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Thermodynamic Machine Learning through Maximum Work Production

Boyd, Alexander B. and Crutchfield, James P. and Gu, Mile (2022) Thermodynamic Machine Learning through Maximum Work Production. New Journal of Physics, 24 (8). Art. No. 083040. ISSN 1367-2630. doi:10.1088/1367-2630/ac4309.

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Adaptive systems---such as a biological organism gaining survival advantage, an autonomous robot executing a functional task, or a motor protein transporting intracellular nutrients---must model the regularities and stochasticity in their environments to take full advantage of thermodynamic resources. Analogously, but in a purely computational realm, machine learning algorithms estimate models to capture predictable structure and identify irrelevant noise in training data. This happens through optimization of performance metrics, such as model likelihood. If physically implemented, is there a sense in which computational models estimated through machine learning are physically preferred? We introduce the thermodynamic principle that work production is the most relevant performance metric for an adaptive physical agent and compare the results to the maximum-likelihood principle that guides machine learning. Within the class of physical agents that most efficiently harvest energy from their environment, we demonstrate that an efficient agent's model explicitly determines its architecture and how much useful work it harvests from the environment. We then show that selecting the maximum-work agent for given environmental data corresponds to finding the maximum-likelihood model. This establishes an equivalence between nonequilibrium thermodynamics and dynamic learning. In this way, work maximization emerges as an organizing principle that underlies learning in adaptive thermodynamic systems.

Item Type:Article
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Boyd, Alexander B.0000-0003-1092-922X
Crutchfield, James P.0000-0003-4466-5410
Additional Information:© 2021 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft and the Institute of Physics. As the Version of Record of this article is going to be/has been published on a gold open access basis under a CC BY 3.0 licence, this Accepted Manuscript is available for reuse under a CC BY 3.0 licence immediately. Accepted Manuscript online 14 December 2021. The authors thank the Telluride Science Research Center for hospitality during visits and the participants of the Information Engines Workshops there. ABB thanks Wesley Boyd for useful conversations and JPC similarly thanks Adam Rupe. JPC acknowledges the kind hospitality of the Santa Fe Institute, Institute for Advanced Study at the University of Amsterdam, and California Institute of Technology for their hospitality during visits. This material is based upon work supported by, or in part by, Grant No. FQXi-RFP-IPW-1902 and FQXi-RFP-1809 from the Foundational Questions Institute and Fetzer Franklin Fund (a donor-advised fund of Silicon Valley Community Foundation), the Templeton World Charity Foundation Power of Information fellowship TWCF0337 and TWCF0560, the National Research Foundation, Singapore, under its NRFF Fellow program (Award No. NRFNRFF2016-02), Singapore Ministry of Education Tier 1 Grants No. RG146/20, and U.S. Army Research Laboratory and the U.S. Army Research Office under grants W911NF-18-1-0028 and W911NF-21-1-0048. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not reflect the views of National Research Foundation, Singapore. During submission we became aware of related work: L. Touzo, M. Marsili, N. Merhav, and E. Roldan. Optimal work extraction and the minimum description length principle. arXiv:2006.04544.
Funding AgencyGrant Number
Foundational Questions Institute (FQXI)FQXi-RFP-IPW-1902
Foundational Questions Institute (FQXI)FQXi-RFP-1809
Fetzer Franklin FundUNSPECIFIED
Templeton World Charity FoundationTWCF0337
Templeton World Charity FoundationTWCF0560
National Research Foundation (Singapore)NRF-NRFF2016-02
Ministry of Education (Singapore)RG146/20
Army Research Laboratory (ARO)W911NF-18-1-0028
Army Research Laboratory (ARO)W911NF-21-1-0048
Subject Keywords:nonequilibrium thermodynamics, Maxwell’s demon, Landauer’s Principle, extremal principles, machine learning, regularized inference, maximum likelihood estimation
Issue or Number:8
Record Number:CaltechAUTHORS:20220107-195197700
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112784
Deposited By: Tony Diaz
Deposited On:09 Jan 2022 00:28
Last Modified:22 Sep 2022 23:24

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