Storage and selection of multiple chaotic attractors in minimal reservoir computers

TL;DR

This study demonstrates that minimal reservoir computer architectures can store multiple chaotic attractors but face challenges in switching between them based on external cues, with performance largely independent of topology.

Contribution

It shows that minimal deterministic reservoirs can learn multiple attractors, challenging the belief that large, random reservoirs are necessary for multi-attractor learning.

Findings

Minimal reservoirs can store multiple chaotic attractors.

Performance does not strongly depend on reservoir topology.

Minimal reservoirs struggle with cue-dependent switching between attractors.

Abstract

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.