# Unfolding recurrence by Green's functions for optimized reservoir computing

arXiv: https://arxiv.org/abs/2010.06247 · HTML: https://mlsanity.com/paper/2010.06247/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2020.

## Built on by (most cited first, 4 of 4)

- [Unsupervised Reservoir Computing for Solving Ordinary Differential Equations](https://mlsanity.com/paper/2108.11417/) (2021)
- [Beyond accuracy: generalization properties of bio-plausible temporal credit assignment rules](https://mlsanity.com/paper/2206.00823/) (2022)
- [Path classification by stochastic linear recurrent neural networks](https://mlsanity.com/paper/2108.03090/) (2021)
- [Neuronal architecture extracts statistical temporal patterns](https://mlsanity.com/paper/2301.10203/) (2023)

## Abstract (arXiv)

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.