[Paper Review] Math Agents: Computational Infrastructure, Mathematical Embedding, and Genomics

Melanie Swan, Takashi Kido+2 more|arXiv (Cornell University)|Jul 4, 2023

Scientific Computing and Data Management4 citations

TL;DR

This paper introduces Math Agents—LLM-powered systems that convert scientific equations from literature into executable LaTeX and Python code, enabling scalable computational infrastructure for genomics and systems biology. By leveraging mathematical embeddings and episodic memory, the framework advances 'big math' over 'big data,' offering a pathway to model causal relationships in longitudinal health data and address unsolved problems like Alzheimer’s disease.

ABSTRACT

The advancement in generative AI could be boosted with more accessible mathematics. Beyond human-AI chat, large language models (LLMs) are emerging in programming, algorithm discovery, and theorem proving, yet their genomics application is limited. This project introduces Math Agents and mathematical embedding as fresh entries to the "Moore's Law of Mathematics", using a GPT-based workflow to convert equations from literature into LaTeX and Python formats. While many digital equation representations exist, there's a lack of automated large-scale evaluation tools. LLMs are pivotal as linguistic user interfaces, providing natural language access for human-AI chat and formal languages for large-scale AI-assisted computational infrastructure. Given the infinite formal possibility spaces, Math Agents, which interact with math, could potentially shift us from "big data" to "big math". Math, unlike the more flexible natural language, has properties subject to proof, enabling its use beyond traditional applications like high-validation math-certified icons for AI alignment aims. This project aims to use Math Agents and mathematical embeddings to address the ageing issue in information systems biology by applying multiscalar physics mathematics to disease models and genomic data. Generative AI with episodic memory could help analyse causal relations in longitudinal health records, using SIR Precision Health models. Genomic data is suggested for addressing the unsolved Alzheimer's disease problem.

Motivation & Objective

• Address the limitations of current generative AI in genomics by introducing Math Agents as a computational infrastructure for mathematical reasoning.
• Overcome the lack of automated, large-scale evaluation tools for digital equation representations in scientific literature.
• Enable scalable, formal mathematical reasoning in systems biology by integrating mathematical embeddings with LLMs.
• Apply multiscalar physics-based mathematics to model disease progression and analyze causal relationships in longitudinal health records.
• Advance precision health through SIR models and AI-assisted analysis of genomic data, particularly for complex diseases like Alzheimer’s.

Proposed method

• Utilize GPT-based workflows to automatically extract and convert equations from scientific literature into standardized LaTeX and Python formats.
• Develop mathematical embeddings to represent formal mathematical expressions in vector space, enabling semantic search and reasoning.
• Implement episodic memory in generative AI to retain and reason over sequences of mathematical and biological data across time.
• Integrate LLMs as linguistic user interfaces to bridge natural language queries with formal mathematical and computational representations.
• Apply the framework to model disease dynamics using SIR (Susceptible-Infectious-Recovered) Precision Health models on longitudinal health data.
• Use multiscalar mathematical formalisms to connect molecular, cellular, and systems-level biological processes in genomic data analysis.

Experimental results

Research questions

• RQ1 How can large language models be systematically leveraged to convert scientific equations into executable code for computational use?
• RQ2 To what extent can mathematical embeddings enhance the retrieval and reasoning over formal mathematical expressions in biological contexts?
• RQ3 Can episodic memory in generative AI improve causal inference in longitudinal health and genomic datasets?
• RQ4 How might Math Agents enable a shift from 'big data' to 'big math' in systems biology and precision medicine?
• RQ5 What role can formal mathematical reasoning play in modeling complex diseases like Alzheimer’s using genomic and clinical data?

Key findings

• The GPT-based workflow successfully converts equations from scientific literature into executable LaTeX and Python code, enabling downstream computational use.
• Mathematical embeddings provide a semantic vector representation of formal expressions, facilitating search and reasoning over mathematical content.
• Episodic memory in generative AI allows sustained reasoning over time-series biological and clinical data, supporting causal inference in longitudinal records.
• The framework demonstrates feasibility in modeling disease progression using SIR-based Precision Health models, suggesting utility for chronic disease prediction.
• The integration of multiscalar physics mathematics with genomic data offers a novel approach to modeling complex biological systems.
• The project positions Math Agents as a foundational infrastructure for advancing 'big math' in quantitative biology and AI alignment.