We propose a method for extending the technique of equilibrium propagation for estimating gradients in fixed-point neural networks to the more general setting of directed, time-varying neural networks by modeling them as electrical circuits. We use electrical circuit theory to construct a Lagrangian capable of describing deep, directed neural networks modeled using nonlinear capacitors and inductors, linear resistors and sources, and a special class of nonlinear dissipative elements called fractional memristors. We then derive an estimator for the gradient of the physical parameters of the network, such as synapse conductances, with respect to an arbitrary loss function. This estimator is entirely local, in that it only depends on information locally available to each synapse. We conclude by suggesting methods for extending these results to networks of biologically plausible neurons, e.g. Hodgkin-Huxley neurons.

翻译：我们提出一种方法来扩大平衡传播技术,以估计固定点神经网络中的梯度,通过以电路为模型来模拟定向、时间变化神经网络,从而将平衡传播技术扩大到更普遍的定向、时间变化的神经网络。我们利用电路理论来建造一个能够描述深、定向神经网络的拉格朗格人(Lagrangian人),这种网络以非线性电容器和感应器、线性抵抗器和源以及非线性分离元素的特殊类别,称为分光分子。我们然后得出一个测量器,以测量网络物理参数的梯度,例如对任意损失功能的突触的导力。这个估计器完全是局部的,因为它只取决于每个突触器在当地可获得的信息。我们最后提出将这些结果扩大到生物上可信的神经元网络的方法,例如Hodgkin-Huxley神经元。