough analysis of their performance and error patterns, providing insights into their recognition, comprehension, and reasoning capabilities, and outlining directions for future improvements. Data and code: https://github.com/junfeng0288/MathReal.

We present PutnamBench, a new multilingual benchmark for evaluating the ability of neural theorem-provers to solve competition mathematics problems. PutnamBench consists of 1697 hand-constructed formalizations of 640 theorems sourced from the William Lowell Putnam Mathematical Competition, the premier undergraduate-level mathematics competition in North America. All the theorems have formalizations in Lean 4 and Isabelle; a substantial subset also has Coq formalizations. Proving the theorems requires significant problem-solving ability and proficiency in a broad range of topics taught in undergraduate mathematics courses. We use PutnamBench to evaluate several established neural and symbolic theorem-provers. These approaches can only solve a handful of the PutnamBench problems, establishing the benchmark as a difficult open challenge for research on neural theorem-proving. PutnamBench is available at https://github.com/trishullab/PutnamBench.

Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages is the lack of parallel datasets that align natural language with formal language proofs. To address this challenge, this paper introduces a novel framework for translating the Mathlib4 corpus (a unified library of mathematics in formal language Lean 4) into natural language. Building upon this, we employ a dual augmentation strategy that combines tactic-based and informal-based approaches, leveraging the Lean-jixia system, a Lean 4 analyzer. We present the results of this pipeline on Mathlib4 as Herald (Hierarchy and Retrieval-based Translated Lean Dataset). We also propose the Herald Translator, which is fine-tuned on Herald. Herald translator achieves a 93.2% accuracy (Pass@128) on formalizing statements in the miniF2F-test and a 22.5% accuracy on our internal graduate-level textbook dataset, outperforming InternLM2-Math-Plus-7B (74.0% and 7.5%) and TheoremLlama (50.1% and 4.0%). Furthermore, we propose a section-level translation framework for real-world applications. As a direct application of Herald translator, we have successfully translated a template section in the Stack project, marking a notable progress in the automatic formalization of graduate-level mathematical literature. Our model, along with the datasets, will be open-sourced to the public soon.

We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most major branches of modern mathematics -- from computationally intensive problems in number theory and real analysis to abstract questions in algebraic geometry and category theory. Solving a typical problem requires multiple hours of effort from a researcher in the relevant branch of mathematics, and for the upper end questions, multiple days. FrontierMath uses new, unpublished problems and automated verification to reliably evaluate models while minimizing risk of data contamination. Current state-of-the-art AI models solve under 2% of problems, revealing a vast gap between AI capabilities and the prowess of the mathematical community. As AI systems advance toward expert-level mathematical abilities, FrontierMath offers a rigorous testbed that quantifies their progress.

Python is one of the fastest-growing programming languages and currently ranks as the top language in many lists, even recently overtaking JavaScript as the top language on GitHub. Given its importance in data science and machine learning, it is imperative to be able to effectively train LLMs to generate good unit test cases for Python code. This motivates the need for a large dataset to provide training and testing data. To date, while other large datasets exist for languages like Java, none publicly exist for Python. Python poses difficult challenges in generating such a dataset, due to its less rigid naming requirements. In this work, we consider two commonly used Python unit testing frameworks: Pytest and unittest. We analyze a large corpus of over 88K open-source GitHub projects utilizing these testing frameworks. Using a carefully designed set of heuristics, we are able to locate over 22 million test methods. We then analyze the test and non-test code and map individual unit tests to the focal method being tested. This provides an explicit traceability link from the test to the tested method. Our pyMethods2Test dataset contains over 2 million of these focal method mappings, as well as the ability to generate useful context for input to LLMs. The pyMethods2Test dataset is publicly available on Zenodo at: https://doi.org/10.5281/zenodo.14264518

