  Recent research shows that the dynamics of an infinitely wide neural network
(NN) trained by gradient descent can be characterized by Neural Tangent Kernel
(NTK) \citep{jacot2018neural}. Under the squared loss, the infinite-width NN
trained by gradient descent with an infinitely small learning rate is
equivalent to kernel regression with NTK \citep{arora2019exact}. However, the
equivalence is only known for ridge regression currently
\citep{arora2019harnessing}, while the equivalence between NN and other kernel
machines (KMs), e.g. support vector machine (SVM), remains unknown. Therefore,
in this work, we propose to establish the equivalence between NN and SVM, and
specifically, the infinitely wide NN trained by soft margin loss and the
standard soft margin SVM with NTK trained by subgradient descent. Our main
theoretical results include establishing the equivalences between NNs and a
broad family of $\ell_2$ regularized KMs with finite-width bounds, which cannot
be handled by prior work, and showing that every finite-width NN trained by
such regularized loss functions is approximately a KM. Furthermore, we
demonstrate our theory can enable three practical applications, including (i)
\textit{non-vacuous} generalization bound of NN via the corresponding KM; (ii)
\textit{non-trivial} robustness certificate for the infinite-width NN (while
existing robustness verification methods would provide vacuous bounds); (iii)
intrinsically more robust infinite-width NNs than those from previous kernel
regression. Our code for the experiments is available at
\url{https://github.com/leslie-CH/equiv-nn-svm}.
