A Geometric Framework for Convolutional Neural Networks

Anthony L. Caterini; Dong Eui Chang

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arXiv · 1608.04374

A Geometric Framework for Convolutional Neural Networks

Anthony L. Caterini·Dong Eui Chang

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Abstract

In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free manner. Convolutional neural networks are described in this framework in a compact form, with the gradients of standard --- and higher-order --- loss functions calculated for each layer of the network. This approach can be applied to other network structures and provides a basis on which to create new networks.

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BibTeX RIS

Anthony L. Caterini, Dong Eui Chang. 2016-08-15. A Geometric Framework for Convolutional Neural Networks. https://arxiv.org/abs/1608.04374

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