  Deep residual networks (ResNets) have demonstrated better generalization
performance than deep feedforward networks (FFNets). However, the theory behind
such a phenomenon is still largely unknown. This paper studies this fundamental
problem in deep learning from a so-called "neural tangent kernel" perspective.
Specifically, we first show that under proper conditions, as the width goes to
infinity, training deep ResNets can be viewed as learning reproducing kernel
functions with some kernel function. We then compare the kernel of deep ResNets
with that of deep FFNets and discover that the class of functions induced by
the kernel of FFNets is asymptotically not learnable, as the depth goes to
infinity. In contrast, the class of functions induced by the kernel of ResNets
does not exhibit such degeneracy. Our discovery partially justifies the
advantages of deep ResNets over deep FFNets in generalization abilities.
Numerical results are provided to support our claim.
