We present a unified geometric framework for modeling learning dynamics in physical, biological, and machine learning systems. The theory reveals three fundamental regimes, each emerging from the power-law relationship \( g \propto \kappa ^\alpha \) between the metric tensor \( g \) in the space of trainable variables and the noise covariance matrix \( \kappa \) . The quantum regime corresponds to \( \alpha = 1 \) and describes Schrödinger-like dynamics that emerges from a discrete shift symmetry. The efficient learning regime corresponds to \( \alpha = \tfrac{1}{2} \) and describes very fast machine learning algorithms. The equilibration regime corresponds to \( \alpha = 0 \) and describes classical models of biological evolution. We argue that the emergence of the intermediate regime \( \alpha = \tfrac{1}{2} \) is a key mechanism underlying the emergence of biological complexity.
