Stochastic Thermodynamics of Learning Parametric Probabilistic Models
This work provides a theoretical framework for analyzing learning processes in machine learning, though it appears incremental as it applies existing thermodynamic concepts to a specific domain.
The authors tackled the problem of understanding the information-theoretic aspects of learning parametric probabilistic models by framing it as a thermodynamic process, resulting in the introduction of two metrics (M-info and L-info) that link information flow to entropy production and parameter roles.
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.