On neuronal capacity**This article is an updated version of: Baldi P and Vershynin R 2018 On neuronal capacity Advances in Neural Information Processing Systems 31 ed S Bengio, H Wallach, H Larochelle, K Grauman, N Cesa-Bianchi and R Garnett (Red Hook, NY: Curran Associates, Inc) pp 7740–7749.

Abstract

We define the capacity of a learning machine to be the logarithm of the number (or volume) of the functions it can implement. We review known results, and derive new results, estimating the capacity of several neuronal models: linear and polynomial threshold gates, linear and polynomial threshold gates with constrained weights (binary weights, positive weights), and ReLU neurons. We also derive some capacity estimates and bounds for fully recurrent networks, as well as feedforward networks.