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Deep learning using neural networks is an effective technique for generatingmodels of complex data. However, training such models can be expensive whennetworks have large model capacity resulting from a large number of layers andnodes. For training in such a computationally prohibitive regime,dimensionality reduction techniques ease the computational burden, and allowimplementations of more robust networks. We propose a novel type of suchdimensionality reduction via a new deep learning architecture based on fastmatrix multiplication of a Kronecker product decomposition; in particular ournetwork construction can be viewed as a Kronecker product-inducedsparsification of an "extended" fully connected network. Analysis and practicalexamples show that this architecture allows a neural network to be trained andimplemented with a significant reduction in computational time and resources,while achieving a similar error level compared to a traditional feedforwardneural network.

Weight Matrix Dimensionality Reduction in Deep Learning via Kronecker Multi-layer Architectures