The claim here is a bit misleading, as already pointed out by other comments, since the kernel is an evolving one that is essentially learned after seeing the data.
Contrary to many related works that compare wide neural networks to kernel methods, our recent work shows that one can study a feature learning infinite-width limit with realistic learning rate.
We identified what separates the kernel regime (e.g., NTK) and the feature learning regime. In the infinite-width limit, OP's work could belong to either regime depending on the parametrization, i.e. the path kernel is either equal to the NTK or performing feature learning.
It's an incredibly interesting research topic. Please feel free to comment with thoughts on our work :)
Contrary to many related works that compare wide neural networks to kernel methods, our recent work shows that one can study a feature learning infinite-width limit with realistic learning rate.
https://arxiv.org/abs/2011.14522
We identified what separates the kernel regime (e.g., NTK) and the feature learning regime. In the infinite-width limit, OP's work could belong to either regime depending on the parametrization, i.e. the path kernel is either equal to the NTK or performing feature learning.
It's an incredibly interesting research topic. Please feel free to comment with thoughts on our work :)