Unfolding recurrence by Green's functions for optimized reservoir computing
Abstract
Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics. This sets them apart from deep feed-forward networks. Despite the tremendous progress in the application of feed-forward networks and their theoretical understanding, it remains unclear how the interplay of recurrence and non-linearities in recurrent cortical networks contributes to their function. The purpose of this work is to present a solvable recurrent network model that links to feed forward networks. By perturbative methods we transform the time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels. The resulting analytical expressions allow us to build optimal time-series classifiers from random reservoir networks. Firstly, this allows us to optimize not only the readout vectors, but also the input projection, demonstrating a strong potential performance gain. Secondly, the analysis exposes how the second order stimulus statistics is a crucial element that interacts with the non-linearity of the dynamics and boosts performance.
Cite
@article{arxiv.2010.06247,
title = {Unfolding recurrence by Green's functions for optimized reservoir computing},
author = {Sandra Nestler and Christian Keup and David Dahmen and Matthieu Gilson and Holger Rauhut and Moritz Helias},
journal= {arXiv preprint arXiv:2010.06247},
year = {2021}
}