Double descent in the condition number
Name
CBMM-Memo-102.pdf
Size
837.18 KB
Format
Adobe PDF
Checksum (MD5)
5eadf9d89e20c6c97346409d35c66e22
Author(s)
Poggio, Tomaso
Kur, Gil
Banburski, Andrzej
Date Issued
December 4, 2019
Publisher
Center for Brains, Minds and Machines (CBMM)
Series/Report no.
CBMM Memo;102
Abstract
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 problems. An example is machine learning where the key task is to estimate an underlying function from a set of measurements at random points in a high dimensional space and where low sensitivity to error in the data is a requirement for good predictive performance. Here we report the simple observation that when the columns of A are random vectors, the condition number of A is highest, that is worse, when d=n, that is when the inverse of A exists. An overdetermined system (n>d) and especially an underdetermined system (n
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