A Geometric Framework for Convolutional Neural Networks
Machine Learning
2016-10-06 v2 Artificial Intelligence
Neural and Evolutionary Computing
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.
Cite
@article{arxiv.1608.04374,
title = {A Geometric Framework for Convolutional Neural Networks},
author = {Anthony L. Caterini and Dong Eui Chang},
journal= {arXiv preprint arXiv:1608.04374},
year = {2016}
}
Comments
Added proofs and algorithms that were missing from previous version