On the Neural Tangent Kernel of Equilibrium Models

Zhili Feng; J. Zico Kolter

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arXiv · 2310.14062

On the Neural Tangent Kernel of Equilibrium Models

Zhili Feng·J. Zico Kolter

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Abstract

This work studies the neural tangent kernel (NTK) of the 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 can be 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 under mild conditions. Moreover, this deterministic NTK can be found efficiently via root-finding.

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Zhili Feng, J. Zico Kolter. 2023-10-21. On the Neural Tangent Kernel of Equilibrium Models. https://arxiv.org/abs/2310.14062

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