Neural networks with topological data analysis

Abstract

Convolutional Neural Networks are trained using a gradient descent back propagation technique which trains weights in each layer for the sole goal of minimizing training error. Hence, the resulting weights cannot be directly explained. Using Topological Data Analysis we can get an insight on how the neural network is thinking, specifically by analyzing the activation values of validation images as they pass through each layer. Auto-encoders instead of Convolutional neural networks are better for examining the homology of the data. We control connectivity properties of latent space of an auto encoder by studying a novel loss that is differentiable