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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On ResNet type neural network architectures and th
eir stability properties - Brynjulf Owren (Norwegi
an University of Science and Technology\, Norwegia
n University of Science and Technology)
DTSTART;TZID=Europe/London:20211102T090000
DTEND;TZID=Europe/London:20211102T100000
UID:TALK165220AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/165220
DESCRIPTION:The study of neural networks as numerical appro
ximations to continuous optimal control problems h
as gained some popularity after they were introduc
ed by E (2017) and discussed in several other pape
rs. This viewpoint paves the way for analysing the
networks as dynamical systems and in particular t
o address their stability properties. This was the
topic in a paper by Haber and Ruthotto (2017).
In this talk we shall first introduce the conti
nuous optimal control approach based on the presen
tation of Benning et al (2019) and discuss briefly
what kind of advantages this viewpoint can offer.
Next we will present some stability results
\;inspired from the literature on the numerical so
lution of ordinary differential equations. This in
volves in particular the use of continuous non-exp
ansive models and their numerical approximations\,
see Celledoni et al. (2021). Finally\, we will ta
lk briefly about some ongoing work using switching
systems to analyse and control the stability of a
mixed type neural network architecture.
\n
\n- E\, W. (2017). A proposal on machine learnin
g via dynamical systems. Commun. Math. Stat. 5(1)\
, 1&ndash\;11
\n- Haber\, E. & Ruthotto\, L.
(2017). Stable architectures for deep neural netw
orks. Inverse Probl. 34(1)
\n- Benning\, M.\
, Celledoni\, E.\, Ehrhardt\, M. J.\, Owren\, B. &
Schö\;nlieb\, C.-B. (2019) Deep learning as o
ptimal control problems: models and numerical meth
ods. J. Comput. Dyn. 6(2)\, 171&ndash\;198.
\n
- E. Celledoni\, M. J. Ehrhardt\, C. Etmann\, R.
I. McLachlan\, B. Owren\, C.-B. Schonlieb and F.
Sherry (2021). Structure preserving deep learning.
European Journal of Applied Mathematics\, 32(5)\,
888-936. doi:10.1017/S0956792521000139
\n
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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