How does topology influence gradient propagation and model performance of deep networks with DenseNet-type skip connections?

TL;DR

This paper investigates how the topology of skip connections in deep neural networks affects gradient flow and performance, introducing the NN-Mass metric to predict and optimize model accuracy and efficiency.

Contribution

The paper introduces NN-Mass, a new metric linking network topology to gradient propagation, applicable across various skip connection types, enabling better model design and compression.

Findings

NN-Mass predicts model accuracy across different architectures.

NN-Mass enables design of compressed networks at initialization.

Empirical validation on datasets like CIFAR and ImageNet supports the metric's effectiveness.

Abstract

DenseNets introduce concatenation-type skip connections that achieve state-of-the-art accuracy in several computer vision tasks. In this paper, we reveal that the topology of the concatenation-type skip connections is closely related to the gradient propagation which, in turn, enables a predictable behavior of DNNs' test performance. To this end, we introduce a new metric called NN-Mass to quantify how effectively information flows through DNNs. Moreover, we empirically show that NN-Mass also works for other types of skip connections, e.g., for ResNets, Wide-ResNets (WRNs), and MobileNets, which contain addition-type skip connections (i.e., residuals or inverted residuals). As such, for both DenseNet-like CNNs and ResNets/WRNs/MobileNets, our theoretically grounded NN-Mass can identify models with similar accuracy, despite having significantly different size/compute requirements. Detailed experiments on both synthetic and real datasets (e.g., MNIST, CIFAR-10, CIFAR-100, ImageNet) provide extensive evidence for our insights. Finally, the closed-form equation of our NN-Mass enables us to design significantly compressed DenseNets (for CIFAR-10) and MobileNets (for ImageNet) directly at initialization without time-consuming training and/or searching.