Complexity for deep neural networks and other characteristics of deep feature representations
This work provides a novel analytical framework for understanding internal structures in neural networks and datasets, with potential applications in neuroscience and statistical physics.
The authors introduced a complexity measure for neural networks that quantifies nonlinearity and effective dimension of feature representations, and found power law scaling in these observables during training across various datasets.
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.