H_MH_QA

Optimizing AI Reasoning: A Hamiltonian Dynamics Approach to Multi-Hop Question Answering

Overview

This repository contains the research paper and accompanying code for the study "Optimizing AI Reasoning: A Hamiltonian Dynamics Approach to Multi-Hop Question Answering" by Javier Marín. The project introduces an innovative framework that applies principles from Hamiltonian mechanics and differential geometry to analyze and optimize reasoning processes in AI systems, particularly focusing on multi-hop question answering tasks.

Contents

• Optimizing AI reasoning.pdf: The full research paper detailing the theoretical framework, methodology, results, and discussions.
• Hamiltonian_final_version.ipynb: Jupyter notebook containing the implementation of experiments, data analysis, and visualizations described in the paper.

Abstract

This study presents a novel approach to analyzing and improving multi-hop reasoning in AI systems by drawing inspiration from Hamiltonian mechanics. We propose a framework that maps reasoning chains in embedding spaces to Hamiltonian systems, allowing us to leverage powerful analytical tools from classical physics. Our method defines a Hamiltonian function that balances the progression of reasoning (kinetic energy) against the relevance to the question at hand (potential energy). Using this framework, we analyze a large dataset of reasoning chains from a multi-hop question-answering task, revealing intriguing patterns that distinguish valid from invalid reasoning.

Key Features

Application of Hamiltonian mechanics to AI reasoning processes Analysis of reasoning trajectories using differential geometry Implementation of conservation laws and canonical transformations in cognitive spaces Comprehensive statistical analysis and visualization of reasoning patterns Novel metrics for evaluating the quality and efficiency of AI reasoning

Dataset

This project uses the OpenBookQA (OBQA) dataset. We used the OpenBookQA (OBQA) dataset for our research, which provides a standard to assess the question answering and reasoning abilities of AI systems. The OBQA dataset was presented by Mihaylov et al. (2018) in their research on open-book question answering.

Mihaylov, T., Clark, P., Khot, T., & Sabharwal, A. (2018). Can a suit of armor conduct electricity? a new dataset for open book question answering. Ar Xiv PreprintArXiv:1809.02789.

Results

The main findings of this study include:

• Valid reasoning chains exhibit lower and more stable Hamiltonian energy profiles compared to invalid chains. Trajectory curvature and conservation of angular momentum-like quantities are effective discriminators of reasoning validity. The framework reveals potential fundamental principles governing effective cognitive processes in AI systems.

• For detailed results and discussions, please refer to the full paper.

Citation

If you use this work in your research, please cite: Marín, J. (2024). Optimizing AI Reasoning: A Hamiltonian Dynamics Approach to Multi-Hop Question Answering. arXiv preprint arXiv:2410.04415 (DOI:10.48550/arXiv.2410.04415)

License

This project is licensed under the MIT License.

Contact

For any questions or feedback, please contact Javier Marín at [email protected].