Daily Papers

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.

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.

Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most existing work and datasets concentrate on computational tasks, leaving gaps in areas like mathematical analysis, which demands rigorous proofs and formal reasoning. We developed the DEMI-MathAnalysis dataset, comprising proof-based problems from mathematical analysis topics such as Sequences and Limits, Infinite Series, and Convex Functions. We also designed a guiding framework to rigorously enhance LLMs' ability to solve these problems. Through fine-tuning LLMs on this dataset and employing our framework, we observed significant improvements in their capability to generate logical, complete, and elegant proofs. This work addresses critical gaps in mathematical reasoning and contributes to advancing trustworthy AI capable of handling formalized mathematical language. The code is publicly accessible at LLMs for Mathematical Analysis.

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a comprehensive survey of mathematical LMs, systematically categorizing pivotal research endeavors from two distinct perspectives: tasks and methodologies. The landscape reveals a large number of proposed mathematical LLMs, which are further delineated into instruction learning, tool-based methods, fundamental CoT techniques, and advanced CoT methodologies. In addition, our survey entails the compilation of over 60 mathematical datasets, including training datasets, benchmark datasets, and augmented datasets. Addressing the primary challenges and delineating future trajectories within the field of mathematical LMs, this survey is positioned as a valuable resource, poised to facilitate and inspire future innovation among researchers invested in advancing this domain.

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.

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 demand for Large Language Models (LLMs) capable of sophisticated mathematical reasoning is growing across industries. However, the development of performant mathematical LLMs is critically bottlenecked by the scarcity of difficult, novel training data. We introduce SAND-Math (Synthetic Augmented Novel and Difficult Mathematics problems and solutions), a pipeline that addresses this by first generating high-quality problems from scratch and then systematically elevating their complexity via a new Difficulty Hiking step. We demonstrate the effectiveness of our approach through two key findings. First, augmenting a strong baseline with SAND-Math data significantly boosts performance, outperforming the next-best synthetic dataset by uparrow 17.85 absolute points on the AIME25 benchmark. Second, in a dedicated ablation study, we show our Difficulty Hiking process is highly effective: by increasing average problem difficulty from 5.02 to 5.98, this step lifts AIME25 performance from 46.38\% to 49.23\%. The full generation pipeline, final dataset, and a fine-tuned model form a practical and scalable toolkit for building more capable and efficient mathematical reasoning LLMs. SAND-Math dataset is released here: https://huggingface.co/datasets/amd/SAND-MATH{https://huggingface.co/datasets/amd/SAND-MATH}

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!

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.

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 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.

While automatic dialogue tutors hold great potential in making education personalized and more accessible, research on such systems has been hampered by a lack of sufficiently large and high-quality datasets. Collecting such datasets remains challenging, as recording tutoring sessions raises privacy concerns and crowdsourcing leads to insufficient data quality. To address this, we propose a framework to generate such dialogues by pairing human teachers with a Large Language Model (LLM) prompted to represent common student errors. We describe how we use this framework to collect MathDial, a dataset of 3k one-to-one teacher-student tutoring dialogues grounded in multi-step math reasoning problems. While models like GPT-3 are good problem solvers, they fail at tutoring because they generate factually incorrect feedback or are prone to revealing solutions to students too early. To overcome this, we let teachers provide learning opportunities to students by guiding them using various scaffolding questions according to a taxonomy of teacher moves. We demonstrate MathDial and its extensive annotations can be used to finetune models to be more effective tutors (and not just solvers). We confirm this by automatic and human evaluation, notably in an interactive setting that measures the trade-off between student solving success and telling solutions. The dataset is released publicly.

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.

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 .

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

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.

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.

To improve language models' proficiency in mathematical reasoning via continual pretraining, we introduce a novel strategy that leverages base language models for autonomous data selection. Departing from conventional supervised fine-tuning or trained classifiers with human-annotated data, our approach utilizes meta-prompted language models as zero-shot verifiers to autonomously evaluate and select high-quality mathematical content, and we release the curated open-source AutoMathText dataset encompassing over 200GB of data. To demonstrate the efficacy of our method, we continuously pretrained a 7B-parameter Mistral language model on the AutoMathText dataset, achieving substantial improvements in downstream performance on the MATH dataset with a token amount reduced by orders of magnitude compared to previous continuous pretraining works. Our method showcases a 2 times increase in pretraining token efficiency compared to baselines, underscoring the potential of our approach in enhancing models' mathematical reasoning capabilities. The AutoMathText dataset is available at https://huggingface.co/datasets/math-ai/AutoMathText. The code is available at https://github.com/yifanzhang-pro/AutoMathText.

Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's uses of shortcuts and wrong reasoning while the later poses challenges in accommodating alternative solutions. In this work, we seek to use symbolic programs as a means for automated evaluation if a model can consistently produce correct final answers across various inputs to the program. We begin by extracting programs for popular math datasets (GSM8K and MATH) using GPT4-o. For those executable programs verified using the original input-output pairs, they are found to encapsulate the proper reasoning required to solve the original text questions. We then prompt GPT4-o to generate new questions using alternative input-output pairs based the extracted program. We apply the resulting datasets to evaluate a collection of LLMs. In our experiments, we observe significant accuracy drops using our proposed evaluation compared with original static examples, suggesting the fragility of math reasoning in state-of-the-art LLMs.

This paper introduces DOoM, a new open-source benchmark designed to assess the capabilities of language models in solving mathematics and physics problems in Russian. The benchmark includes problems of varying difficulty, ranging from school-level tasks to university Olympiad and entrance exam questions. In this paper we discuss the motivation behind its creation, describe dataset's structure and evaluation methodology, and present initial results from testing various models. Analysis of the results shows a correlation between model performance and the number of tokens used, and highlights differences in performance between mathematics and physics tasks.

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.

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.

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.

The rapid advancement of large language models (LLMs) such as GPT-3, PaLM, and Llama has significantly transformed natural language processing, showcasing remarkable capabilities in understanding and generating language. However, these models often struggle with tasks requiring complex reasoning, particularly in mathematical problem-solving, due in part to the scarcity of large-scale, high-quality, domain-specific datasets necessary for training sophisticated reasoning abilities. To address this limitation, we introduce Template-based Data Generation (TDG), a novel approach that leverages LLMs (GPT-4) to automatically generate parameterized meta-templates, which are then used to synthesize a vast array of high-quality problems and solutions. Leveraging TDG, we create TemplateMath Part I: TemplateGSM, a dataset comprising over 7 million synthetically generated grade school math problems--each accompanied by code-based and natural language solutions--with the potential to generate an effectively unlimited number more. This dataset alleviates the scarcity of large-scale mathematical datasets and serves as a valuable resource for pre-training, fine-tuning, and evaluating LLMs in mathematical reasoning. Our method not only enables the generation of virtually infinite data but also elevates data augmentation to a new level by using GPT-4 for meta-template generation, ensuring diverse and high-quality problem structures. The TemplateMath Part I: TemplateGSM dataset is publicly available at https://huggingface.co/datasets/math-ai/TemplateGSM. The code is available at https://github.com/iiis-ai/TemplateMath.

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.

Efficient and accurate autoformalization methods, which leverage large-scale datasets of extensive natural language mathematical problems to construct formal language datasets, are key to advancing formal mathematical reasoning. In this paper, we propose an autoformalization pipeline based on large language models with error feedback, achieving a fully automatic and training-free formalization approach. Using this pipeline, we curate an Olympiad-level dataset aligning natural language problems with Lean formalizations. The dataset comprises 3,922 mathematical problems in natural language and 9,787 in Lean, of which 64.46% were assessed as at least above-average quality, making it suitable as a benchmark for automated theorem provers. Additionally, we investigate the formalization and reasoning capabilities of various LLMs and empirically demonstrate that few-shot learning, error feedback, and increasing sampling numbers enhance the autoformalization process. Experiments of three automated theorem provers on the \dataset\ dataset also highlight its challenging nature and its value as a benchmark for formal reasoning tasks.

Modern machine learning relies on datasets to develop and validate research ideas. Given the growth of publicly available data, finding the right dataset to use is increasingly difficult. Any research question imposes explicit and implicit constraints on how well a given dataset will enable researchers to answer this question, such as dataset size, modality, and domain. We operationalize the task of recommending datasets given a short natural language description of a research idea, to help people find relevant datasets for their needs. Dataset recommendation poses unique challenges as an information retrieval problem; datasets are hard to directly index for search and there are no corpora readily available for this task. To facilitate this task, we build the DataFinder Dataset which consists of a larger automatically-constructed training set (17.5K queries) and a smaller expert-annotated evaluation set (392 queries). Using this data, we compare various information retrieval algorithms on our test set and present a superior bi-encoder retriever for text-based dataset recommendation. This system, trained on the DataFinder Dataset, finds more relevant search results than existing third-party dataset search engines. To encourage progress on dataset recommendation, we release our dataset and models to the public.

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.

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.

Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities across various tasks, but still struggle with complex mathematical reasoning. Existing research primarily focuses on dataset construction and method optimization, often overlooking two critical aspects: comprehensive knowledge-driven design and model-centric data space modeling. In this paper, we introduce We-Math 2.0, a unified system that integrates a structured mathematical knowledge system, model-centric data space modeling, and a reinforcement learning (RL)-based training paradigm to comprehensively enhance the mathematical reasoning abilities of MLLMs. The key contributions of We-Math 2.0 are fourfold: (1) MathBook Knowledge System: We construct a five-level hierarchical system encompassing 491 knowledge points and 1,819 fundamental principles. (2) MathBook-Standard & Pro: We develop MathBook-Standard, a dataset that ensures broad conceptual coverage and flexibility through dual expansion. Additionally, we define a three-dimensional difficulty space and generate 7 progressive variants per problem to build MathBook-Pro, a challenging dataset for robust training. (3) MathBook-RL: We propose a two-stage RL framework comprising: (i) Cold-Start Fine-tuning, which aligns the model with knowledge-oriented chain-of-thought reasoning; and (ii) Progressive Alignment RL, leveraging average-reward learning and dynamic data scheduling to achieve progressive alignment across difficulty levels. (4) MathBookEval: We introduce a comprehensive benchmark covering all 491 knowledge points with diverse reasoning step distributions. Experimental results show that MathBook-RL performs competitively with existing baselines on four widely-used benchmarks and achieves strong results on MathBookEval, suggesting promising generalization in mathematical reasoning.

Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries. Hypothesizing that difficult queries are crucial to learn complex reasoning, we propose Difficulty-Aware Rejection Tuning (DART), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples. Utilizing DART, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4. We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called DART-MATH. In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, DART-MATH outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models. Furthermore, our results position our synthetic datasets as the most effective and cost-efficient publicly available resources for advancing mathematical problem-solving.

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

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.

Machine learning based decision-support tools in criminal justice systems are subjects of intense discussions and academic research. There are important open questions about the utility and fairness of such tools. Academic researchers often rely on a few small datasets that are not sufficient to empirically study various real-world aspects of these questions. In this paper, we contribute WCLD, a curated large dataset of 1.5 million criminal cases from circuit courts in the U.S. state of Wisconsin. We used reliable public data from 1970 to 2020 to curate attributes like prior criminal counts and recidivism outcomes. The dataset contains large number of samples from five racial groups, in addition to information like sex and age (at judgment and first offense). Other attributes in this dataset include neighborhood characteristics obtained from census data, detailed types of offense, charge severity, case decisions, sentence lengths, year of filing etc. We also provide pseudo-identifiers for judge, county and zipcode. The dataset will not only enable researchers to more rigorously study algorithmic fairness in the context of criminal justice, but also relate algorithmic challenges with various systemic issues. We also discuss in detail the process of constructing the dataset and provide a datasheet. The WCLD dataset is available at https://clezdata.github.io/wcld/.

In this paper, we present MusPy, an open source Python library for symbolic music generation. MusPy provides easy-to-use tools for essential components in a music generation system, including dataset management, data I/O, data preprocessing and model evaluation. In order to showcase its potential, we present statistical analysis of the eleven datasets currently supported by MusPy. Moreover, we conduct a cross-dataset generalizability experiment by training an autoregressive model on each dataset and measuring held-out likelihood on the others---a process which is made easier by MusPy's dataset management system. The results provide a map of domain overlap between various commonly used datasets and show that some datasets contain more representative cross-genre samples than others. Along with the dataset analysis, these results might serve as a guide for choosing datasets in future research. Source code and documentation are available at https://github.com/salu133445/muspy .

Advanced applied mathematics problems are underrepresented in existing Large Language Model (LLM) benchmark datasets. To address this, we introduce HARDMath, a dataset inspired by a graduate course on asymptotic methods, featuring challenging applied mathematics problems that require analytical approximation techniques. These problems demand a combination of mathematical reasoning, computational tools, and subjective judgment, making them difficult for LLMs. Our framework auto-generates a large number of problems with solutions validated against numerical ground truths. We evaluate both open- and closed-source LLMs on HARDMath-mini, a sub-sampled test set of 366 problems, as well as on 40 word problems formulated in applied science contexts. Even leading closed-source models like GPT-4 achieve only 43.8% overall accuracy with few-shot Chain-of-Thought prompting, and all models demonstrate significantly lower performance compared to results on existing mathematics benchmark datasets. We additionally conduct a detailed error analysis to gain insights into the failure cases of LLMs. These results demonstrate limitations of current LLM performance on advanced graduate-level applied math problems and underscore the importance of datasets like HARDMath to advance mathematical abilities of LLMs.

This paper introduces a public dataset of 1.4 million procedurally-generated bicycle designs represented parametrically, as JSON files, and as rasterized images. The dataset is created through the use of a rendering engine which harnesses the BikeCAD software to generate vector graphics from parametric designs. This rendering engine is discussed in the paper and also released publicly alongside the dataset. Though this dataset has numerous applications, a principal motivation is the need to train cross-modal predictive models between parametric and image-based design representations. For example, we demonstrate that a predictive model can be trained to accurately estimate Contrastive Language-Image Pretraining (CLIP) embeddings from a parametric representation directly. This allows similarity relations to be established between parametric bicycle designs and text strings or reference images. Trained predictive models are also made public. The dataset joins the BIKED dataset family which includes thousands of mixed-representation human-designed bicycle models and several datasets quantifying design performance. The code and dataset can be found at: https://github.com/Lyleregenwetter/BIKED_multimodal/tree/main

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 rapid development of large language models (LLMs) has spurred extensive research into their domain-specific capabilities, particularly mathematical reasoning. However, most open-source LLMs focus solely on mathematical reasoning, neglecting the integration with visual injection, despite the fact that many mathematical tasks rely on visual inputs such as geometric diagrams, charts, and function plots. To fill this gap, we introduce MultiMath-7B, a multimodal large language model that bridges the gap between math and vision. MultiMath-7B is trained through a four-stage process, focusing on vision-language alignment, visual and math instruction-tuning, and process-supervised reinforcement learning. We also construct a novel, diverse and comprehensive multimodal mathematical dataset, MultiMath-300K, which spans K-12 levels with image captions and step-wise solutions. MultiMath-7B achieves state-of-the-art (SOTA) performance among open-source models on existing multimodal mathematical benchmarks and also excels on text-only mathematical benchmarks. Our model and dataset are available at {blue{https://github.com/pengshuai-rin/MultiMath}}.

There is growing evidence that pretraining on high quality, carefully thought-out tokens such as code or mathematics plays an important role in improving the reasoning abilities of large language models. For example, Minerva, a PaLM model finetuned on billions of tokens of mathematical documents from arXiv and the web, reported dramatically improved performance on problems that require quantitative reasoning. However, because all known open source web datasets employ preprocessing that does not faithfully preserve mathematical notation, the benefits of large scale training on quantitive web documents are unavailable to the research community. We introduce OpenWebMath, an open dataset inspired by these works containing 14.7B tokens of mathematical webpages from Common Crawl. We describe in detail our method for extracting text and LaTeX content and removing boilerplate from HTML documents, as well as our methods for quality filtering and deduplication. Additionally, we run small-scale experiments by training 1.4B parameter language models on OpenWebMath, showing that models trained on 14.7B tokens of our dataset surpass the performance of models trained on over 20x the amount of general language data. We hope that our dataset, openly released on the Hugging Face Hub, will help spur advances in the reasoning abilities of large language models.

Pre-training on large-scale, high-quality datasets is crucial for enhancing the reasoning capabilities of Large Language Models (LLMs), especially in specialized domains such as mathematics. Despite the recognized importance, the Multimodal LLMs (MLLMs) field currently lacks a comprehensive open-source pre-training dataset specifically designed for mathematical reasoning. To address this gap, we introduce InfiMM-WebMath-40B, a high-quality dataset of interleaved image-text documents. It comprises 24 million web pages, 85 million associated image URLs, and 40 billion text tokens, all meticulously extracted and filtered from CommonCrawl. We provide a detailed overview of our data collection and processing pipeline. To demonstrate the robustness of InfiMM-WebMath-40B, we conducted evaluations in both text-only and multimodal settings. Our evaluations on text-only benchmarks show that, despite utilizing only 40 billion tokens, our dataset significantly enhances the performance of our 1.3B model, delivering results comparable to DeepSeekMath-1.3B, which uses 120 billion tokens for the same model size. Nevertheless, with the introduction of our multi-modal math pre-training dataset, our models set a new state-of-the-art among open-source models on multi-modal math benchmarks such as MathVerse and We-Math. We release our data at https://huggingface.co/datasets/Infi-MM/InfiMM-WebMath-40B.

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.

This paper presents the UniMER dataset to provide the first study on Mathematical Expression Recognition (MER) towards complex real-world scenarios. The UniMER dataset consists of a large-scale training set UniMER-1M offering an unprecedented scale and diversity with one million training instances and a meticulously designed test set UniMER-Test that reflects a diverse range of formula distributions prevalent in real-world scenarios. Therefore, the UniMER dataset enables the training of a robust and high-accuracy MER model and comprehensive evaluation of model performance. Moreover, we introduce the Universal Mathematical Expression Recognition Network (UniMERNet), an innovative framework designed to enhance MER in practical scenarios. UniMERNet incorporates a Length-Aware Module to process formulas of varied lengths efficiently, thereby enabling the model to handle complex mathematical expressions with greater accuracy. In addition, UniMERNet employs our UniMER-1M data and image augmentation techniques to improve the model's robustness under different noise conditions. Our extensive experiments demonstrate that UniMERNet outperforms existing MER models, setting a new benchmark in various scenarios and ensuring superior recognition quality in real-world applications. The dataset and model are available at https://github.com/opendatalab/UniMERNet.

