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Double descent in the condition number
(Center for Brains, Minds and Machines (CBMM), 2019-12-04)
In solving a system of n linear equations in d variables Ax=b, the condition number of the (n,d) matrix A measures how much errors in the data b affect the solution x. Bounds of this type are important in many inverse ...
Theoretical Issues in Deep Networks
(Center for Brains, Minds and Machines (CBMM), 2019-08-17)
While deep learning is successful in a number of applications, it is not yet well understood theoretically. A theoretical characterization of deep learning should answer questions about their approximation power, the ...
An analysis of training and generalization errors in shallow and deep networks
(Center for Brains, Minds and Machines (CBMM), arXiv.org, 2019-05-30)
This paper is motivated by an open problem around deep networks, namely, the apparent absence of overfitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we analyze ...