Transition to Linearity of General Neural Networks with Directed Acyclic Graph Architecture

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

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Libin Zhu, Chaoyue Liu, Misha Belkin


In this paper we show that feedforward neural networks corresponding to arbitrary directed acyclic graphs undergo transition to linearity as their ``width'' approaches infinity. The width of these general networks is characterized by the minimum in-degree of their neurons, except for the input and first layers. Our results identify the mathematical structure underlying transition to linearity and generalize a number of recent works aimed at characterizing transition to linearity or constancy of the Neural Tangent Kernel for standard architectures.