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.

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.

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 striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and biochemistry. Each system is paired with precomputed multivariate and univariate time series. Our dataset has comparable scale to existing static time series databases; however, our systems can be re-integrated to produce additional datasets of arbitrary length and granularity. Our dataset is annotated with known mathematical properties of each system, and we perform feature analysis to broadly categorize the diverse dynamics present across the collection. Chaotic systems inherently challenge forecasting models, and across extensive benchmarks we correlate forecasting performance with the degree of chaos present. We also exploit the unique generative properties of our dataset in several proof-of-concept experiments: surrogate transfer learning to improve time series classification, importance sampling to accelerate model training, and benchmarking symbolic regression algorithms.

Recent works improving LLM math reasoning with synthetic data have used unique setups, making comparison of data synthesis strategies impractical. This leaves many unanswered questions about the roles of different factors in the synthetic data pipeline, such as the impact of filtering low-quality problems. To address this gap, we introduce FLAMES, a Framework for LLM Assessment of Math rEasoning Data Synthesis, and perform a systematic study of 10 existing data synthesis strategies and multiple other factors impacting the performance of synthetic math reasoning data. Our FLAMES experiments provide several valuable insights about the optimal balance of difficulty and diversity of synthetic data. First, data agents designed to increase problem complexity lead to best improvements on most math metrics. Second, with a fixed data generation budget, keeping higher problem coverage is more important than keeping only problems with reliable solutions. Third, GSM8K- and MATH-based synthetic data can lead to improvements on competition-level benchmarks, showcasing easy-to-hard generalization. Leveraging insights from our FLAMES experiments, we design two novel data synthesis strategies for improving out-of-domain generalization and robustness. Further, we develop the FLAMES dataset, an effective blend of our novel and existing data synthesis strategies, outperforming public datasets on OlympiadBench (+15.7), CollegeMath (+4.5), GSMPlus (+6.5), and MATH (+3.1). Fine-tuning Qwen2.5-Math-7B on the FLAMES dataset achieves 81.4% on MATH, surpassing larger Llama3 405B, GPT-4o and Claude 3.5 Sonnet.

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.

This report overviews our ongoing work in enriching chain-of-thoughts datasets requiring arithmetical reasoning with the integration of non-parametric components, such as a calculator. We conduct an analysis of prominent relevant datasets such as GSM8K, Ape210K, AQuA-RAT, and MathQA and propose a machine-processable HTML-like format specifically tailored for working with semi-structured chains. By converting the datasets into this unified format, we enable the effective integration of large language models and symbolic systems, empowering them to tackle arithmetical reasoning tasks more efficiently.

Teachers and students are increasingly relying on online learning resources to supplement the ones provided in school. This increase in the breadth and depth of available resources is a great thing for students, but only provided they are able to find answers to their queries. Question-answering and information retrieval systems have benefited from public datasets to train and evaluate their algorithms, but most of these datasets have been in English text written by and for adults. We introduce a new public French question-answering dataset collected from Alloprof, a Quebec-based primary and high-school help website, containing 29 349 questions and their explanations in a variety of school subjects from 10 368 students, with more than half of the explanations containing links to other questions or some of the 2 596 reference pages on the website. We also present a case study of this dataset in an information retrieval task. This dataset was collected on the Alloprof public forum, with all questions verified for their appropriateness and the explanations verified both for their appropriateness and their relevance to the question. To predict relevant documents, architectures using pre-trained BERT models were fine-tuned and evaluated. This dataset will allow researchers to develop question-answering, information retrieval and other algorithms specifically for the French speaking education context. Furthermore, the range of language proficiency, images, mathematical symbols and spelling mistakes will necessitate algorithms based on a multimodal comprehension. The case study we present as a baseline shows an approach that relies on recent techniques provides an acceptable performance level, but more work is necessary before it can reliably be used and trusted in a production setting.

Due to the cost of developing and training deep learning models from scratch, machine learning engineers have begun to reuse pre-trained models (PTMs) and fine-tune them for downstream tasks. PTM registries known as "model hubs" support engineers in distributing and reusing deep learning models. PTM packages include pre-trained weights, documentation, model architectures, datasets, and metadata. Mining the information in PTM packages will enable the discovery of engineering phenomena and tools to support software engineers. However, accessing this information is difficult - there are many PTM registries, and both the registries and the individual packages may have rate limiting for accessing the data. We present an open-source dataset, PTMTorrent, to facilitate the evaluation and understanding of PTM packages. This paper describes the creation, structure, usage, and limitations of the dataset. The dataset includes a snapshot of 5 model hubs and a total of 15,913 PTM packages. These packages are represented in a uniform data schema for cross-hub mining. We describe prior uses of this data and suggest research opportunities for mining using our dataset. The PTMTorrent dataset (v1) is available at: https://app.globus.org/file-manager?origin_id=55e17a6e-9d8f-11ed-a2a2-8383522b48d9&origin_path=%2F~%2F. Our dataset generation tools are available on GitHub: https://doi.org/10.5281/zenodo.7570357.

Large language models (LLMs) have demonstrated significant capabilities in mathematical reasoning, particularly with text-based mathematical problems. However, current multi-modal large language models (MLLMs), especially those specialized in mathematics, tend to focus predominantly on solving geometric problems but ignore the diversity of visual information available in other areas of mathematics. Moreover, the geometric information for these specialized mathematical MLLMs is derived from several public datasets, which are typically limited in diversity and complexity. To address these limitations, we aim to construct a fine-tuning dataset named MathVL, and develop a series of specialized mathematical MLLMs termed MathGLM-Vision by conducting Supervised Fine-Tuning (SFT) on MathVL with various parameter-scale backbones. To extensively evaluate the effectiveness of MathGLM-Vision, we conduct experiments on several public benchmarks and our curated MathVL-test consisting of 2,000 problems. Experimental results demonstrate that MathGLM-Vision achieves significant improvements compared with some existing models, including backbone models and open-source mathematical MLLMs. These findings indicate the importance of diversity dataset in enhancing the mathematical reasoning abilities of MLLMs.

Mathematical reasoning is an important capability of large language models~(LLMs) for real-world applications. To enhance this capability, existing work either collects large-scale math-related texts for pre-training, or relies on stronger LLMs (\eg GPT-4) to synthesize massive math problems. Both types of work generally lead to large costs in training or synthesis. To reduce the cost, based on open-source available texts, we propose an efficient way that trains a small LLM for math problem synthesis, to efficiently generate sufficient high-quality pre-training data. To achieve it, we create a dataset using GPT-4 to distill its data synthesis capability into the small LLM. Concretely, we craft a set of prompts based on human education stages to guide GPT-4, to synthesize problems covering diverse math knowledge and difficulty levels. Besides, we adopt the gradient-based influence estimation method to select the most valuable math-related texts. The both are fed into GPT-4 for creating the knowledge distillation dataset to train the small LLM. We leverage it to synthesize 6 million math problems for pre-training our JiuZhang3.0 model, which only needs to invoke GPT-4 API 9.3k times and pre-train on 4.6B data. Experimental results have shown that JiuZhang3.0 achieves state-of-the-art performance on several mathematical reasoning datasets, under both natural language reasoning and tool manipulation settings. Our code and data will be publicly released in https://github.com/RUCAIBox/JiuZhang3.0.

With advances in Artificial Intelligence in Education (AIEd) and the ever-growing scale of Interactive Educational Systems (IESs), data-driven approach has become a common recipe for various tasks such as knowledge tracing and learning path recommendation. Unfortunately, collecting real students' interaction data is often challenging, which results in the lack of public large-scale benchmark dataset reflecting a wide variety of student behaviors in modern IESs. Although several datasets, such as ASSISTments, Junyi Academy, Synthetic and STATICS, are publicly available and widely used, they are not large enough to leverage the full potential of state-of-the-art data-driven models and limits the recorded behaviors to question-solving activities. To this end, we introduce EdNet, a large-scale hierarchical dataset of diverse student activities collected by Santa, a multi-platform self-study solution equipped with artificial intelligence tutoring system. EdNet contains 131,441,538 interactions from 784,309 students collected over more than 2 years, which is the largest among the ITS datasets released to the public so far. Unlike existing datasets, EdNet provides a wide variety of student actions ranging from question-solving to lecture consumption and item purchasing. Also, EdNet has a hierarchical structure where the student actions are divided into 4 different levels of abstractions. The features of EdNet are domain-agnostic, allowing EdNet to be extended to different domains easily. The dataset is publicly released under Creative Commons Attribution-NonCommercial 4.0 International license for research purposes. We plan to host challenges in multiple AIEd tasks with EdNet to provide a common ground for the fair comparison between different state of the art models and encourage the development of practical and effective methods.

