Thermodynamic Machine Learning through Maximum Work Production

Alexander B. Boyd and Mile Gu

Complexity Institute, Nanyang Technological University, Singapore
School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore and Centre for Quantum
Technologies, National University of Singapore, Singapore

James P. Crutchfield

Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616

ABSTRACT: 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.

Alexander B. Boyd, James P. Crutchfield, and Mile Gu, “Thermodynamic Machine Learning through Maximum Work Production”, New Journal of Physics (2021) in press.
[pdf] [cond-mat.stat-mech].