Expressive Power of Randomized Signature
Type
conference paper
Date Issued
2021
Author(s)
Cuchiero, Christa
;
;
;
;
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
Eprints ID
269611
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26_expressive_power_of_randomized.pdf
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267.64 KB
Format
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