The AM-DeepSeek-R1-Distilled is a large-scale dataset with thinking traces for general reasoning tasks, composed of high-quality and challenging reasoning problems. These problems are collected from a multitude of open-source datasets, subjected to semantic deduplication and meticulous cleaning to eliminate test set contamination. All responses within the dataset are distilled from reasoning models (predominantly DeepSeek-R1) and have undergone rigorous verification procedures. Mathematical problems are validated by checking against reference answers, code problems are verified using test cases, and other tasks are evaluated with the aid of a reward model. The AM-Distill-Qwen-32B model, which was trained through only simple Supervised Fine-Tuning (SFT) using this batch of data, outperformed the DeepSeek-R1-Distill-Qwen-32B model on four benchmarks: AIME2024, MATH-500, GPQA-Diamond, and LiveCodeBench. Additionally, the AM-Distill-Qwen-72B model surpassed the DeepSeek-R1-Distill-Llama-70B model on all benchmarks as well. We are releasing these 1.4 million problems and their corresponding responses to the research community with the objective of fostering the development of powerful reasoning-oriented Large Language Models (LLMs). The dataset was published in https://huggingface.co/datasets/a-m-team/AM-DeepSeek-R1-Distilled-1.4M{https://huggingface.co/datasets/a-m-team/AM-DeepSeek-R1-Distilled-1.4M}.

Large Language Models (LLMs) have shown strong performance in solving mathematical problems, with code-based solutions proving particularly effective. However, the best practice to leverage coding instruction data to enhance mathematical reasoning remains underexplored. This study investigates three key questions: (1) How do different coding styles of mathematical code-based rationales impact LLMs' learning performance? (2) Can general-domain coding instructions improve performance? (3) How does integrating textual rationales with code-based ones during training enhance mathematical reasoning abilities? Our findings reveal that code-based rationales with concise comments, descriptive naming, and hardcoded solutions are beneficial, while improvements from general-domain coding instructions and textual rationales are relatively minor. Based on these insights, we propose CoinMath, a learning strategy designed to enhance mathematical reasoning by diversifying the coding styles of code-based rationales. CoinMath generates a variety of code-based rationales incorporating concise comments, descriptive naming conventions, and hardcoded solutions. Experimental results demonstrate that CoinMath significantly outperforms its baseline model, MAmmoTH, one of the SOTA math LLMs.

We present Archer, a challenging bilingual text-to-SQL dataset specific to complex reasoning, including arithmetic, commonsense and hypothetical reasoning. It contains 1,042 English questions and 1,042 Chinese questions, along with 521 unique SQL queries, covering 20 English databases across 20 domains. Notably, this dataset demonstrates a significantly higher level of complexity compared to existing publicly available datasets. Our evaluation shows that Archer challenges the capabilities of current state-of-the-art models, with a high-ranked model on the Spider leaderboard achieving only 6.73% execution accuracy on Archer test set. Thus, Archer presents a significant challenge for future research in this field.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities for MWPs. Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt, providing the correct reasoning path for the generation model to refer to. Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method, which achieves a significant improvement of up to 6.7 percent on average in absolute value, compared to baseline methods. These results highlight our method's potential in addressing the reasoning challenges in current LLMs.

With video games now generating the highest revenues in the entertainment industry, optimizing game development workflows has become essential for the sector's sustained growth. Recent advancements in Vision-Language Models (VLMs) offer considerable potential to automate and enhance various aspects of game development, particularly Quality Assurance (QA), which remains one of the industry's most labor-intensive processes with limited automation options. To accurately evaluate the performance of VLMs in video game QA tasks and determine their effectiveness in handling real-world scenarios, there is a clear need for standardized benchmarks, as existing benchmarks are insufficient to address the specific requirements of this domain. To bridge this gap, we introduce VideoGameQA-Bench, a comprehensive benchmark that covers a wide array of game QA activities, including visual unit testing, visual regression testing, needle-in-a-haystack tasks, glitch detection, and bug report generation for both images and videos of various games. Code and data are available at: https://asgaardlab.github.io/videogameqa-bench/