Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth

TL;DR

This paper investigates how varying the depth and width of neural networks influences their internal representations and output behaviors, revealing a characteristic block structure in larger models and differences in error patterns despite similar accuracy.

Contribution

It uncovers the relationship between model capacity and internal representation structure, highlighting how width and depth affect learned features and model errors.

Findings

Larger capacity models exhibit a block structure in hidden representations.

Representation outside the block structure is similar across architectures.

Wide and deep models show distinctive error patterns despite similar accuracy.

Abstract

A key factor in the success of deep neural networks is the ability to scale models to improve performance by varying the architecture depth and width. This simple property of neural network design has resulted in highly effective architectures for a variety of tasks. Nevertheless, there is limited understanding of effects of depth and width on the learned representations. In this paper, we study this fundamental question. We begin by investigating how varying depth and width affects model hidden representations, finding a characteristic block structure in the hidden representations of larger capacity (wider or deeper) models. We demonstrate that this block structure arises when model capacity is large relative to the size of the training set, and is indicative of the underlying layers preserving and propagating the dominant principal component of their representations. This discovery has important ramifications for features learned by different models, namely, representations outside the block structure are often similar across architectures with varying widths and depths, but the block structure is unique to each model. We analyze the output predictions of different model architectures, finding that even when the overall accuracy is similar, wide and deep models exhibit distinctive error patterns and variations across classes.