Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Multiple Descent of Minimum-Norm Interpolants and Restricted
  Lower Isometry of Kernels   We study the risk of minimum-norm interpolants of data in Reproducing Kernel
Hilbert Spaces. Our upper bounds on the risk are of a multiple-descent shape
for the various scalings of $d = n^{\alpha}$, $\alpha\in(0,1)$, for the input
dimension $d$ and sample size $n$. Empirical evidence supports our finding that
minimum-norm interpolants in RKHS can exhibit this unusual non-monotonicity in
sample size; furthermore, locations of the peaks in our experiments match our
theoretical predictions. Since gradient flow on appropriately initialized wide
neural networks converges to a minimum-norm interpolant with respect to a
certain kernel, our analysis also yields novel estimation and generalization
guarantees for these over-parametrized models.
  At the heart of our analysis is a study of spectral properties of the random
kernel matrix restricted to a filtration of eigen-spaces of the population
covariance operator, and may be of independent interest.

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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int