Equilibrium Propagation for Dissipative Dynamics

TL;DR

This paper extends equilibrium propagation to damped dynamical systems, enabling local learning rules in physical systems like mechanical structures and circuits, with applications in signal classification and intelligent materials.

Contribution

It introduces an effective action framework for damped systems, deriving local learning rules applicable to both periodic and resting conditions, expanding equilibrium propagation's scope.

Findings

Demonstrates viability in mechanical and electronic systems.

Enables classification of temporal sound signals.

Opens pathways for intelligent materials processing dynamical signals.

Abstract

Computing gradients of a cost function is central to design-based optimization and machine learning algorithms. Equilibrium propagation provides an exact method to compute gradients in hardware by exploiting the inherent physical laws. The locality of these algorithms, in conjunction with local updates, enables mechanical and electronic systems that autonomously learn a function. We extend these methods to damped dynamical systems operating in the linear regime, such as mechanical structures obeying damped Newtonian dynamics and RLC circuits. By introducing an effective action whose extremum corresponds to the underlying dynamics, we derive local learning rules. This approach applies both to problems with periodic boundary conditions and to those with resting initial conditions. We demonstrate the viability of our method in mechanical and electronic systems and explore novel functionality such as classifying temporal sound signals. Our work opens the door to intelligent materials that process dynamical signals, enabling temporal computations, passive and active sensors, and materials that act as frequency-dependent filters.