# Basin Geometry and Reliable Recall of Dynamical Memories in Reservoir Computing

arXiv: https://arxiv.org/abs/2609.01914 · HTML: https://mlsanity.com/paper/2609.01914/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Interpreting recurrent neural networks behaviour via excitable network attractors](https://mlsanity.com/paper/1807.10478/) (2018)
- [Designing spontaneous behavioral switching via chaotic itinerancy](https://mlsanity.com/paper/2002.08332/) (2020)
- [Balanced Excitation and Inhibition are Required for High-Capacity, Noise-Robust Neuronal Selectivity](https://mlsanity.com/paper/1705.01502/) (2017)
- [Exploring the limits of multifunctionality across different reservoir computers](https://mlsanity.com/paper/2205.11375/) (2022)
- [Forgetting leads to chaos in attractor networks](https://mlsanity.com/paper/2112.00119/) (2021)

## Abstract (arXiv)

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.