The VNHSGE (VietNamese High School Graduation Examination) dataset, developed exclusively for evaluating large language models (LLMs), is introduced in this article. The dataset, which covers nine subjects, was generated from the Vietnamese National High School Graduation Examination and comparable tests. 300 literary essays have been included, and there are over 19,000 multiple-choice questions on a range of topics. The dataset assesses LLMs in multitasking situations such as question answering, text generation, reading comprehension, visual question answering, and more by including both textual data and accompanying images. Using ChatGPT and BingChat, we evaluated LLMs on the VNHSGE dataset and contrasted their performance with that of Vietnamese students to see how well they performed. The results show that ChatGPT and BingChat both perform at a human level in a number of areas, including literature, English, history, geography, and civics education. They still have space to grow, though, especially in the areas of mathematics, physics, chemistry, and biology. The VNHSGE dataset seeks to provide an adequate benchmark for assessing the abilities of LLMs with its wide-ranging coverage and variety of activities. We intend to promote future developments in the creation of LLMs by making this dataset available to the scientific community, especially in resolving LLMs' limits in disciplines involving mathematics and the natural sciences.

Understanding how machine learning models respond to distributional shifts is a key research challenge. Mazes serve as an excellent testbed due to varied generation algorithms offering a nuanced platform to simulate both subtle and pronounced distributional shifts. To enable systematic investigations of model behavior on out-of-distribution data, we present maze-dataset, a comprehensive library for generating, processing, and visualizing datasets consisting of maze-solving tasks. With this library, researchers can easily create datasets, having extensive control over the generation algorithm used, the parameters fed to the algorithm of choice, and the filters that generated mazes must satisfy. Furthermore, it supports multiple output formats, including rasterized and text-based, catering to convolutional neural networks and autoregressive transformer models. These formats, along with tools for visualizing and converting between them, ensure versatility and adaptability in research applications.

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.

We introduce a new challenge to test the STEM skills of neural models. The problems in the real world often require solutions, combining knowledge from STEM (science, technology, engineering, and math). Unlike existing datasets, our dataset requires the understanding of multimodal vision-language information of STEM. Our dataset features one of the largest and most comprehensive datasets for the challenge. It includes 448 skills and 1,073,146 questions spanning all STEM subjects. Compared to existing datasets that often focus on examining expert-level ability, our dataset includes fundamental skills and questions designed based on the K-12 curriculum. We also add state-of-the-art foundation models such as CLIP and GPT-3.5-Turbo to our benchmark. Results show that the recent model advances only help master a very limited number of lower grade-level skills (2.5% in the third grade) in our dataset. In fact, these models are still well below (averaging 54.7%) the performance of elementary students, not to mention near expert-level performance. To understand and increase the performance on our dataset, we teach the models on a training split of our dataset. Even though we observe improved performance, the model performance remains relatively low compared to average elementary students. To solve STEM problems, we will need novel algorithmic innovations from the community.

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 describes the HASYv2 dataset. HASY is a publicly available, free of charge dataset of single symbols similar to MNIST. It contains 168233 instances of 369 classes. HASY contains two challenges: A classification challenge with 10 pre-defined folds for 10-fold cross-validation and a verification challenge.

The way in which data are shared can affect their utility and reusability. Here, we demonstrate how data that we had previously shared in bulk can be mobilized further through a knowledge graph that allows for much more granular exploration and interrogation. The original dataset is about the computational reproducibility of GitHub-hosted Jupyter notebooks associated with biomedical publications. It contains rich metadata about the publications, associated GitHub repositories and Jupyter notebooks, and the notebooks' reproducibility. We took this dataset, converted it into semantic triples and loaded these into a triple store to create a knowledge graph, FAIR Jupyter, that we made accessible via a web service. This enables granular data exploration and analysis through queries that can be tailored to specific use cases. Such queries may provide details about any of the variables from the original dataset, highlight relationships between them or combine some of the graph's content with materials from corresponding external resources. We provide a collection of example queries addressing a range of use cases in research and education. We also outline how sets of such queries can be used to profile specific content types, either individually or by class. We conclude by discussing how such a semantically enhanced sharing of complex datasets can both enhance their FAIRness, i.e., their findability, accessibility, interoperability, and reusability, and help identify and communicate best practices, particularly with regards to data quality, standardization, automation and reproducibility.

This paper revisits datasets and evaluation criteria for Symbolic Regression, a task of expressing given data using mathematical equations, specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on Physics, we recreate 120 datasets to discuss the performance of symbolic regression for scientific discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the properties of the formula and its variables to design reasonably realistic sampling range of values so that our new SRSD datasets can be used for evaluating the potential of SRSD such as whether or not an SR method can (re)discover physical laws from such datasets. As an evaluation metric, we also propose to use normalized edit distances between a predicted equation and the ground-truth equation trees. While existing metrics are either binary or errors between the target values and an SR model's predicted values for a given input, normalized edit distances evaluate a sort of similarity between the ground-truth and predicted equation trees. We have conducted experiments on our new SRSD datasets using five state-of-the-art SR methods in SRBench and a simple baseline based on a recent Transformer architecture. The results show that we provide a more realistic performance evaluation and open up a new machine learning-based approach for scientific discovery. Our datasets and code repository are publicly available.

Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.

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.

This work presents a new dataset for the Martian digital elevation model prediction task, ready for machine learning applications called MCTED. The dataset has been generated using a comprehensive pipeline designed to process high-resolution Mars orthoimage and DEM pairs from Day et al., yielding a dataset consisting of 80,898 data samples. The source images are data gathered by the Mars Reconnaissance Orbiter using the CTX instrument, providing a very diverse and comprehensive coverage of the Martian surface. Given the complexity of the processing pipelines used in large-scale DEMs, there are often artefacts and missing data points in the original data, for which we developed tools to solve or mitigate their impact. We divide the processed samples into training and validation splits, ensuring samples in both splits cover no mutual areas to avoid data leakage. Every sample in the dataset is represented by the optical image patch, DEM patch, and two mask patches, indicating values that were originally missing or were altered by us. This allows future users of the dataset to handle altered elevation regions as they please. We provide statistical insights of the generated dataset, including the spatial distribution of samples, the distributions of elevation values, slopes and more. Finally, we train a small U-Net architecture on the MCTED dataset and compare its performance to a monocular depth estimation foundation model, DepthAnythingV2, on the task of elevation prediction. We find that even a very small architecture trained on this dataset specifically, beats a zero-shot performance of a depth estimation foundation model like DepthAnythingV2. We make the dataset and code used for its generation completely open source in public repositories.

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.

Empirically validating new 3D-printing related algorithms and implementations requires testing data representative of inputs encountered in the wild. An ideal benchmarking dataset should not only draw from the same distribution of shapes people print in terms of class (e.g., toys, mechanisms, jewelry), representation type (e.g., triangle soup meshes) and complexity (e.g., number of facets), but should also capture problems and artifacts endemic to 3D printing models (e.g., self-intersections, non-manifoldness). We observe that the contextual and geometric characteristics of 3D printing models differ significantly from those used for computer graphics applications, not to mention standard models (e.g., Stanford bunny, Armadillo, Fertility). We present a new dataset of 10,000 models collected from an online 3D printing model-sharing database. Via analysis of both geometric (e.g., triangle aspect ratios, manifoldness) and contextual (e.g., licenses, tags, classes) characteristics, we demonstrate that this dataset represents a more concise summary of real-world models used for 3D printing compared to existing datasets. To facilitate future research endeavors, we also present an online query interface to select subsets of the dataset according to project-specific characteristics. The complete dataset and per-model statistical data are freely available to the public.

Rapid advancement of machine learning solutions has often coincided with the production of a test public data set. Such datasets reduce the largest barrier to entry for tackling a problem -- procuring data -- while also providing a benchmark to compare different solutions. Furthermore, large datasets have been used to train high-performing feature finders which are then used in new approaches to problems beyond that initially defined. In order to encourage the rapid development in the analysis of data collected using liquid argon time projection chambers, a class of particle detectors used in high energy physics experiments, we have produced the PILArNet, first 2D and 3D open dataset to be used for a couple of key analysis tasks. The initial dataset presented in this paper contains 300,000 samples simulated and recorded in three different volume sizes. The dataset is stored efficiently in sparse 2D and 3D matrix format with auxiliary information about simulated particles in the volume, and is made available for public research use. In this paper we describe the dataset, tasks, and the method used to procure the sample.

Distribution shifts are a major source of failure of deployed machine learning models. However, evaluating a model's reliability under distribution shifts can be challenging, especially since it may be difficult to acquire counterfactual examples that exhibit a specified shift. In this work, we introduce dataset interfaces: a framework which allows users to scalably synthesize such counterfactual examples from a given dataset. Specifically, we represent each class from the input dataset as a custom token within the text space of a text-to-image diffusion model. By incorporating these tokens into natural language prompts, we can then generate instantiations of objects in that dataset under desired distribution shifts. We demonstrate how applying our framework to the ImageNet dataset enables us to study model behavior across a diverse array of shifts, including variations in background, lighting, and attributes of the objects themselves. Code available at https://github.com/MadryLab/dataset-interfaces.

This paper presents MathBode, a dynamic diagnostic for mathematical reasoning in large language models (LLMs). Instead of one-shot accuracy, MathBode treats each parametric problem as a system: we drive a single parameter sinusoidally and fit first-harmonic responses of model outputs and exact solutions. This yields interpretable, frequency-resolved metrics -- gain (amplitude tracking) and phase (lag) -- that form Bode-style fingerprints. Across five closed-form families (linear solve, ratio/saturation, compound interest, 2x2 linear systems, similar triangles), the diagnostic surfaces systematic low-pass behavior and growing phase lag that accuracy alone obscures. We compare several models against a symbolic baseline that calibrates the instrument (G approx 1, phi approx 0). Results separate frontier from mid-tier models on dynamics, providing a compact, reproducible protocol that complements standard benchmarks with actionable measurements of reasoning fidelity and consistency. We open-source the dataset and code to enable further research and adoption.

