REVIEW 1 cited by
A Priori Estimates of the Population Risk for Two-layer Neural Networks
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
New estimates for the population risk are established for two-layer neural networks. These estimates are nearly optimal in the sense that the error rates scale in the same way as the Monte Carlo error rates. They are equally effective in the over-parametrized regime when the network size is much larger than the size of the dataset. These new estimates are a priori in nature in the sense that the bounds depend only on some norms of the underlying functions to be fitted, not the parameters in the model, in contrast with most existing results which are a posteriori in nature. Using these a priori estimates, we provide a perspective for understanding why two-layer neural networks perform better than the related kernel methods.
Forward citations
Cited by 1 Pith paper
-
Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method
Harmonic functions with Barron Dirichlet data fail to be Lipschitz or H², yet admit Barron approximants of norm ~|log ε| with error ~ε on half-spaces and 2D rectangles, giving Deep Ritz a priori rates.
Discussion (0). Continue with ORCID to comment.