Meta-Equilibrium in Learning Systems: A Physics-Inspired Framework for Generalization

This paper proposes a novel framework for understanding machine learning generalization through the lens of meta-equilibrium, a dynamic balance near the edge of chaos where order and flexibility coexist. Drawing parallels between physical systems and learning dynamics, we conceptualize overfitting as excessive symmetry (equilibrium, high bias, low variance) and underfitting as chaotic asymmetry (non-equilibrium, low bias, high variance). The meta-equilibrium regime, inspired by concepts like self-organized criticality and the information bottleneck, offers a “sweet spot” for robust generalization. By integrating insights from physics, complexity science, graph theory, and learning phenomena such as double descent and echo state networks, this framework suggests designing loss functions, optimizers, and architectures that maintain networks near this critical boundary. This perspective shifts machine learning toward symmetry- and physics-based mathematics, potentially redefining optimization, learning, and information theories.Note: A minimal correction:Equilibrium = Symmetry = Underfitting = High Bias, Low VarianceNon-equilibrium = Asymmetry = Overfitting = Low Bias, High Variance