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.

This paper introduces the human-curated PandasPlotBench dataset, designed to evaluate language models' effectiveness as assistants in visual data exploration. Our benchmark focuses on generating code for visualizing tabular data - such as a Pandas DataFrame - based on natural language instructions, complementing current evaluation tools and expanding their scope. The dataset includes 175 unique tasks. Our experiments assess several leading Large Language Models (LLMs) across three visualization libraries: Matplotlib, Seaborn, and Plotly. We show that the shortening of tasks has a minimal effect on plotting capabilities, allowing for the user interface that accommodates concise user input without sacrificing functionality or accuracy. Another of our findings reveals that while LLMs perform well with popular libraries like Matplotlib and Seaborn, challenges persist with Plotly, highlighting areas for improvement. We hope that the modular design of our benchmark will broaden the current studies on generating visualizations. Our benchmark is available online: https://huggingface.co/datasets/JetBrains-Research/plot_bench. The code for running the benchmark is also available: https://github.com/JetBrains-Research/PandasPlotBench.

Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems at scale. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. We introduce MATHWELL, a Llama-2 (70B) model iteratively finetuned to generate K-8 math word problems using data from expert annotation. Using MATHWELL, we generate the largest English word problem dataset to date, containing 20,490 problems. 3,484 are scored by domain experts who find MATHWELL has a 40% higher share of problems that have executable solutions and meet all criteria than alternatives, with 74% of its problems with executable solutions being solvable, accurate, and appropriate.

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.

The work of this paper presents a dataset that contains the data of 4011 videos about the ongoing outbreak of measles published on 264 websites on the internet between January 1, 2024, and May 31, 2024. The dataset is available at https://dx.doi.org/10.21227/40s8-xf63. These websites primarily include YouTube and TikTok, which account for 48.6% and 15.2% of the videos, respectively. The remainder of the websites include Instagram and Facebook as well as the websites of various global and local news organizations. For each of these videos, the URL of the video, title of the post, description of the post, and the date of publication of the video are presented as separate attributes in the dataset. After developing this dataset, sentiment analysis (using VADER), subjectivity analysis (using TextBlob), and fine-grain sentiment analysis (using DistilRoBERTa-base) of the video titles and video descriptions were performed. This included classifying each video title and video description into (i) one of the sentiment classes i.e. positive, negative, or neutral, (ii) one of the subjectivity classes i.e. highly opinionated, neutral opinionated, or least opinionated, and (iii) one of the fine-grain sentiment classes i.e. fear, surprise, joy, sadness, anger, disgust, or neutral. These results are presented as separate attributes in the dataset for the training and testing of machine learning algorithms for performing sentiment analysis or subjectivity analysis in this field as well as for other applications. Finally, this paper also presents a list of open research questions that may be investigated using this dataset.

Recent advances in large language models (LLMs) have demonstrated notable progress on many mathematical benchmarks. However, most of these benchmarks only feature problems grounded in junior and senior high school subjects, contain only multiple-choice questions, and are confined to a limited scope of elementary arithmetic operations. To address these issues, this paper introduces an expansive benchmark suite SciBench that aims to systematically examine the reasoning capabilities required for complex scientific problem solving. SciBench contains two carefully curated datasets: an open set featuring a range of collegiate-level scientific problems drawn from mathematics, chemistry, and physics textbooks, and a closed set comprising problems from undergraduate-level exams in computer science and mathematics. Based on the two datasets, we conduct an in-depth benchmark study of two representative LLMs with various prompting strategies. The results reveal that current LLMs fall short of delivering satisfactory performance, with an overall score of merely 35.80%. Furthermore, through a detailed user study, we categorize the errors made by LLMs into ten problem-solving abilities. Our analysis indicates that no single prompting strategy significantly outperforms others and some strategies that demonstrate improvements in certain problem-solving skills result in declines in other skills. We envision that SciBench will catalyze further developments in the reasoning abilities of LLMs, thereby ultimately contributing to scientific research and discovery.

Distillation has emerged as a practical and effective approach to enhance the reasoning capabilities of open-source language models. In this work, we conduct a large-scale empirical study on reasoning data distillation by collecting verified outputs from three state-of-the-art teacher models-AM-Thinking-v1, Qwen3-235B-A22B, and DeepSeek-R1-on a shared corpus of 1.89 million queries. We construct three parallel datasets and analyze their distributions, revealing that AM-Thinking-v1-distilled data exhibits greater token length diversity and lower perplexity. Student models trained on each dataset are evaluated on reasoning benchmarks including AIME2024, AIME2025, MATH500, and LiveCodeBench. The AM-based model consistently achieves the best performance (e.g., 84.3 on AIME2024, 72.2 on AIME2025, 98.4 on MATH500, and 65.9 on LiveCodeBench) and demonstrates adaptive output behavior-producing longer responses for harder tasks and shorter ones for simpler tasks. These findings highlight the value of high-quality, verified reasoning traces. We release the AM-Thinking-v1 and Qwen3-235B-A22B distilled datasets to support future research on open and high-performing reasoning-oriented language models. The datasets are publicly available on Hugging FaceDatasets are available on Hugging Face: \href{https://huggingface.co/datasets/a-m-team/AM-Thinking-v1-Distilled{AM-Thinking-v1-Distilled}, https://huggingface.co/datasets/a-m-team/AM-Qwen3-Distilled{AM-Qwen3-Distilled}.}.

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.

In this paper, we present DendroMap, a novel approach to interactively exploring large-scale image datasets for machine learning (ML). ML practitioners often explore image datasets by generating a grid of images or projecting high-dimensional representations of images into 2-D using dimensionality reduction techniques (e.g., t-SNE). However, neither approach effectively scales to large datasets because images are ineffectively organized and interactions are insufficiently supported. To address these challenges, we develop DendroMap by adapting Treemaps, a well-known visualization technique. DendroMap effectively organizes images by extracting hierarchical cluster structures from high-dimensional representations of images. It enables users to make sense of the overall distributions of datasets and interactively zoom into specific areas of interests at multiple levels of abstraction. Our case studies with widely-used image datasets for deep learning demonstrate that users can discover insights about datasets and trained models by examining the diversity of images, identifying underperforming subgroups, and analyzing classification errors. We conducted a user study that evaluates the effectiveness of DendroMap in grouping and searching tasks by comparing it with a gridified version of t-SNE and found that participants preferred DendroMap. DendroMap is available at https://div-lab.github.io/dendromap/.

In this paper, we evaluate the ability of large language models (LLMs) to perform multiple choice symbol binding (MCSB) for multiple choice question answering (MCQA) tasks in zero-shot, one-shot, and few-shot settings. We focus on Vietnamese, with fewer challenging MCQA datasets than in English. The two existing datasets, ViMMRC 1.0 and ViMMRC 2.0, focus on literature. Recent research in Vietnamese natural language processing (NLP) has focused on the Vietnamese National High School Graduation Examination (VNHSGE) from 2019 to 2023 to evaluate ChatGPT. However, these studies have mainly focused on how ChatGPT solves the VNHSGE step by step. We aim to create a novel and high-quality dataset by providing structured guidelines for typing LaTeX formulas for mathematics, physics, chemistry, and biology. This dataset can be used to evaluate the MCSB ability of LLMs and smaller language models (LMs) because it is typed in a strict LaTeX style. We focus on predicting the character (A, B, C, or D) that is the most likely answer to a question, given the context of the question. Our evaluation of six well-known LLMs, namely BLOOMZ-7.1B-MT, LLaMA-2-7B, LLaMA-2-70B, GPT-3, GPT-3.5, and GPT-4.0, on the ViMMRC 1.0 and ViMMRC 2.0 benchmarks and our proposed dataset shows promising results on the MCSB ability of LLMs for Vietnamese. The dataset is available for research purposes only.

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.

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 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.

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

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.

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.

Mathematical reasoning remains challenging for LLMs due to complex logic and the need for precise computation. Existing methods enhance LLM reasoning by synthesizing datasets through problem rephrasing, but face issues with generation quality and problem complexity. To address this, we propose to extract structural information with generated problem-solving code from mathematical reasoning and guide data generation with structured solutions. Applied to MATH and GSM8K, our approach produces 39K problems with labeled intermediate steps and a 6.1K-problem benchmark of higher difficulty. Results on our benchmark show that model performance declines as reasoning length increases. Additionally, we conducted fine-tuning experiments using the proposed training data on a range of LLMs, and the results validate the effectiveness of our dataset. We hope the proposed method and dataset will contribute to future research in enhancing LLM reasoning capabilities. Our code and data are available at https://github.com/OpenCausaLab/StructuralGeneration.

