# Nonlinear memory capacity of parallel time-delay reservoir computers in the processing of multidimensional signals

arXiv: https://arxiv.org/abs/1510.03891 · HTML: https://mlsanity.com/paper/1510.03891/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2015.

## Built on by (most cited first, 3 of 3)

- [Memory of recurrent networks: Do we compute it right?](https://mlsanity.com/paper/2305.01457/) (2023)
- [Memory Capacity of Nonlinear Recurrent Networks: Is it Informative?](https://mlsanity.com/paper/2502.04832/) (2025)
- [Interpretable Design of Reservoir Computing Networks using Realization Theory](https://mlsanity.com/paper/2112.06891/) (2021)

## Abstract (arXiv)

This paper addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking. First, an approximating reservoir model is presented in those frameworks that provides an explicit functional link between the reservoir parameters and architecture and its performance in the execution of a specific task. Second, the inference properties of the ridge regression estimator in the multivariate context is used to assess the impact of finite sample training on the decrease of the reservoir capacity. Finally, an empirical study is conducted that shows the adequacy of the theoretical results with the empirical performances exhibited by various reservoir architectures in the execution of several nonlinear tasks with multidimensional inputs. Our results confirm the robustness properties of the parallel reservoir architecture with respect to task misspecification and parameter choice that had already been documented in the literature.