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

Optimizing AI Reasoning: A Hamiltonian Dynamics Approach to Multi-Hop Question Answering | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 9 January 2025 V1 Latest version Share on Optimizing AI Reasoning: A Hamiltonian Dynamics Approach to Multi-Hop Question Answering Authors : Javier Marin Valenzuela 0000-0003-0957-1283 [email protected] , A Preprint , and Javier Marín Authors Info & Affiliations https://doi.org/10.22541/au.173645367.74451514/v1 234 views 122 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This paper introduces an innovative approach to analyzing and improving multi-hop reasoning in AI systems by drawing inspiration from Hamiltonian mechanics. We propose a novel 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 multihop question-answering task, revealing intriguing patterns that distinguish valid from invalid reasoning. We show that valid reasoning chains have lower Hamiltonian energy and move in ways that make the best trade-off between getting more information and answering the right question. Furthermore, we demonstrate the application of this framework to steer the creation of more efficient reasoning algorithms within AI systems. Our results not only provide new insights into the nature of valid reasoning but also open up exciting possibilities for physics-inspired approaches to understanding and improving artificial intelligence. Supplementary Material File (optimizing ai reasoning- a hamiltonian dynamics approach to multi-hop question answering.pdf) Download 2.11 MB Information & Authors Information Version history V1 Version 1 09 January 2025 Copyright This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License Keywords cognitive computing explainable ai hamiltonian mechanics multi-hop reasoning natural language processing Authors Affiliations Javier Marin Valenzuela 0000-0003-0957-1283 [email protected] View all articles by this author A Preprint View all articles by this author Javier Marín View all articles by this author Metrics & Citations Metrics Article Usage 234 views 122 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Javier Marin Valenzuela, A Preprint, Javier Marín. Optimizing AI Reasoning: A Hamiltonian Dynamics Approach to Multi-Hop Question Answering. Authorea . 09 January 2025. DOI: https://doi.org/10.22541/au.173645367.74451514/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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