MathOdyssey: Benchmarking Mathematical Problem-Solving Skills in Large Language Models Using Odyssey Math Data
- URL: http://arxiv.org/abs/2406.18321v1
- Date: Wed, 26 Jun 2024 13:02:35 GMT
- Title: MathOdyssey: Benchmarking Mathematical Problem-Solving Skills in Large Language Models Using Odyssey Math Data
- Authors: Meng Fang, Xiangpeng Wan, Fei Lu, Fei Xing, Kai Zou,
- Abstract summary: Large language models (LLMs) have significantly advanced natural language understanding and demonstrated strong problem-solving abilities.
This paper investigates the mathematical problem-solving capabilities of LLMs using the newly developed "MathOdyssey" dataset.
- Score: 20.31528845718877
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
Related papers
- MathConstruct: Challenging LLM Reasoning with Constructive Proofs [0.9320657506524149]
mc is a new benchmark of 126 challenging problems sourced from various math competitions.
mc is suitable for Large Language Models evaluation, as solution correctness can be easily verified.
arXiv Detail & Related papers (2025-02-14T14:44:22Z) - Leveraging Online Olympiad-Level Math Problems for LLMs Training and Contamination-Resistant Evaluation [55.21013307734612]
AoPS-Instruct is a dataset of more than 600,000 high-quality QA pairs.
LiveAoPSBench is an evolving evaluation set with timestamps, derived from the latest forum data.
Our work presents a scalable approach to creating and maintaining large-scale, high-quality datasets for advanced math reasoning.
arXiv Detail & Related papers (2025-01-24T06:39:38Z) - Large Language Models for Mathematical Analysis [3.7325315394927023]
This work addresses critical gaps in mathematical reasoning and contributes to advancing trustworthy AI.
We developed the DEMI-MathAnalysis dataset, comprising proof-based problems from mathematical analysis topics.
We also designed a guiding framework to rigorously enhance LLMs' ability to solve these problems.
arXiv Detail & Related papers (2024-12-28T20:37:55Z) - HARDMath: A Benchmark Dataset for Challenging Problems in Applied Mathematics [1.5716764919736026]
We introduce HARDMath, a dataset featuring challenging applied mathematics problems that require analytical approximation techniques.
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.
arXiv Detail & Related papers (2024-10-13T20:09:41Z) - MathChat: Benchmarking Mathematical Reasoning and Instruction Following in Multi-Turn Interactions [58.57255822646756]
This paper introduces MathChat, a benchmark designed to evaluate large language models (LLMs) across a broader spectrum of mathematical tasks.
We evaluate the performance of various SOTA LLMs on the MathChat benchmark, and we observe that while these models excel in single turn question answering, they significantly underperform in more complex scenarios.
We develop MathChat sync, a synthetic dialogue based math dataset for LLM finetuning, focusing on improving models' interaction and instruction following capabilities in conversations.
arXiv Detail & Related papers (2024-05-29T18:45:55Z) - MindStar: Enhancing Math Reasoning in Pre-trained LLMs at Inference Time [51.5039731721706]
MindStar is a purely inference-based searching method for large language models.
It formulates reasoning tasks as searching problems and proposes two search ideas to identify the optimal reasoning paths.
It significantly enhances the reasoning abilities of open-source models, such as Llama-2-13B and Mistral-7B, and achieves comparable performance to GPT-3.5 and Grok-1.
arXiv Detail & Related papers (2024-05-25T15:07:33Z) - Mathify: Evaluating Large Language Models on Mathematical Problem Solving Tasks [34.09857430966818]
We introduce an extensive mathematics dataset called "MathQuest" sourced from the 11th and 12th standard Mathematics NCERT textbooks.
We conduct fine-tuning experiments with three prominent large language models: LLaMA-2, WizardMath, and MAmmoTH.
Our experiments reveal that among the three models, MAmmoTH-13B emerges as the most proficient, achieving the highest level of competence in solving the presented mathematical problems.
arXiv Detail & Related papers (2024-04-19T08:45:42Z) - GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers [68.77382332826167]
Large language models (LLMs) have achieved impressive performance across various mathematical reasoning benchmarks.
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.
arXiv Detail & Related papers (2024-02-29T15:26:14Z) - Evaluating LLMs' Mathematical and Coding Competency through Ontology-guided Interventions [47.83142414018448]
We focus on two popular reasoning tasks: arithmetic reasoning and code generation.
We introduce (i) a general ontology of perturbations for math and coding questions, (ii) a semi-automatic method to apply these perturbations, and (iii) two datasets.
We show a significant performance drop across all the models against perturbed questions.
arXiv Detail & Related papers (2024-01-17T18:13:07Z) - SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models [70.5763210869525]
We introduce an expansive benchmark suite SciBench for Large Language Model (LLM)
SciBench contains a dataset featuring a range of collegiate-level scientific problems from mathematics, chemistry, and physics domains.
The results reveal that the current LLMs fall short of delivering satisfactory performance, with the best overall score of merely 43.22%.
arXiv Detail & Related papers (2023-07-20T07:01:57Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.