A Differentiable Point Process with Its Application to Spiking Neural Networks

This paper is concerned about a learning algorithm for a probabilistic model\nof spiking neural networks (SNNs). Jimenez Rezende & Gerstner (2014) proposed a\nstochastic variational inference algorithm to train SNNs with hidden neurons.\nThe algorithm updates the variational distribution using the score function\ngradient estimator, whose high variance often impedes the whole learning\nalgorithm. This paper presents an alternative gradient estimator for SNNs based\non the path-wise gradient estimator. The main technical difficulty is a lack of\na general method to differentiate a realization of an arbitrary point process,\nwhich is necessary to derive the path-wise gradient estimator. We develop a\ndifferentiable point process, which is the technical highlight of this paper,\nand apply it to derive the path-wise gradient estimator for SNNs. We\ninvestigate the effectiveness of our gradient estimator through numerical\nsimulation.\n