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SUMMARY:On ResNet type neural network architectures and their stability pr
 operties - Brynjulf Owren (Norwegian University of Science and Technology\
 , Norwegian University of Science and Technology)
DTSTART:20211102T090000Z
DTEND:20211102T100000Z
UID:TALK165220@talks.cam.ac.uk
DESCRIPTION:<p>The study of neural networks as numerical approximations to
  continuous optimal control problems has gained some popularity after they
  were introduced by E (2017) and discussed in several other papers. This v
 iewpoint paves the way for analysing the networks as dynamical systems and
  in particular to address their stability properties. This was the topic i
 n a paper by Haber and Ruthotto (2017).<br />In this talk we shall first i
 ntroduce the continuous optimal control approach based on the presentation
  of Benning et al (2019) and discuss briefly what kind of advantages this 
 viewpoint can offer. Next we will present some stability results &nbsp\;in
 spired from the literature on the numerical solution of ordinary different
 ial equations. This involves in particular the use of continuous non-expan
 sive models and their numerical approximations\, see Celledoni et al. (202
 1). Finally\, we will talk briefly about some ongoing work using switching
  systems to analyse and control the stability of a mixed type neural netwo
 rk architecture.</p>\n<ul>\n<li>E\, W. (2017). A proposal on machine learn
 ing via dynamical systems. Commun. Math. Stat. 5(1)\, 1&ndash\;11</li>\n<l
 i>Haber\, E. & Ruthotto\, L. (2017). Stable architectures for deep neural 
 networks. Inverse Probl. 34(1)</li>\n<li>Benning\, M.\, Celledoni\, E.\, E
 hrhardt\, M. J.\, Owren\, B. & Sch&ouml\;nlieb\, C.-B. (2019) Deep learnin
 g as optimal control problems: models and numerical methods. J. Comput. Dy
 n. 6(2)\, 171&ndash\;198.</li>\n<li>E. Celledoni\, M. J. Ehrhardt\, C. Etm
 ann\, R. I. McLachlan\, B. Owren\, C.-B. Schonlieb and F. Sherry (2021). S
 tructure preserving deep learning. European Journal of Applied Mathematics
 \, 32(5)\, 888-936. doi:10.1017/S0956792521000139</li>\n</ul>
LOCATION:Seminar Room 2\, Newton Institute
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