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.

翻译：平衡传播是近期提出的一种用于使用和训练人工神经网络的方法，其中网络处于能量泛函的最小值（更一般地为极值）状态。该方法已在多项基准任务中展现出良好性能。本文从两个方向对平衡传播进行扩展。首先，我们证明了平衡传播存在自然的量子推广形式，即量子神经网络处于网络哈密顿量的基态（更一般地为任意本征态），其训练机制利用了平均能量在本征态上取极值的特性。其次，我们将平衡传播的分析推广至有限温度情形，揭示热涨落可自然实现网络训练，而无需在训练过程中对输出层进行钳制。此外，我们还研究了平衡传播的低温极限性质。