On the Neural Tangent Kernel of Equilibrium Models

This work studies the neural tangent kernel (NTK) of deep equilibrium (DEQ) model, a practical ``infinite-depth'' architecture which directly computes the infinite-depth limit of a weight-tied network via root-finding. Even though the NTK of a fully-connected neural network is stochastic if its width and depth both tend to infinity simultaneously, we show that contrarily a DEQ model still enjoys a deterministic NTK despite its width and depth going to infinity at the same time. Moreover, such deterministic NTK can be found efficiently via root-finding.