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CATEGORIES:Applied and Computational Analysis
SUMMARY:v Tangent Kernels - Akshunna S. Dogra (Imperial Co
llege)
DTSTART;TZID=Europe/London:20240314T150000
DTEND;TZID=Europe/London:20240314T160000
UID:TALK210139AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/210139
DESCRIPTION:Machine learning (ML) has been profitably leverage
d across a wide variety of problems in recent year
s. Empirical observations show that ML models from
suitable functional spaces are capable of adequat
ely efficient learning across a wide variety of di
sciplines. In this work (first in a planned sequen
ce of three)\, we build the foundations for a gene
ric perspective on ML model optimization and gener
alization dynamics. Specifically\, we prove that u
nder variants of gradient descent\, “well-initiali
zed” models solve sufficiently well-posed problems
at \\textit{a priori} or \\textit{in situ} determ
inable rates. Notably\, these results are obtained
for a wider class of problems\, loss functions\,
and models than the standard mean squared error an
d large width regime that is the focus of conventi
onal Neural Tangent Kernel (NTK) analysis. The $\\
nu$ - Tangent Kernel ($\\nu$TK)\, a functional ana
lytic object reminiscent of the NTK\, emerges natu
rally as a key object in our analysis and its prop
erties function as the control for learning.\nWe e
xemplify the power of our proposed perspective by
showing that it applies to diverse practical probl
ems solved using real ML models\, such as classifi
cation tasks\, data/regression fitting\, different
ial equations\, shape observable analysis\, etc. W
e end with a small discussion of the numerical evi
dence\, and the role $\\nu$TKs may play in charact
erizing the search phase of optimization\, which l
eads to the “well-initialized” models that are the
crux of this work.
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Nicolas Boulle
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