Mapping a class of neural networks on k-ary n-cubes

Abstract

In this paper we propose a scheme for mapping two important artificial neural network (ANN) models on the popular k-ary n-cube parallel architectures (KNCs). The scheme is based on generalizing the mapping of a bipartite graph onto the KNC architecture and thus can be adapted to any model whose computations can be represented by a bipartite task graph. Our approach is the first to adjust the granularity of parallelism so as to achieve the best possible performance based on properties of the computational model and the target architecture. We first introduce a methodology for optimal implementation of multi-layer feedforward artificial neural networks (FFANNs) trained with the backpropagation algorithm on KNCs. We prove that our mapping methodology is time-optimal and that it provides for maximum processor utilization regardless of the structure of the FFANN. We show that the same methodology can be utilized for efficient mapping of Radial Basis Function neural networks (RBFs) on KNCs.