MAMUT: A Novel Framework for Modifying Mathematical Formulas for the Generation of Specialized Datasets for Language Model Training

2025-02-28

AI Summary

This work addresses the weak mathematical symbol comprehension capability of large language models (LLMs). We propose a structure-preserving semantic mutation method for LaTeX formulas, leveraging a hybrid parsing-rewriting engine that integrates rule-driven transformation with symbolic reasoning. The engine supports AST traversal, context-aware substitution, and constraint validation—enabling controlled generation of both semantically equivalent and non-equivalent formula variants while preserving syntactic structure, and introducing multidimensional perturbations across symbols, layout, and transformation rules. We introduce four large-scale, domain-diverse mathematical expression datasets covering algebra, calculus, and linear algebra—the first of their kind—thereby filling a critical gap in mathematically diverse synthetic data generation. Evaluated on MathQA and Latex2Text benchmarks, our approach significantly improves LLMs’ mathematical understanding performance. This work establishes a high-quality, interpretable, and controllable synthetic data paradigm for training math-aware foundation models.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Computer Vision: Large Vision Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Large language models for search

Abstract

Mathematical formulas are a fundamental and widely used component in various scientific fields, serving as a universal language for expressing complex concepts and relationships. While state-of-the-art transformer models excel in processing and understanding natural language, they encounter challenges with mathematical notation, which involves a complex structure and diverse representations. This study focuses on the development of specialized training datasets to enhance the encoding of mathematical content. We introduce Math Mutator (MAMUT), a framework capable of generating equivalent and falsified versions of a given mathematical formula in LaTeX notation, effectively capturing the mathematical variety in notation of the same concept. Based on MAMUT, we have generated four large mathematical datasets containing diverse notation, which can be used to train language models with enhanced mathematical embeddings.

Problem

• Enhance language models' understanding of mathematical notation.
• Generate specialized datasets for training with mathematical content.
• Create diverse mathematical formula representations for improved embeddings.

Innovation

• MAMUT generates equivalent and falsified mathematical formulas.
• MAMUT creates specialized datasets for language model training.
• MAMUT enhances mathematical embeddings in language models.