Neural Network Layer Algebra: A Framework to Measure Capacity and Compression in Deep Learning
This work addresses the need for better theoretical understanding of neural network properties for researchers, though it appears incremental as it builds on existing concepts like VC dimension.
The authors tackled the problem of measuring intrinsic properties like capacity and compression in deep neural networks by proposing a new framework based on layer algebra, resulting in metrics that can be computed more conveniently than VC dimension and used to analyze state-of-the-art architectures on benchmark datasets.
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.