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Perturbative Contrastive Physical Learning (PCPL) offers a framework where learning emerges implicitly from physical system responses to perturbations, eliminating the need for centralized gradient computation or external processors. By unifying concepts like Equilibrium Propagation and Frequency Propagation, the approach successfully trains diverse platforms ranging from spring networks to photonic circuits for classification tasks. This method represents a significant step toward autonomous physical learning systems that leverage inherent system dynamics rather than explicit backpropagation.
Perturbative Contrastive Physical Learning
arXiv:2606.09756v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn)
arXiv:2606.09756 [cs.LG]
(or arXiv:2606.09756v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.09756 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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