Deep Maxout Network Gaussian Process

TL;DR

This paper establishes the equivalence between deep, infinite-width maxout networks and Gaussian processes, characterizes the maxout kernel, and demonstrates competitive Bayesian inference results, suggesting broader applicability of maxout activations.

Contribution

It introduces the deep maxout network Gaussian process, deriving its kernel and connecting it to existing neural network kernels, enabling efficient Bayesian inference.

Findings

Deep maxout networks correspond to specific Gaussian processes.

The proposed kernel can be efficiently computed and adapted.

Bayesian inference with this kernel yields competitive results.

Abstract

Study of neural networks with infinite width is important for better understanding of the neural network in practical application. In this work, we derive the equivalence of the deep, infinite-width maxout network and the Gaussian process (GP) and characterize the maxout kernel with a compositional structure. Moreover, we build up the connection between our deep maxout network kernel and deep neural network kernels. We also give an efficient numerical implementation of our kernel which can be adapted to any maxout rank. Numerical results show that doing Bayesian inference based on the deep maxout network kernel can lead to competitive results compared with their finite-width counterparts and deep neural network kernels. This enlightens us that the maxout activation may also be incorporated into other infinite-width neural network structures such as the convolutional neural network (CNN).