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Efficient Mapping of Neural Network Models on a Class of Parallel Architectures.

This dissertation develops a formal and systematic methodology for efficient mapping of several contemporary artificial neural network (ANN) models on k-ary n-cube parallel architectures (KNC’s). We apply the general mapping to several important ANN models including feedforward ANNs trained with backpropagation algorithm, radial basis function networks, cascade correlation learning, and adaptive resonance theory networks. Our approach utilizes a parallel task graph representing concurrent operations of the ANN model during training. The mapping of the ANN is performed in two steps. First, the parallel task graph of the ANN is mapped to a virtual KNC of compatible dimensionality. This involves decomposing each operation into its atomic tasks. Second, the dimensionality of the virtual KNC architecture is recursively reduced through a sequence of transformations until a desired metric is optimized. We refer to this process as folding the virtual architecture. The optimization criteria we consider in this dissertation are defined in terms of the iteration time of the algorithm on the folded architecture. If necessary, the mapping scheme may utilize a subset of the processors of a given KNC architecture if it results in the most efficient simulation. A unique feature of our mapping is that it systematically selects an appropriate degree of parallelism leading to a highly efficient realization of the ANN model on KNC architectures. A novel feature of our work is its ability to efficiently map unit-allocating ANNs. These networks possess a dynamic structure which grows during training. We present a highly efficient scheme for simulating such networks on existing KNC parallel architectures. We assume an upper bound on size of the neural network. We perform the folding such that