A Tensor Analysis on Dense Connectivity via Convolutional Arithmetic Circuits

Emilio Rafael Balda, Arash Behboodi, Rudolf Mathar

Abstract: Several state of the art convolutional networks rely on inter-connecting different layers to ease the flow of information and gradient between their input and output layers. These techniques have enabled practitioners to successfully train deep convolutional networks with hundreds of layers. Particularly, a novel way of interconnecting layers was introduced as the Dense Convolutional Network (DenseNet) and has achieved state of the art performance on relevant image recognition tasks. Despite their notable empirical success, their theoretical understanding is still limited. In this work, we address this problem by analyzing the effect of layer interconnection on the overall expressive power of a convolutional network. In particular, the connections used in DenseNet are compared with other types of inter-layer connectivity. We carry out a tensor analysis on the expressive power inter-connections on convolutional arithmetic circuits (ConvACs) and relate our results to standard convolutional networks. The analysis leads to performance bounds and practical guidelines for design of ConvACs. The generalization of these results are discussed for other kinds of convolutional networks via generalized tensor decompositions.

TL;DR: We analyze the expressive power of the connections used in DenseNets via tensor decompositions.

Keywords: DenseNets, Tensor Analysis, Convolutional Arithmetic Circuits