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arXiv · 2609.01914

Basin Geometry and Reliable Recall of Dynamical Memories in Reservoir Computing

Ling-Wei Kong·Ying-Cheng Lai
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Abstract

Reliable attractor recall conventionally requires broad basins of attraction. However, in reservoir-computing based associative memory, temporal cues reliably recover dynamical memories despite basins dominated by unpredictable, riddled-like regions. We reveal that memory basins exhibit an ``octopus-like'' structure: a robust ``head'' near the attractor and thin, intertwined ``tentacles'' spanning state space. Initial states in tentacular regions yield near-zero uncertainty exponents, making the recalled memory effectively unpredictable at finite precision. Yet, cue-driven generalized synchronization bypasses this unpredictability, driving the system into the robust basin head. This mechanism yields a quantitative relation linking minimum cue duration, synchronization rate, and basin-head radius. Trained recurrent neural networks exhibit similar geometry, suggesting this phenomenon extends beyond reservoir computing.

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Ling-Wei Kong, Ying-Cheng Lai. 2026-09-01. Basin Geometry and Reliable Recall of Dynamical Memories in Reservoir Computing. https://arxiv.org/abs/2609.01914

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