# Storage and selection of multiple chaotic attractors in minimal reservoir computers

arXiv: https://arxiv.org/abs/2603.15155 · HTML: https://mlsanity.com/paper/2603.15155/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 104 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 30 of 36)

- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers](https://mlsanity.com/paper/1910.00659/) (2019)
- [Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI](https://mlsanity.com/paper/1902.07186/) (2019)
- [Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems](https://mlsanity.com/paper/2207.02542/) (2022)
- [Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius](https://mlsanity.com/paper/1910.04426/) (2019)
- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [Toward a Foundation Model for Time Series Data](https://mlsanity.com/paper/2310.03916/) (2023)
- [Zero-shot forecasting of chaotic systems](https://mlsanity.com/paper/2409.15771/) (2024)
- [Multifunctionality in a Reservoir Computer](https://mlsanity.com/paper/2008.06348/) (2020)
- [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025)
- [Reservoir Computing with Diverse Timescales for Prediction of Multiscale Dynamics](https://mlsanity.com/paper/2108.09446/) (2021)
- [Panda: A pretrained forecast model for chaotic dynamics](https://mlsanity.com/paper/2505.13755/) (2025)
- [Seeing double with a multifunctional reservoir computer](https://mlsanity.com/paper/2305.05799/) (2023)
- [Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction](https://mlsanity.com/paper/2401.00885/) (2023)
- [ReservoirComputing.jl: An Efficient and Modular Library for Reservoir Computing Models](https://mlsanity.com/paper/2204.05117/) (2022)
- [Optimal Recurrent Network Topologies for Dynamical Systems Reconstruction](https://mlsanity.com/paper/2406.04934/) (2024)
- [Deep Learning for predicting rate-induced tipping](https://mlsanity.com/paper/2409.07590/) (2024)
- [Exploring the limits of multifunctionality across different reservoir computers](https://mlsanity.com/paper/2205.11375/) (2022)
- [Chaotic attractor reconstruction using small reservoirs -- the influence of topology](https://mlsanity.com/paper/2402.16888/) (2024)
- [Learning Continuous Chaotic Attractors with a Reservoir Computer](https://mlsanity.com/paper/2110.08631/) (2021)
- [Exploring the origins of switching dynamics in a multifunctional reservoir computer](https://mlsanity.com/paper/2408.15400/) (2024)
- [Confabulation dynamics in a reservoir computer: Filling in the gaps with untrained attractors](https://mlsanity.com/paper/2505.04792/) (2025)
- [Multifunctionality in a Connectome-Based Reservoir Computer](https://mlsanity.com/paper/2306.01885/) (2023)
- [Deterministic Reservoir Computing for Chaotic Time Series Prediction](https://mlsanity.com/paper/2501.15615/) (2025)
- [Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing](https://mlsanity.com/paper/2506.05292/) (2025)

## Abstract (arXiv)

Modern predictive modeling increasingly calls for a single learned dynamical substrate to operate across multiple regimes. From a dynamical-systems viewpoint, this capability decomposes into the storage of multiple attractors and the selection of the appropriate attractor in response to contextual cues. In reservoir computing (RC), multi-attractor learning has largely been pursued using large, randomly wired reservoirs, on the assumption that stochastic connectivity is required to generate sufficiently rich internal dynamics. At the same time, recent work shows that minimal deterministic reservoirs can match random designs for single-system chaotic forecasting. Under which conditions can minimal topologies learn multiple chaotic attractors? In this paper, we find that minimal architectures can successfully store multiple chaotic attractors. However, these same architectures struggle with task switching, in which the system must transition between attractors in response to external cues. We test storage and selection on all 28 unordered system pairs formed from eight three-dimensional chaotic systems. We do not observe a robust dependence of multi-attractor performance on reservoir topology. Over the ten topologies investigated, we find that no single one consistently outperforms the others for either storage or cue-dependent selection. Our results suggest that while minimal substrates possess the representational capacity to model coexisting attractors, they may lack the robust temporal memory required for cued transitions.