Scientific reasoning is critical for developing AI scientists and supporting human researchers in advancing the frontiers of natural science discovery. However, the open-source community has primarily focused on mathematics and coding while neglecting the scientific domain, largely due to the absence of open, large-scale, high-quality, verifiable scientific reasoning datasets. To bridge this gap, we first present TextbookReasoning, an open dataset featuring truthful reference answers extracted from 12k university-level scientific textbooks, comprising 650k reasoning questions spanning 7 scientific disciplines. We further introduce MegaScience, a large-scale mixture of high-quality open-source datasets totaling 1.25 million instances, developed through systematic ablation studies that evaluate various data selection methodologies to identify the optimal subset for each publicly available scientific dataset. Meanwhile, we build a comprehensive evaluation system covering diverse subjects and question types across 15 benchmarks, incorporating comprehensive answer extraction strategies to ensure accurate evaluation metrics. Our experiments demonstrate that our datasets achieve superior performance and training efficiency with more concise response lengths compared to existing open-source scientific datasets. Furthermore, we train Llama3.1, Qwen2.5, and Qwen3 series base models on MegaScience, which significantly outperform the corresponding official instruct models in average performance. In addition, MegaScience exhibits greater effectiveness for larger and stronger models, suggesting a scaling benefit for scientific tuning. We release our data curation pipeline, evaluation system, datasets, and seven trained models to the community to advance scientific reasoning research.

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent efforts have focused on two categories for SR methods. One is using a neural network or genetic programming to search the expression tree directly. Although this has shown promising results, the large search space poses difficulties in learning constant factors and processing high-dimensional problems. Another approach is leveraging a transformer-based model training on synthetic data and offers advantages in inference speed. However, this method is limited to fixed small numbers of dimensions and may encounter inference problems when given data is out-of-distribution compared to the synthetic data. In this work, we propose DySymNet, a novel neural-guided Dynamic Symbolic Network for SR. Instead of searching for expressions within a large search space, we explore DySymNet with various structures and optimize them to identify expressions that better-fitting the data. With a topology structure like neural networks, DySymNet not only tackles the challenge of high-dimensional problems but also proves effective in optimizing constants. Based on extensive numerical experiments using low-dimensional public standard benchmarks and the well-known SRBench with more variables, our method achieves state-of-the-art performance in terms of fitting accuracy and robustness to noise.

Short-video platforms show an increasing impact on people's daily lives nowadays, with billions of active users spending plenty of time each day. The interactions between users and online platforms give rise to many scientific problems across computational social science and artificial intelligence. However, despite the rapid development of short-video platforms, currently there are serious shortcomings in existing relevant datasets on three aspects: inadequate user-video feedback, limited user attributes and lack of video content. To address these problems, we provide a large-scale dataset with rich user behavior, attributes and video content from a real mobile short-video platform. This dataset covers 10,000 voluntary users and 153,561 videos, and we conduct four-fold technical validations of the dataset. First, we verify the richness of the behavior and attribute data. Second, we confirm the representing ability of the content features. Third, we provide benchmarking results on recommendation algorithms with our dataset. Finally, we explore the filter bubble phenomenon on the platform using the dataset. We believe the dataset could support the broad research community, including but not limited to user modeling, social science, human behavior understanding, etc. The dataset and code is available at https://github.com/tsinghua-fib-lab/ShortVideo_dataset.

The scale, variety, and quantity of publicly-available NLP datasets has grown rapidly as researchers propose new tasks, larger models, and novel benchmarks. Datasets is a community library for contemporary NLP designed to support this ecosystem. Datasets aims to standardize end-user interfaces, versioning, and documentation, while providing a lightweight front-end that behaves similarly for small datasets as for internet-scale corpora. The design of the library incorporates a distributed, community-driven approach to adding datasets and documenting usage. After a year of development, the library now includes more than 650 unique datasets, has more than 250 contributors, and has helped support a variety of novel cross-dataset research projects and shared tasks. The library is available at https://github.com/huggingface/datasets.

Data plays the most prominent role in how language models acquire skills and knowledge. The lack of massive, well-organized pre-training datasets results in costly and inaccessible data pipelines. We present Essential-Web v1.0, a 24-trillion-token dataset in which every document is annotated with a twelve-category taxonomy covering topic, format, content complexity, and quality. Taxonomy labels are produced by EAI-Distill-0.5b, a fine-tuned 0.5b-parameter model that achieves an annotator agreement within 3% of Qwen2.5-32B-Instruct. With nothing more than SQL-style filters, we obtain competitive web-curated datasets in math (-8.0% relative to SOTA), web code (+14.3%), STEM (+24.5%) and medical (+8.6%). Essential-Web v1.0 is available on HuggingFace: https://huggingface.co/datasets/EssentialAI/essential-web-v1.0

This work presents the BanglishRev Dataset, the largest e-commerce product review dataset to date for reviews written in Bengali, English, a mixture of both and Banglish, Bengali words written with English alphabets. The dataset comprises of 1.74 million written reviews from 3.2 million ratings information collected from a total of 128k products being sold in online e-commerce platforms targeting the Bengali population. It includes an extensive array of related metadata for each of the reviews including the rating given by the reviewer, date the review was posted and date of purchase, number of likes, dislikes, response from the seller, images associated with the review etc. With sentiment analysis being the most prominent usage of review datasets, experimentation with a binary sentiment analysis model with the review rating serving as an indicator of positive or negative sentiment was conducted to evaluate the effectiveness of the large amount of data presented in BanglishRev for sentiment analysis tasks. A BanglishBERT model is trained on the data from BanglishRev with reviews being considered labeled positive if the rating is greater than 3 and negative if the rating is less than or equal to 3. The model is evaluated by being testing against a previously published manually annotated dataset for e-commerce reviews written in a mixture of Bangla, English and Banglish. The experimental model achieved an exceptional accuracy of 94\% and F1 score of 0.94, demonstrating the dataset's efficacy for sentiment analysis. Some of the intriguing patterns and observations seen within the dataset and future research directions where the dataset can be utilized is also discussed and explored. The dataset can be accessed through https://huggingface.co/datasets/BanglishRev/bangla-english-and-code-mixed-ecommerce-review-dataset.

We introduce a high-quality dataset that contains 3,397 samples comprising (i) multiple choice questions, (ii) answers (including distractors), and (iii) their source documents, from the educational domain. Each question is phrased in two forms, normal and close. Correct answers are linked to source documents with sentence-level annotations. Thus, our versatile dataset can be used for both question and distractor generation, as well as to explore new challenges such as question format conversion. Furthermore, 903 questions are accompanied by their cognitive complexity level as per Bloom's taxonomy. All questions have been generated by educational experts rather than crowd workers to ensure they are maintaining educational and learning standards. Our analysis and experiments suggest distinguishable differences between our dataset and commonly used ones for question generation for educational purposes. We believe this new dataset can serve as a valuable resource for research and evaluation in the educational domain. The dataset and baselines will be released to support further research in question generation.

This paper embarks on an exploration into the Large Language Model (LLM) datasets, which play a crucial role in the remarkable advancements of LLMs. The datasets serve as the foundational infrastructure analogous to a root system that sustains and nurtures the development of LLMs. Consequently, examination of these datasets emerges as a critical topic in research. In order to address the current lack of a comprehensive overview and thorough analysis of LLM datasets, and to gain insights into their current status and future trends, this survey consolidates and categorizes the fundamental aspects of LLM datasets from five perspectives: (1) Pre-training Corpora; (2) Instruction Fine-tuning Datasets; (3) Preference Datasets; (4) Evaluation Datasets; (5) Traditional Natural Language Processing (NLP) Datasets. The survey sheds light on the prevailing challenges and points out potential avenues for future investigation. Additionally, a comprehensive review of the existing available dataset resources is also provided, including statistics from 444 datasets, covering 8 language categories and spanning 32 domains. Information from 20 dimensions is incorporated into the dataset statistics. The total data size surveyed surpasses 774.5 TB for pre-training corpora and 700M instances for other datasets. We aim to present the entire landscape of LLM text datasets, serving as a comprehensive reference for researchers in this field and contributing to future studies. Related resources are available at: https://github.com/lmmlzn/Awesome-LLMs-Datasets.

This paper proposes a new large-scale dataset called "ToyADMOS2" for anomaly detection in machine operating sounds (ADMOS). As did for our previous ToyADMOS dataset, we collected a large number of operating sounds of miniature machines (toys) under normal and anomaly conditions by deliberately damaging them but extended with providing controlled depth of damages in anomaly samples. Since typical application scenarios of ADMOS often require robust performance under domain-shift conditions, the ToyADMOS2 dataset is designed for evaluating systems under such conditions. The released dataset consists of two sub-datasets for machine-condition inspection: fault diagnosis of machines with geometrically fixed tasks and fault diagnosis of machines with moving tasks. Domain shifts are represented by introducing several differences in operating conditions, such as the use of the same machine type but with different machine models and parts configurations, different operating speeds, microphone arrangements, etc. Each sub-dataset contains over 27 k samples of normal machine-operating sounds and over 8 k samples of anomalous sounds recorded with five to eight microphones. The dataset is freely available for download at https://github.com/nttcslab/ToyADMOS2-dataset and https://doi.org/10.5281/zenodo.4580270.

