Perturbative Contrastive Physical Learning
2026-06-08 • Machine Learning
Machine Learning
AI summaryⓘ
The authors introduce a method called Perturbative Contrastive Physical Learning (PCPL), which helps systems learn by comparing how they respond to small changes in their inputs or environments. This approach builds on earlier methods but doesn't need a central computer to calculate gradients, as the system's own physical reactions guide learning. They tested PCPL on physical spring networks and photonic circuits, showing these systems can learn to classify data and perform multiplication. The work points toward physical devices that can learn more independently without traditional computing.
Perturbative Contrastive Physical LearningEquilibrium PropagationFrequency Propagationenergy-based systemsgradient computationspring networksphotonic circuitsclassification tasksJacobiananalog multiplication
Authors
Kyungeun Kim, Amanuel Anteneh, Israel Klich, Olivier Pfister, J. M. Schwarz
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.