2016/08/15 by Caterini, Anthony L., Chang, Dong Eui
#Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #I.2.6 #I.5.1 #Machine Learning (stat.ML) #Neural and Evolutionary Computing (cs.NE)
paper · doi:10.48550/arxiv.1608.04374
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.