Fitness Landscape Analysis of Product Unit Neural Networks

A fitness landscape analysis of the loss surfaces produced by product unit neural networks is performed in order to gain a better understanding of the impact of product units on the characteristics of the loss surfaces. The loss surface characteristics of product unit neural networks are then compared to the characteristics of loss surfaces produced by neural networks that make use of summation units. The failure of certain optimization algorithms in training product neural networks is explained through trends observed between loss surface characteristics and optimization algorithm performance. The paper shows that the loss surfaces of product unit neural networks have extremely large gradients with many deep ravines and valleys, which explains why gradient-based optimization algorithms fail at training these neural networks.