Synthetic datasets have successfully been used to probe visual question-answering datasets for their reasoning abilities. CLEVR (johnson2017clevr), for example, tests a range of visual reasoning abilities. The questions in CLEVR focus on comparisons of shapes, colors, and sizes, numerical reasoning, and existence claims. This paper introduces a minimally biased, diagnostic visual question-answering dataset, QLEVR, that goes beyond existential and numerical quantification and focus on more complex quantifiers and their combinations, e.g., asking whether there are more than two red balls that are smaller than at least three blue balls in an image. We describe how the dataset was created and present a first evaluation of state-of-the-art visual question-answering models, showing that QLEVR presents a formidable challenge to our current models. Code and Dataset are available at https://github.com/zechenli03/QLEVR

This paper presents a dataset for closest opposite questions in Arabic language. The dataset is the first of its kind for the Arabic language. It is beneficial for the assessment of systems on the aspect of antonymy detection. The structure is similar to that of the Graduate Record Examination (GRE) closest opposite questions dataset for the English language. The introduced dataset consists of 500 questions, each contains a query word for which the closest opposite needs to be determined from among a set of candidate words. Each question is also associated with the correct answer. We publish the dataset publicly in addition to providing standard splits of the dataset into development and test sets. Moreover, the paper provides a benchmark for the performance of different Arabic word embedding models on the introduced dataset.

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various domains. Math Word Problems (MWPs) serve as a crucial benchmark for evaluating LLMs' reasoning abilities. While most research primarily focuses on improving accuracy, it often neglects understanding and addressing the underlying patterns of errors. Current error classification methods rely on static and predefined categories, which limit their ability to capture the full spectrum of error patterns in mathematical reasoning. To enable systematic error analysis, we collect error samples from 15 different LLMs of varying sizes across four distinct MWP datasets using multiple sampling strategies. Based on this extensive collection, we introduce MWPES-300K, a comprehensive dataset containing 304,865 error samples that cover diverse error patterns and reasoning paths. To reduce human bias and enable fine-grained analysis of error patterns, we propose a novel framework for automated dynamic error classification in mathematical reasoning. Experimental results demonstrate that dataset characteristics significantly shape error patterns, which evolve from basic to complex manifestations as model capabilities increase. With deeper insights into error patterns, we propose error-aware prompting that incorporates common error patterns as explicit guidance, leading to significant improvements in mathematical reasoning performance.

Visuals are valuable tools for teaching math word problems (MWPs), helping young learners interpret textual descriptions into mathematical expressions before solving them. However, creating such visuals is labor-intensive and there is a lack of automated methods to support this process. In this paper, we present Math2Visual, an automatic framework for generating pedagogically meaningful visuals from MWP text descriptions. Math2Visual leverages a pre-defined visual language and a design space grounded in interviews with math teachers, to illustrate the core mathematical relationships in MWPs. Using Math2Visual, we construct an annotated dataset of 1,903 visuals and evaluate Text-to-Image (TTI) models for their ability to generate visuals that align with our design. We further fine-tune several TTI models with our dataset, demonstrating improvements in educational visual generation. Our work establishes a new benchmark for automated generation of pedagogically meaningful visuals and offers insights into key challenges in producing multimodal educational content, such as the misrepresentation of mathematical relationships and the omission of essential visual elements.

Large language models (LLMs) have shown excellent mastering of human language, but still struggle in real-world applications that require mathematical problem-solving. While many strategies and datasets to enhance LLMs' mathematics are developed, it remains a challenge to simultaneously maintain and improve both language and mathematical capabilities in deployed LLM systems.In this work, we tailor the Self-Critique pipeline, which addresses the challenge in the feedback learning stage of LLM alignment. We first train a general Math-Critique model from the LLM itself to provide feedback signals. Then, we sequentially employ rejective fine-tuning and direct preference optimization over the LLM's own generations for data collection. Based on ChatGLM3-32B, we conduct a series of experiments on both academic and our newly created challenging dataset, MathUserEval. Results show that our pipeline significantly enhances the LLM's mathematical problem-solving while still improving its language ability, outperforming LLMs that could be two times larger. Related techniques have been deployed to ChatGLM\url{https://chatglm.cn}, an online serving LLM. Related evaluation dataset and scripts are released at https://github.com/THUDM/ChatGLM-Math.

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.

Machine learning is now used in many applications thanks to its ability to predict, generate, or discover patterns from large quantities of data. However, the process of collecting and transforming data for practical use is intricate. Even in today's digital era, where substantial data is generated daily, it is uncommon for it to be readily usable; most often, it necessitates meticulous manual data preparation. The haste in developing new models can frequently result in various shortcomings, potentially posing risks when deployed in real-world scenarios (eg social discrimination, critical failures), leading to the failure or substantial escalation of costs in AI-based projects. This chapter provides a comprehensive overview of established methodological tools, enriched by our practical experience, in the development of datasets for machine learning. Initially, we develop the tasks involved in dataset development and offer insights into their effective management (including requirements, design, implementation, evaluation, distribution, and maintenance). Then, we provide more details about the implementation process which includes data collection, transformation, and quality evaluation. Finally, we address practical considerations regarding dataset distribution and maintenance.

Current dataset collection methods typically scrape large amounts of data from the web. While this technique is extremely scalable, data collected in this way tends to reinforce stereotypical biases, can contain personally identifiable information, and typically originates from Europe and North America. In this work, we rethink the dataset collection paradigm and introduce GeoDE, a geographically diverse dataset with 61,940 images from 40 classes and 6 world regions, and no personally identifiable information, collected through crowd-sourcing. We analyse GeoDE to understand differences in images collected in this manner compared to web-scraping. Despite the smaller size of this dataset, we demonstrate its use as both an evaluation and training dataset, highlight shortcomings in current models, as well as show improved performances when even small amounts of GeoDE (1000 - 2000 images per region) are added to a training dataset. We release the full dataset and code at https://geodiverse-data-collection.cs.princeton.edu/

This study introduces an evaluation benchmark for middle school algebra to be used in artificial intelligence(AI) based educational platforms. The goal is to support the design of AI systems that can enhance learner conceptual understanding of algebra by taking into account their current level of algebra comprehension. The data set comprises 55 misconceptions about algebra, common errors, and 220 diagnostic examples identified in previous peer-reviewed studies. We provide an example application using a large language model, observing a range of precision and recall scores depending on the topic and experimental setup that reaches 83.9% when including educator feedback and restricting it by topic. We found that topics such as ratios and proportions prove as difficult for LLMs as they are for students. We included a human assessment of LLMs results and feedback from five middle school math educators on the clarity and occurrence of misconceptions in the dataset and the potential use of AI in conjunction with the dataset. Most educators (80% or more) indicated that they encounter these misconceptions among their students, suggesting the relevance of the data set to teaching middle school algebra. Despite varying familiarity with AI tools, four out of five educators expressed interest in using the data set with AI to diagnose student misconceptions or train teachers. The results emphasize the importance of topic-constrained testing, the need for multimodal approaches, and the relevance of human expertise to gain practical insights when using AI for human learning.

While generalization over tasks from easy to hard is crucial to profile language models (LLMs), the datasets with fine-grained difficulty annotations for each problem across a broad range of complexity are still blank. Aiming to address this limitation, we present Easy2Hard-Bench, a consistently formatted collection of 6 benchmark datasets spanning various domains, such as mathematics and programming problems, chess puzzles, and reasoning questions. Each problem within these datasets is annotated with numerical difficulty scores. To systematically estimate problem difficulties, we collect abundant performance data on attempts to each problem by humans in the real world or LLMs on the prominent leaderboard. Leveraging the rich performance data, we apply well-established difficulty ranking systems, such as Item Response Theory (IRT) and Glicko-2 models, to uniformly assign numerical difficulty scores to problems. Moreover, datasets in Easy2Hard-Bench distinguish themselves from previous collections by a higher proportion of challenging problems. Through extensive experiments with six state-of-the-art LLMs, we provide a comprehensive analysis of their performance and generalization capabilities across varying levels of difficulty, with the aim of inspiring future research in LLM generalization. The datasets are available at https://huggingface.co/datasets/furonghuang-lab/Easy2Hard-Bench.

Recent breakthroughs in large language models (LLMs) exemplified by the impressive mathematical and scientific reasoning capabilities of the o1 model have spotlighted the critical importance of high-quality training data in advancing LLM performance across STEM disciplines. While the mathematics community has benefited from a growing body of curated datasets, the scientific domain at the higher education level has long suffered from a scarcity of comparable resources. To address this gap, we present SCP-116K, a new large-scale dataset of 116,756 high-quality problem-solution pairs, automatically extracted from heterogeneous sources using a streamlined and highly generalizable pipeline. Our approach involves stringent filtering to ensure the scientific rigor and educational level of the extracted materials, while maintaining adaptability for future expansions or domain transfers. By openly releasing both the dataset and the extraction pipeline, we seek to foster research on scientific reasoning, enable comprehensive performance evaluations of new LLMs, and lower the barrier to replicating the successes of advanced models like o1 in the broader science community. We believe SCP-116K will serve as a critical resource, catalyzing progress in high-level scientific reasoning tasks and promoting further innovations in LLM development. The dataset and code are publicly available at https://github.com/AQA6666/SCP-116K-open.

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.

