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  4. Expressive Power of Randomized Signature
 
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Expressive Power of Randomized Signature

Type
conference paper
Date Issued
2021
Author(s)
Cuchiero, Christa
Gonon, Lukas  orcid-logo
Lyudmila Grigoryeva  orcid-logo
Ortega Lahuerta, Juan-Pablo  
Teichmann, Josef
Abstract
We consider the question whether the time evolution of controlled differential equations on general state spaces can be arbitrarily well approximated by (regularized) regressions on features generated themselves through randomly chosen dynamical systems of moderately high dimension. On the one hand this is motivated by paradigms of reservoir computing, on the other hand by ideas from rough path theory and compressed sensing. Appropriately interpreted this yields provable approximation and generalization results for generic dynamical systems by regressions on states of random, otherwise untrained dynamical systems, which usually are approximated by recurrent or LSTM networks. The results have important implications for transfer learning and energy efficiency of training.
Language
English
HSG Classification
contribution to scientific community
HSG Profile Area
SEPS - Quantitative Economic Methods
Volume
NeurIPS 2021 Workshop DLDE
Event Title
The Symbiosis of Deep Learning and Differential Equations
Event Location
NeurIPS
Event Date
2021
Official URL
https://openreview.net/forum?id=KWWFPULvmVw
URL
https://www.alexandria.unisg.ch/handle/20.500.14171/110897
Subject(s)

other research area

econometrics

computer science

finance

statistics

Division(s)

SEPS - School of Econ...

MS - Faculty of Mathe...

Eprints ID
269611
File(s)
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Thumbnail Image

open.access

Name

26_expressive_power_of_randomized.pdf

Size

267.64 KB

Format

Adobe PDF

Checksum (MD5)

9d4f3c3e28d89474b65128f2ae97136d

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