Understanding Deep Architectures using a Recursive Convolutional Network

TL;DR

This paper investigates how the number of layers, feature maps, and parameters affect convolutional network performance using a recursive model with tied weights, revealing that depth and parameters are more impactful than feature map size.

Contribution

It provides an empirical analysis of the independent effects of layers, feature maps, and parameters on convolutional network capacity using a novel recursive architecture.

Findings

Increasing layers enhances computational power.

Number of parameters is more critical than feature map size.

Feature map size has limited impact on performance.

Abstract

A key challenge in designing convolutional network models is sizing them appropriately. Many factors are involved in these decisions, including number of layers, feature maps, kernel sizes, etc. Complicating this further is the fact that each of these influence not only the numbers and dimensions of the activation units, but also the total number of parameters. In this paper we focus on assessing the independent contributions of three of these linked variables: The numbers of layers, feature maps, and parameters. To accomplish this, we employ a recursive convolutional network whose weights are tied between layers; this allows us to vary each of the three factors in a controlled setting. We find that while increasing the numbers of layers and parameters each have clear benefit, the number of feature maps (and hence dimensionality of the representation) appears ancillary, and finds most of its benefit through the introduction of more weights. Our results (i) empirically confirm the notion that adding layers alone increases computational power, within the context of convolutional layers, and (ii) suggest that precise sizing of convolutional feature map dimensions is itself of little concern; more attention should be paid to the number of parameters in these layers instead.