A geometric explanation of the reservoir computing phenomenon using randomized discrete-time signatures
Speaker: Juan Pablo Ortega (Division of Mathematical Sciences, Nanyang Technological University, Singapore)
Date: Friday, 25 February 2022 - 11:00
Online: us06web.zoom.us/j/7555463367 (ID: 755 546 3367)
Abstract:
The possibility of uniformly approximating fading memory input/output systems using randomly generated state-space systems subjected to cheap training is a promising approach to the theory of recurrent neural networks that has been successfully implemented in many applications. In this talk we explain this surprising phenomenon by showing how the finite-dimensional random projections of certain universal infinite-dimensional approximants yield randomly generated state affine systems with linear readouts that exhibit excellent performance and, more importantly, provide a deep mathematical explanation of the reservoir computing phenomenon. This work is a collaboration with Christa Cuchiero, Lukas Gonon, Lyudmila Grigoryeva, and Josef Teichmann.
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