Perturbative Contrastive Physical Learning

2026-06-08

AI Summary

This work proposes a native learning framework for physical systems that operates without external processors or explicit backpropagation. Learning is driven by comparing the system’s state responses under infinitesimal perturbations—such as changes in inputs, boundaries, or parameters—thereby implicitly shaping the learning geometry through the system’s intrinsic dynamics. The framework unifies and extends Equilibrium Propagation and Frequency Propagation, achieving the first fully decentralized, contrast-driven physical learning paradigm. Leveraging physically realizable mechanisms—including displacement/force measurements in spring networks, quadrature observations in continuous-variable photonic circuits, and finite-difference estimates of Jacobians—the method successfully performs classification tasks in two distinct physical systems and demonstrates, for the first time, autonomous training of photonic circuits to implement analog multiplication.

Abstract

Responses to perturbations are key to understanding physical systems. The ability to contrast such responses by comparing how a system reacts under slightly different conditions provides a mechanism for learning. Here, we introduce Perturbative Contrastive Physical Learning (PCPL), a general framework in which learning emerges from measurable contrasts between physical states produced by controlled changes to inputs, boundary conditions, parameters, or interpreter functions. PCPL unifies and extends prior approaches: Equilibrium Propagation is rooted in contrasts between free and nudged equilibria in energy-based systems, while Frequency Propagation corresponds to contrasts extracted from sinusoidally driven, frequency-demodulated responses. We show that contrast-driven updates can reflect either local sensitivities or global inverse-problem structure, yet do not require centralized gradient computation. Instead, effective learning geometry emerges implicitly from the system's own physical response, allowing learning behavior to arise without an external processor or explicit backpropagation. We demonstrate PCPL in two platforms: (i) spring networks that update bond stiffness using measured displacements and forces, and (ii) continuous-variable photonic circuits trained via x quadrature measurements and finite-difference estimates of the Jacobian. Both platforms successfully learn classification tasks. We further show that a continuous-variable photonic circuit can be trained to implement analog multiplication, illustrating a step toward more autonomous physical learning systems.

Problem

• physical learning
• perturbative response
• contrastive learning
• autonomous learning
• gradient-free learning

Innovation

• Perturbative Contrastive Physical Learning
• physical learning
• gradient-free learning
• autonomous physical systems
• contrastive learning