Channel redundancy and overlap in convolutional neural networks with channel-wise NNK graphs

TL;DR

This paper investigates the redundancy and overlap among channels in CNNs using channel-wise NNK graphs, revealing significant redundancy, its variation with depth and regularization, and its correlation with model performance.

Contribution

The study introduces a theoretical analysis of channel overlap in CNNs using CW-NNK graphs, providing new insights into the intrinsic data manifold and model generalization.

Findings

Significant channel redundancy varies with layer depth and regularization.

Channel overlap in the last layer correlates with generalization performance.

Techniques improve understanding of deep feature representations.

Abstract

Feature spaces in the deep layers of convolutional neural networks (CNNs) are often very high-dimensional and difficult to interpret. However, convolutional layers consist of multiple channels that are activated by different types of inputs, which suggests that more insights may be gained by studying the channels and how they relate to each other. In this paper, we first analyze theoretically channel-wise non-negative kernel (CW-NNK) regression graphs, which allow us to quantify the overlap between channels and, indirectly, the intrinsic dimension of the data representation manifold. We find that redundancy between channels is significant and varies with the layer depth and the level of regularization during training. Additionally, we observe that there is a correlation between channel overlap in the last convolutional layer and generalization performance. Our experimental results demonstrate that these techniques can lead to a better understanding of deep representations.