Preisach Attention: A Hysteretic Model of Sequential Memory
We introduce the Preisach Attention Layer (PAL), a novel sequence modelling architecture grounded in the classical Preisach hysteresis operator from mathematical physics. PAL replaces the softmax attention mechanism with a binary relay operator parameterised by learned activation and deactivation thresholds, maintaining a stack of local extrema as its internal state. A single-layer PAL-Transformer with O(1) depth is Turing-complete under arbitrary precision arithmetic, achievable through simulation of a two-stack pushdown automaton -- in contrast to the O(log n) depth required by standard hard-attention transformers. Second, we prove that the function classes computable by PAL and by the ...
| Authors | Piotr Frydrych |
|---|---|
| Primary category | cs.LG |
| Published | 22 May 2026 |
| Last updated at source | 22 May 2026 |
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