Equilibrium Propagation: the Quantum and the Thermal Cases

TL;DR

This paper extends equilibrium propagation to quantum neural networks and finite temperature scenarios, enabling new training methods that leverage quantum states and thermal fluctuations for improved neural network optimization.

Contribution

It introduces a quantum generalization of equilibrium propagation and analyzes training at finite temperatures, broadening the method's applicability.

Findings

Quantum equilibrium propagation uses eigenstates for training.

Thermal fluctuations enable training without clamping output layers.

Low temperature limit of the method is analyzed.

Abstract

Equilibrium propagation is a recently introduced method to use and train artificial neural networks in which the network is at the minimum (more generally extremum) of an energy functional. Equilibrium propagation has shown good performance on a number of benchmark tasks. Here we extend equilibrium propagation in two directions. First we show that there is a natural quantum generalization of equilibrium propagation in which a quantum neural network is taken to be in the ground state (more generally any eigenstate) of the network Hamiltonian, with a similar training mechanism that exploits the fact that the mean energy is extremal on eigenstates. Second we extend the analysis of equilibrium propagation at finite temperature, showing that thermal fluctuations allow one to naturally train the network without having to clamp the output layer during training. We also study the low temperature limit of equilibrium propagation.