[Paper] Perturbative Contrastive Physical Learning
Source: arXiv - 2606.09756v1
Overview
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.
Key Contributions
This paper presents research in the following areas:
- cs.LG
- cond-mat.dis-nn
Methodology
Please refer to the full paper for detailed methodology.
Practical Implications
This research contributes to the advancement of cs.LG.
Authors
- Kyungeun Kim
- Amanuel Anteneh
- Israel Klich
- Olivier Pfister
- J. M. Schwarz
Paper Information
- arXiv ID: 2606.09756v1
- Categories: cs.LG, cond-mat.dis-nn
- Published: June 8, 2026
- PDF: Download PDF