Tight conditions for when the NTK approximation is valid

We study when the neural tangent kernel (NTK) approximation is valid for training a model with the square loss. In the lazy training setting of Chizat et al. 2019, we show that rescaling the model by a factor of \(\alpha = O(T)\) suffices for the NTK approximation to be valid until training time \(T\). Our bound is tight and improves on the previous bound of Chizat et al. 2019, which required a larger rescaling factor of \(\alpha = O(T^2)\).