Basins of Attraction to Multiple Fixed Points in Discrete-time Hysteresis Neural Networks
arXiv:2608.23225
2026
Dynamics
2 ideas extracted · analyzed Aug 29, 2026
What the math gives to ML
The paper studies binary recurrent dynamics with a hysteresis deadband: units switch only when their weighted input crosses a threshold and otherwise retain their previous state. This creates multiple stable fixed points with distinct basins of attraction, offering a route to robust discrete latent memory and attractor-based classification. The threshold is also a controllable architectural parameter that changes attractor multiplicity and basin balance. The most actionable adaptations are a hysteretic recurrent layer trained with a straight-through surrogate and an empirical basin-entropy procedure for avoiding collapse to a single attractor.
Ideas from this paper
Unverified
Re-invented
2026
Replace a binary recurrent layer's ordinary sign activation with a hysteretic update that retains each unit's previous state when its incoming weighted sum is inconclusive. This creates discrete attractors that are robust to small perturbations and can serve as persistent latent memories, iterative classifiers, or compact associative states.
Useful6/10
Difficulty5/10
Novelty7/10
Unverified
2026
Use the hysteresis threshold as a regularizer for attractor diversity. Estimate how many initial states converge to each fixed point and select thresholds that maximize basin entropy or penalize domination by one attractor, reducing attractor collapse in discrete recurrent classifiers and memory modules.
Useful5/10
Difficulty4/10
Novelty8/10