Lukas Gonon

Lukas Gonon

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Gonon

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Lukas

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Risk bounds for reservoir computing

( 2019-09-19)
Gonon, Lukas
;
Grigoryeva, Lyudmila
;
Ortega, Juan-Pablo

Type: conference paper

URI: https://www.alexandria.unisg.ch/handle/20.500.14171/98204
The Universality Problem in Dynamic Machine Learning with Applications to Realized Covolatilities Forecasting

( 2019-06-07)
Gonon, Lukas
;
Grigoryeva, Lyudmila
;
Ortega, Juan-Pablo

Type: conference paper

URI: https://www.alexandria.unisg.ch/handle/20.500.14171/98571
Approximation bounds for random neural networks and reservoir systems

(Institute of Mathematical Statistics, 2023-02)
Gonon, Lukas
;
Grigoryeva, Lyudmila
;
Ortega Lahuerta, Juan-Pablo

Journal: The Annals of Applied Probability

Volume: 33

Issue: 1

URL: https://doi.org/10.1214/22-AAP1806

URI: https://www.alexandria.unisg.ch/handle/20.500.14171/107767
Expressive Power of Randomized Signature

( 2021)
Cuchiero, Christa
;
Gonon, Lukas
;
Grigoryeva, Lyudmila
;
Ortega Lahuerta, Juan-Pablo
;
Teichmann, Josef

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.

Volume: NeurIPS 2021 Workshop DLDE

URL: https://openreview.net/forum?id=KWWFPULvmVw

URI: https://www.alexandria.unisg.ch/handle/20.500.14171/110897
Discrete-time signatures and randomness in reservoir computing

Cuchiero, Christa
;
Gonon, Lukas
;
Grigoryeva, Lyudmila
;
Ortega Lahuerta, Juan-Pablo
;
Teichmann, Josef

A new explanation of geometric nature of the reservoir computing phenomenon is presented. Reservoir computing is understood in the literature as the possibility of approximating input/output systems with randomly chosen recurrent neural systems and a trained linear readout layer. Light is shed on this phenomenon by constructing what is called strongly universal reservoir systems as random projections of a family of state-space systems that generate Volterra series expansions. This procedure yields a state-affine reservoir system with randomly generated coefficients in a dimension that is logarithmically reduced with respect to the original system. This reservoir system is able to approximate any element in the fading memory filters class just by training a different linear readout for each different filter. Explicit expressions for the probability distributions needed in the generation of the projected reservoir system are stated and bounds for the committed approximation error are provided.

Type: forthcoming

URI: https://www.alexandria.unisg.ch/handle/20.500.14171/116759
Reservoir kernels and Volterra series

( 2022-12-30)
Gonon, Lukas
;
Grigoryeva, Lyudmila
;
Ortega Lahuerta, Juan-Pablo

Type: working paper

URI: https://www.alexandria.unisg.ch/handle/20.500.14171/107950

Lukas Gonon

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