  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.
