# Structuring Multiple Simple Cycle Reservoirs with Particle Swarm Optimization

arXiv: https://arxiv.org/abs/2504.05347 · HTML: https://mlsanity.com/paper/2504.05347/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 6 Apr 2025.

## Builds on (most cited first, 6 of 6)

- [Dynamical Systems as Temporal Feature Spaces](https://mlsanity.com/paper/1907.06382/) (2019)
- [Simple Cycle Reservoirs are Universal](https://mlsanity.com/paper/2308.10793/) (2023)
- [Universality of Real Minimal Complexity Reservoir](https://mlsanity.com/paper/2408.08071/) (2024)
- [Linear Simple Cycle Reservoirs at the edge of stability perform Fourier decomposition of the input driving signals](https://mlsanity.com/paper/2412.00295/) (2024)
- [Predictive Modeling in the Reservoir Kernel Motif Space](https://mlsanity.com/paper/2405.07045/) (2024)
- [A Framework for Population-Based Stochastic Optimization on Abstract Riemannian Manifolds](https://mlsanity.com/paper/1908.06783/) (2019)

## Built on by (most cited first, 1 of 1)

- [Storage and selection of multiple chaotic attractors in minimal reservoir computers](https://mlsanity.com/paper/2603.15155/) (2026)

## Abstract (arXiv)

Reservoir Computing (RC) is a time-efficient computational paradigm derived from Recurrent Neural Networks (RNNs). The Simple Cycle Reservoir (SCR) is an RC model that stands out for its minimalistic design, offering extremely low construction complexity and proven capability of universally approximating time-invariant causal fading memory filters, even in the linear dynamics regime. This paper introduces Multiple Simple Cycle Reservoirs (MSCRs), a multi-reservoir framework that extends Echo State Networks (ESNs) by replacing a single large reservoir with multiple interconnected SCRs. We demonstrate that optimizing MSCR using Particle Swarm Optimization (PSO) outperforms existing multi-reservoir models, achieving competitive predictive performance with a lower-dimensional state space. By modeling interconnections as a weighted Directed Acyclic Graph (DAG), our approach enables flexible, task-specific network topology adaptation. Numerical simulations on three benchmark time-series prediction tasks confirm these advantages over rival algorithms. These findings highlight the potential of MSCR-PSO as a promising framework for optimizing multi-reservoir systems, providing a foundation for further advancements and applications of interconnected SCRs for developing efficient AI devices.