Complexity for deep neural networks and other characteristics of deep feature representations

Abstract

We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for trained networks for various datasets as well as explore their dynamics during training, uncovering in particular power law scaling. These observables can be understood in a dual way as uncovering hidden internal structure of the datasets themselves as a function of scale or depth. The entropic character of the proposed notion of complexity should allow to transfer modes of analysis from neuroscience and statistical physics to the domain of artificial neural networks. The introduced observables can be applied without any change to the analysis of biological neuronal systems.

Significant extension including developments in neuroscience context and more. 36 pages

References in corpus (8)

• Complexity and Shock Wave Geometries
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Ultimate tensorization: compressing convolutional and FC layers alike
• Path integral optimization as circuit complexity
• AdS/CFT as a deep Boltzmann machine
• Complexity of Linear Regions in Deep Networks
• Entropy from Machine Learning
• Spectral Analysis of Latent Representations

Cited by in corpus (1)

• Neural networks adapting to datasets: learning network size and topology