Fitness Landscape Analysis of Feed-Forward Neural Networks

Abstract

Neural network training is a highly non-convex optimisation problem with poorly understood properties. Due to the inherent high dimensionality, neural network search spaces cannot be intuitively visualised, thus other means to establish search space properties have to be employed. Fitness landscape analysis encompasses a selection of techniques designed to estimate the properties of a search landscape associated with an optimisation problem. Applied to neural network training, fitness landscape analysis can be used to establish a link between the properties of the error landscape and various neural network hyperparameters. This study applies fitness landscape analysis to investigate the influence of the search space boundaries, regularisation parameters, loss functions, activation functions, and feed-forward neural network architectures on the properties of the resulting error landscape. A novel gradient-based sampling technique is proposed, together with a novel method to quantify and visualise stationary points and the associated basins of attraction in neural network error landscapes.