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.

翻译：本文关注的是神经网络跳动概率模型的学习算法。 Jimenez Rezende & Gerstner (2014年) 提议了一个随机变化推算法来用隐藏神经元来培训 SNNS 。 该算法使用分数函数梯度估测器来更新变异分布, 其差异很大往往阻碍整个学习算法。 本文根据路径偏向梯度测算器为 SNNS 提供了一个替代梯度测算器。 主要的技术困难在于缺乏一种总的方法来区分一个任意点过程的实现, 而这种过程对于得出路径偏向梯度估测器是必要的。 我们开发了一个可变点算法过程, 这是本文的技术亮点, 并应用它来为 SNNS 绘制路径偏向梯度估测仪。 我们通过数字模拟来调查我们的梯度测算器的有效性 。