mlsanityData to 14 Oct 2026

Storage and selection of multiple chaotic attractors in minimal reservoir computers

arXiv 2603.15155 ↗First posted 16 Mar 2026nlin.CD cs.LGcited by 0

Not on the map. Why?

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.

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

36 of 104 references.

References · 36

  1. 2024Chronos: Learning the Language of Time Seriescited by 759
  2. 2023A decoder-only foundation model for time-series forecastingcited by 692
  3. 2018Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networkscited by 155
  4. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 88
  5. 2023Generalized Teacher Forcing for Learning Chaotic Dynamicscited by 58
  6. 2020Machine learning prediction of critical transition and system collapsecited by 54
  7. 2019Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computerscited by 43
  8. 2019Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRIcited by 41
  9. 2022Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systemscited by 36
  10. 2019Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radiuscited by 34
  11. 2024Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 33
  12. 2023Toward a Foundation Model for Time Series Datacited by 28
24 more
  1. 2024Zero-shot forecasting of chaotic systemscited by 28
  2. 2020Multifunctionality in a Reservoir Computercited by 21
  3. 2025True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statisticscited by 20
  4. 2021Reservoir Computing with Diverse Timescales for Prediction of Multiscale Dynamicscited by 13
  5. 2025Panda: A pretrained forecast model for chaotic dynamicscited by 13
  6. 2023Seeing double with a multifunctional reservoir computercited by 12
  7. 2023Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstructioncited by 9
  8. 2022ReservoirComputing.jl: An Efficient and Modular Library for Reservoir Computing Modelscited by 8
  9. 2024Optimal Recurrent Network Topologies for Dynamical Systems Reconstructioncited by 8
  10. 2024Deep Learning for predicting rate-induced tippingcited by 8
  11. 2022Exploring the limits of multifunctionality across different reservoir computerscited by 7
  12. 2024Chaotic attractor reconstruction using small reservoirs -- the influence of topologycited by 7
  13. 2021Learning Continuous Chaotic Attractors with a Reservoir Computercited by 5
  14. 2024Exploring the origins of switching dynamics in a multifunctional reservoir computercited by 4
  15. 2025Confabulation dynamics in a reservoir computer: Filling in the gaps with untrained attractorscited by 4
  16. 2023Multifunctionality in a Connectome-Based Reservoir Computercited by 3
  17. 2025Deterministic Reservoir Computing for Chaotic Time Series Predictioncited by 3
  18. 2025Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computingcited by 2
  19. 2025Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamicscited by 2
  20. 2025Multifunctional physical reservoir computing in soft tensegrity robotscited by 2
  21. 2024Asymmetrically connected reservoir networks learn bettercited by 1
  22. 2025Structuring Multiple Simple Cycle Reservoirs with Particle Swarm Optimizationcited by 1
  23. 2025Optimizing the Network Topology of a Linear Reservoir Computercited by 1
  24. 2025Prediction performance of random reservoirs with different topology for nonlinear dynamical systems with different number of degrees of freedomcited by 1

Built on by

Not cited yet.