Stochastic Thermodynamics of Learning Parametric Probabilistic Models
Abstract
We have formulated a family of machine learning problems as the time evolution of Parametric Probabilistic Models (PPMs), inherently rendering a thermodynamic process. Our primary motivation is to leverage the rich toolbox of thermodynamics of information to assess the information-theoretic content of learning a probabilistic model. We first introduce two information-theoretic metrics: Memorized-information (M-info) and Learned-information (L-info), which trace the flow of information during the learning process of PPMs. Then, we demonstrate that the accumulation of L-info during the learning process is associated with entropy production, and parameters serve as a heat reservoir in this process, capturing learned information in the form of M-info.
Keywords
Cite
@article{arxiv.2310.19802,
title = {Stochastic Thermodynamics of Learning Parametric Probabilistic Models},
author = {Shervin Sadat Parsi},
journal= {arXiv preprint arXiv:2310.19802},
year = {2024}
}