MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs

• URL: http://arxiv.org/abs/2402.16352v2
• Date: Wed, 11 Sep 2024 08:23:58 GMT
• Title: MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs
• Authors: Zimu Lu, Aojun Zhou, Houxing Ren, Ke Wang, Weikang Shi, Junting Pan, Mingjie Zhan, Hongsheng Li,
• Abstract summary: MathGenie is a novel method for generating diverse and reliable math problems from a small-scale problem-solution dataset. Various pretrained models, ranging from 7B to 70B, are trained on the newly curated data to test the effectiveness of the proposed augmentation technique. 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.
• Score: 38.127313175508746
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• ControlMath: Controllable Data Generation Promotes Math Generalist Models [38.0858432336873]
  We propose ControlMath, an iterative method involving an equation-generator module and two LLM-based agents. The module creates diverse equations, which the Problem-Crafter agent then transforms into math word problems. We collect ControlMathQA, which involves 190k math word problems.
  arXiv  Detail & Related papers  (2024-09-20T03:58:26Z)
• Building Math Agents with Multi-Turn Iterative Preference Learning [56.71330214021884]
  This paper studies the complementary direct preference learning approach to further improve model performance. Existing direct preference learning algorithms are originally designed for the single-turn chat task. We introduce a multi-turn direct preference learning framework, tailored for this context.
  arXiv  Detail & Related papers  (2024-09-04T02:41:04Z)
• SIaM: Self-Improving Code-Assisted Mathematical Reasoning of Large Language Models [54.78329741186446]
  We propose a novel paradigm that uses a code-based critic model to guide steps including question-code data construction, quality control, and complementary evaluation. Experiments across both in-domain and out-of-domain benchmarks in English and Chinese demonstrate the effectiveness of the proposed paradigm.
  arXiv  Detail & Related papers  (2024-08-28T06:33:03Z)
• Benchmarking Large Language Models for Math Reasoning Tasks [12.91916443702145]
  We compare seven state-of-the-art in-context learning algorithms for mathematical problem solving across five widely used mathematical datasets on four powerful foundation models. Our results indicate that larger foundation models like GPT-4o and LLaMA 3-70B can solve mathematical reasoning independently from the concrete prompting strategy. We open-source our benchmark code to support the integration of additional models in future research.
  arXiv  Detail & Related papers  (2024-08-20T13:34:17Z)
• 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)
• MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipeline [12.186691561822256]
  We postulate that the inherent nature of large language models (LLMs) presents challenges in modeling mathematical reasoning. This paper introduces a novel math dataset, enhanced with a capability to utilize a Python code interpreter. We propose a tentative, easily replicable protocol for the fine-tuning of math-specific LLMs.
  arXiv  Detail & Related papers  (2024-01-16T08:08:01Z)
• MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning [52.97768001837269]
  We present a method to fine-tune open-source language models, enabling them to use code for modeling and deriving math equations. We propose a method of generating novel and high-quality datasets with math problems and their code-based solutions. This approach yields the MathCoder models, a family of models capable of generating code-based solutions for solving challenging math problems.
  arXiv  Detail & Related papers  (2023-10-05T17:52:09Z)
• MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning [60.208045804204076]
  We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset.
  arXiv  Detail & Related papers  (2023-09-11T17:47:22Z)

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.