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Basin Geometry and Reliable Recall of Dynamical Memories in Reservoir Computing

arXiv · AI, language, vision and robotics · article · Sep 1, 2026 · UTC

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 synchron

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