Learnable Sequential Memory in Coupled Oscillator Networks
arXiv:2607.18439
2026
Dynamics
2 ideas extracted · analyzed Aug 30, 2026
What the math gives to ML
The paper offers a constructive multi-timescale attractor mechanism for sequential memory: fast Kuramoto phase dynamics store individual patterns, an intermediate hysteresis process enforces reliable dwell times, and a slow context-dependent routing matrix selects the next attractor. The transferable asset is the separation between memory geometry and transition policy, allowing stored representations to remain fixed while sequence structure is learned independently. A practical neural implementation is a phase-based recurrent module with contractive attractor states, hysteretic switching, and measurable stability boundaries determined by coupling spectra and timescale ratios.
Ideas from this paper
✗ Failed on benchmark
2026
Replace a conventional recurrent hidden state with a phase oscillator state whose stored memories are exponentially stable phase-locked configurations. Each memory has a coupling matrix or low-rank coupling parameter, while an external context selects which coupling landscape is active; this separates representation storage from sequence routing.
Useful8/10
Difficulty6/10
Novelty7/10
✗ Failed on benchmark
2026
Insert a slow routing state and an intermediate hysteresis variable between a neural memory and its next-state selector. The hysteresis prevents small prediction fluctuations from repeatedly changing the active attractor, while the slower router learns transition probabilities independently of the attractor parameters.
Useful7/10
Difficulty5/10
Novelty6/10