Dimensionality Reduction in Deep Learning via Kronecker Multi-layer Architectures

• URL: http://arxiv.org/abs/2204.04273v1
• Date: Fri, 8 Apr 2022 19:54:52 GMT
• Title: Dimensionality Reduction in Deep Learning via Kronecker Multi-layer Architectures
• Authors: Jarom D. Hogue and Robert M. Kirby and Akil Narayan
• Abstract summary: We propose a new deep learning architecture based on fast matrix multiplication of a Kronecker product decomposition. We show that this architecture allows a neural network to be trained and implemented with a significant reduction in computational time and resources.
• Score: 4.836352379142503
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep learning using neural networks is an effective technique for generating models of complex data. However, training such models can be expensive when networks have large model capacity resulting from a large number of layers and nodes. For training in such a computationally prohibitive regime, dimensionality reduction techniques ease the computational burden, and allow implementations of more robust networks. We propose a novel type of such dimensionality reduction via a new deep learning architecture based on fast matrix multiplication of a Kronecker product decomposition; in particular our network construction can be viewed as a Kronecker product-induced sparsification of an "extended" fully connected network. Analysis and practical examples show that this architecture allows a neural network to be trained and implemented with a significant reduction in computational time and resources, while achieving a similar error level compared to a traditional feedforward neural network.

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