Multimodal summarization with multimodal output (MSMO) has emerged as a promising research direction. Nonetheless, numerous limitations exist within existing public MSMO datasets, including insufficient upkeep, data inaccessibility, limited size, and the absence of proper categorization, which pose significant challenges to effective research. To address these challenges and provide a comprehensive dataset for this new direction, we have meticulously curated the MultiSum dataset. Our new dataset features (1) Human-validated summaries for both video and textual content, providing superior human instruction and labels for multimodal learning. (2) Comprehensively and meticulously arranged categorization, spanning 17 principal categories and 170 subcategories to encapsulate a diverse array of real-world scenarios. (3) Benchmark tests performed on the proposed dataset to assess varied tasks and methods, including video temporal segmentation, video summarization, text summarization, and multimodal summarization. To champion accessibility and collaboration, we release the MultiSum dataset and the data collection tool as fully open-source resources, fostering transparency and accelerating future developments. Our project website can be found at https://multisum-dataset.github.io/.

We introduce Kvasir-VQA, an extended dataset derived from the HyperKvasir and Kvasir-Instrument datasets, augmented with question-and-answer annotations to facilitate advanced machine learning tasks in Gastrointestinal (GI) diagnostics. This dataset comprises 6,500 annotated images spanning various GI tract conditions and surgical instruments, and it supports multiple question types including yes/no, choice, location, and numerical count. The dataset is intended for applications such as image captioning, Visual Question Answering (VQA), text-based generation of synthetic medical images, object detection, and classification. Our experiments demonstrate the dataset's effectiveness in training models for three selected tasks, showcasing significant applications in medical image analysis and diagnostics. We also present evaluation metrics for each task, highlighting the usability and versatility of our dataset. The dataset and supporting artifacts are available at https://datasets.simula.no/kvasir-vqa.

Data science plays a critical role in clinical research, but it requires professionals with expertise in coding and medical data analysis. Large language models (LLMs) have shown great potential in supporting medical tasks and performing well in general coding tests. However, these tests do not assess LLMs' ability to handle data science tasks in medicine, nor do they explore their practical utility in clinical research. To address this, we developed a dataset consisting of 293 real-world data science coding tasks, based on 39 published clinical studies, covering 128 tasks in Python and 165 tasks in R. This dataset simulates realistic clinical research scenarios using patient data. Our findings reveal that cutting-edge LLMs struggle to generate perfect solutions, frequently failing to follow input instructions, understand target data, and adhere to standard analysis practices. Consequently, LLMs are not yet ready to fully automate data science tasks. We benchmarked advanced adaptation methods and found two to be particularly effective: chain-of-thought prompting, which provides a step-by-step plan for data analysis, which led to a 60% improvement in code accuracy; and self-reflection, enabling LLMs to iteratively refine their code, yielding a 38% accuracy improvement. Building on these insights, we developed a platform that integrates LLMs into the data science workflow for medical professionals. In a user study with five medical doctors, we found that while LLMs cannot fully automate coding tasks, they significantly streamline the programming process. We found that 80% of their submitted code solutions were incorporated from LLM-generated code, with up to 96% reuse in some cases. Our analysis highlights the potential of LLMs, when integrated into expert workflows, to enhance data science efficiency in clinical research.

Small-scale models offer various computational advantages, and yet to which extent size is critical for problem-solving abilities remains an open question. Specifically for solving grade school math, the smallest model size so far required to break the 80\% barrier on the GSM8K benchmark remains to be 34B. Our work studies how high-quality datasets may be the key for small language models to acquire mathematical reasoning. We introduce TinyGSM, a synthetic dataset of 12.3M grade school math problems paired with Python solutions, generated fully by GPT-3.5. After finetuning on TinyGSM, we find that a duo of a 1.3B generation model and a 1.3B verifier model can achieve 81.5\% accuracy, outperforming existing models that are orders of magnitude larger. This also rivals the performance of the GPT-3.5 ``teacher'' model (77.4\%), from which our model's training data is generated. Our approach is simple and has two key components: 1) the high-quality dataset TinyGSM, 2) the use of a verifier, which selects the final outputs from multiple candidate generations.

Instant messaging has become a predominant form of communication, with texts and emoticons enabling users to express emotions and ideas efficiently. Emoticons, in particular, have gained significant traction as a medium for conveying sentiments and information, leading to the growing importance of emoticon retrieval and recommendation systems. However, one of the key challenges in this area has been the absence of datasets that capture both the temporal dynamics and user-specific interactions with emoticons, limiting the progress of personalized user modeling and recommendation approaches. To address this, we introduce the emoticon dataset, a comprehensive resource that includes time-based data along with anonymous user identifiers across different conversations. As the largest publicly accessible emoticon dataset to date, it comprises 22K unique users, 370K emoticons, and 8.3M messages. The data was collected from a widely-used messaging platform across 67 conversations and 720 hours of crawling. Strict privacy and safety checks were applied to ensure the integrity of both text and image data. Spanning across 10 distinct domains, the emoticon dataset provides rich insights into temporal, multilingual, and cross-domain behaviors, which were previously unavailable in other emoticon-based datasets. Our in-depth experiments, both quantitative and qualitative, demonstrate the dataset's potential in modeling user behavior and personalized recommendation systems, opening up new possibilities for research in personalized retrieval and conversational AI. The dataset is freely accessible.

Large language models (LLMs) have demonstrated strong capabilities across various language tasks, notably through instruction-tuning methods. However, LLMs face challenges in visualizing complex, real-world data through charts and plots. Firstly, existing datasets rarely cover a full range of chart types, such as 3D, volumetric, and gridded charts. Secondly, supervised fine-tuning methods do not fully leverage the intricate relationships within rich datasets, including text, code, and figures. To address these challenges, we propose a hierarchical pipeline and a new dataset for chart generation. Our dataset, Text2Chart31, includes 31 unique plot types referring to the Matplotlib library, with 11.1K tuples of descriptions, code, data tables, and plots. Moreover, we introduce a reinforcement learning-based instruction tuning technique for chart generation tasks without requiring human feedback. Our experiments show that this approach significantly enhances the model performance, enabling smaller models to outperform larger open-source models and be comparable to state-of-the-art proprietary models in data visualization tasks. We make the code and dataset available at https://github.com/fatemehpesaran310/Text2Chart31.

Dataset summarisation is a fruitful approach to dataset inspection. However, when applied to a single dataset the discovery of visual concepts is restricted to those most prominent. We argue that a comparative approach can expand upon this paradigm to enable richer forms of dataset inspection that go beyond the most prominent concepts. To enable dataset comparison we present a module that learns concept-level prototypes across datasets. We leverage self-supervised learning to discover these prototypes without supervision, and we demonstrate the benefits of our approach in two case-studies. Our findings show that dataset comparison extends dataset inspection and we hope to encourage more works in this direction. Code and usage instructions available at https://github.com/Nanne/ProtoSim

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.

The ultimate goal of Dataset Distillation is to synthesize a small synthetic dataset such that a model trained on this synthetic set will perform equally well as a model trained on the full, real dataset. Until now, no method of Dataset Distillation has reached this completely lossless goal, in part due to the fact that previous methods only remain effective when the total number of synthetic samples is extremely small. Since only so much information can be contained in such a small number of samples, it seems that to achieve truly loss dataset distillation, we must develop a distillation method that remains effective as the size of the synthetic dataset grows. In this work, we present such an algorithm and elucidate why existing methods fail to generate larger, high-quality synthetic sets. Current state-of-the-art methods rely on trajectory-matching, or optimizing the synthetic data to induce similar long-term training dynamics as the real data. We empirically find that the training stage of the trajectories we choose to match (i.e., early or late) greatly affects the effectiveness of the distilled dataset. Specifically, early trajectories (where the teacher network learns easy patterns) work well for a low-cardinality synthetic set since there are fewer examples wherein to distribute the necessary information. Conversely, late trajectories (where the teacher network learns hard patterns) provide better signals for larger synthetic sets since there are now enough samples to represent the necessary complex patterns. Based on our findings, we propose to align the difficulty of the generated patterns with the size of the synthetic dataset. In doing so, we successfully scale trajectory matching-based methods to larger synthetic datasets, achieving lossless dataset distillation for the very first time. Code and distilled datasets are available at https://gzyaftermath.github.io/DATM.

Recent advances in Large Language Models (LLMs) and Vision Language Models (VLMs) have shown significant progress in mathematical reasoning, yet they still face a critical bottleneck with problems requiring visual assistance, such as drawing auxiliary lines or plotting functions to solve the problems. Most LLMs and VLMs are constrained to text-only reasoning chains, while multimodal unified models that can generate interleaved text and images lack the necessary precision and controllability for such tasks. To address this, we propose CodePlot-CoT, a code-driven Chain-of-Thought paradigm for "thinking with images" in mathematics. Our approach leverages the VLM to generate text reasoning as well as executable plotting code, which is then rendered into images as "visual thought", to solve mathematical problems. To achieve this, we first construct Math-VR, the first large-scale, bilingual dataset and benchmark for Mathematics problems with Visual Reasoning, comprising 178K samples. Second, to create high-quality training data, we develop a state-of-the-art image-to-code converter specialized for parsing complex mathematical figures into codes. Finally, using these training data, we train the CodePlot-CoT model for solving mathematical problems. Experimental results show that our model achieves up to 21% increase over base model on our new benchmark, fully validating the efficacy of our proposed code-driven reasoning paradigm. Our work opens a new direction for multimodal mathematical reasoning and provides the community with the first large-scale dataset, comprehensive benchmark, and strong approach for such problems. To facilitate future research, we make our datasets, code, and pretrained models publicly available at https://github.com/HKU-MMLab/Math-VR-CodePlot-CoT.