Entropy Production in Machine Learning Under Fokker-Planck Probability Flow

TL;DR

This paper introduces an entropy-based framework for detecting data drift in machine learning models using concepts from nonequilibrium physics, enabling more efficient retraining decisions in nonstationary environments.

Contribution

It develops a novel entropy production measure based on Fokker-Planck equations to guide retraining, bridging physics and machine learning for drift detection.

Findings

Entropy-based retraining reduces frequency by 10-100 times in various domains.

The approach maintains predictive performance comparable to frequent retraining.

Limitations observed in complex biomedical drift scenarios.

Abstract

Machine learning models deployed in nonstationary environments inevitably experience performance degradation due to data drift. While numerous drift detection heuristics exist, most lack a dynamical interpretation and provide limited guidance on how retraining decisions should be balanced against operational cost. In this work, we propose an entropy-based retraining framework grounded in nonequilibrium statistical physics. Interpreting drift as probability flow governed by a Fokker-Planck equation, we quantify model-data mismatch using relative entropy and show that its time derivative admits an entropy-balance decomposition featuring a nonnegative entropy production term driven by probability currents. Guided by this theory, we implement an entropy-triggered retraining policy using an exponentially weighted moving-average (EWMA) control statistic applied to a streaming kernel density estimator of the Kullback-Leibler divergence. We evaluate this approach across multiple nonstationary data streams. In synthetic, financial, and web-traffic domains, entropy-based retraining achieves predictive performance comparable to frequent retraining while reducing retraining frequency by one to two orders of magnitude. However, in a challenging biomedical ECG setting, the entropy-based trigger underperforms the maximum-frequency baseline, highlighting limitations of feature-space entropy monitoring under complex label-conditional drift.