This paper is concerned about a learning algorithm for a probabilistic model of spiking neural networks (SNNs). Jimenez Rezende & Gerstner (2014) proposed a stochastic variational inference algorithm to train SNNs with hidden neurons. The algorithm updates the variational distribution using the score function gradient estimator, whose high variance often impedes the whole learning algorithm. This paper presents an alternative gradient estimator for SNNs based on the path-wise gradient estimator. The main technical difficulty is a lack of a general method to differentiate a realization of an arbitrary point process, which is necessary to derive the path-wise gradient estimator. We develop a differentiable point process, which is the technical highlight of this paper, and apply it to derive the path-wise gradient estimator for SNNs. We investigate the effectiveness of our gradient estimator through numerical simulation.

本文介绍了一种用于训练具有隐藏神经元的脉冲神经网络（SNNs）的学习算法，探讨了一种基于路径梯度估计器的SNNs的替代梯度估计器，并开发了一种可微的点过程，用于导出替代梯度估计器。通过数值模拟，研究了梯度估计器的有效性。

一种可微分点过程及其在脉冲神经网络中的应用