Paper ID: 2203.05104

Transition to Linearity of Wide Neural Networks is an Emerging Property of Assembling Weak Models

Chaoyue Liu, Libin Zhu, Mikhail Belkin

Wide neural networks with linear output layer have been shown to be near-linear, and to have near-constant neural tangent kernel (NTK), in a region containing the optimization path of gradient descent. These findings seem counter-intuitive since in general neural networks are highly complex models. Why does a linear structure emerge when the networks become wide? In this work, we provide a new perspective on this "transition to linearity" by considering a neural network as an assembly model recursively built from a set of sub-models corresponding to individual neurons. In this view, we show that the linearity of wide neural networks is, in fact, an emerging property of assembling a large number of diverse "weak" sub-models, none of which dominate the assembly.

Submitted: Mar 10, 2022