This chapter aims to further explore the capabilities of the Higher Order Neural Networks class and especially the Pi-Sigma Neural Networks. The performance of Pi-Sigma Networks is evaluated through several well known neural network training benchmarks. In the experiments reported here, Distributed Evolutionary Algorithms are implemented for Pi-Sigma neural networks training. More specifically, the distributed versions of the Differential Evolution and the Particle Swarm Optimization algorithms have been employed. To this end, each processor of a distributed computing environment is assigned a subpopulation of potential solutions. The subpopulations are independently evolved in parallel and occasional migration is allowed to facilitate the cooperation between them. The novelty of the proposed approach is that it is applied to train Pi-Sigma networks using threshold activation functions, while the weights and biases were confined in a narrow band of integers (constrained in the range [-32, 32]). Thus, the trained Pi-Sigma neural networks can be represented by using only 6 bits. Such networks are better suited for hardware implementation than the real weight ones and this property is very important in real-life applications. Experimental results suggest that the proposed training process is fast, stable and reliable and the distributed trained Pi-Sigma networks exhibit good generalization capabilities.
Integer Weight Higher-Order Neural Network Training Using Distributed Differential Evolution
