Neural Network Layer Algebra: A Framework to Measure Capacity and Compression in Deep Learning

TL;DR

This paper introduces a novel layer algebra framework to measure neural network capacity and compression, providing new metrics that depend solely on architecture and enabling better analysis of deep learning models.

Contribution

It proposes the layer algebra concept and two new metrics—layer complexity and layer intrinsic power—to evaluate neural network properties independent of parameters.

Findings

Metrics can be computed more easily than VC dimension.

Architectural properties correlate with classification accuracy.

Framework applicable to various network architectures.

Abstract

We present a new framework to measure the intrinsic properties of (deep) neural networks. While we focus on convolutional networks, our framework can be extrapolated to any network architecture. In particular, we evaluate two network properties, namely, capacity, which is related to expressivity, and compression, which is related to learnability. Both these properties depend only on the network structure and are independent of the network parameters. To this end, we propose two metrics: the first one, called layer complexity, captures the architectural complexity of any network layer; and, the second one, called layer intrinsic power, encodes how data is compressed along the network. The metrics are based on the concept of layer algebra, which is also introduced in this paper. This concept is based on the idea that the global properties depend on the network topology, and the leaf nodes of any neural network can be approximated using local transfer functions, thereby, allowing a simple computation of the global metrics. We show that our global complexity metric can be calculated and represented more conveniently than the widely-used VC dimension. We also compare the properties of various state-of-the art architectures using our metrics and use the properties to analyze their accuracy on benchmark image classification datasets.