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ARXIV:2605.23603 · SEQUENCE MODELING · SUBMITTED 25 MAY · 20:40 UTC · FRESHNESS STALE
ARXIV:2605.23603SEQUENCE MODELINGSUBMITTED 25 MAY · 20:40 UTCFRESHNESS STALEPiotr Frydrych · arXiv
A novel sequence modeling architecture inspired by hysteresis that offers improved efficiency for tasks with long episodic memory.
Opportunity summary
Pain A novel sequence modeling architecture inspired by hysteresis that offers improved efficiency for tasks with long episodic memory.
Evidence 0 refs | 3 sources | 50% coverage
Blocker Evidence unverified
A novel sequence modeling architecture inspired by hysteresis that offers improved efficiency for tasks with long episodic memory. PAL replaces the softmax attention mechanism with a binary relay operator parameterised by learned activation and…
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…
ScienceToStartup currently rates this 3.0/10 on the public viability pass. Second, we prove that the function classes computable by PAL and by the transformer are incomparable: PAL computes historical range statistics in O(1) layers…
Sequence Modeling moved forward this cycle; last verified May 2026. Public score 3.0/10.
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A novel sequence modeling architecture inspired by hysteresis that offers improved efficiency for tasks with long episodic memory.
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10.48550/arXiv.2605.23603A novel sequence modeling architecture inspired by hysteresis that offers improved efficiency for tasks with long episodic memory.
Abstract
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 transformer are incomparable: PAL computes historical range statistics in O(1) layers that require O(log n) layers for transformers, while transformers support random-access retrieval that PAL cannot perform without auxiliary state. The separating property is rate-independence -- PAL responds only to the sequence of local extrema, not to absolute token positions or temporal spacing. Third, we show that the extremum stack constitutes a minimal sufficient statistic of the input history for all rate-independent functionals, providing a formal analogue of the wiping property in classical hysteresis theory. PAL is thus an efficient architecture for tasks with long episodic memory and weak positional dependence, with O(n log n) total inference cost versus O(n^2) for standard attention.
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PROBLEM
A novel sequence modeling architecture inspired by hysteresis that offers improved efficiency for tasks with long episodic memory. PAL replaces the softmax attention mechanism with a binary relay operator parameterised by learned activation and deactivation thresholds, maintaini...
METHOD
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 activatio...
RESULT
ScienceToStartup currently rates this 3.0/10 on the public viability pass. Second, we prove that the function classes computable by PAL and by the transformer are incomparable: PAL computes historical range statistics in O(1) layers that require O(log n) layers for transformers,...
WHY NOW
Sequence Modeling moved forward this cycle; last verified May 2026. Public score 3.0/10.
Abstract-backed public claims while anchored extraction refreshes.
A novel sequence modeling architecture inspired by hysteresis that offers improved efficiency for tasks with long episodic memory. 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.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 3.0/10 on the public viability pass. Second, we prove that the function classes computable by PAL and by the transformer are incomparable: PAL computes historical range statistics in O(1) layers that require O(log n) layers for transformers, while transformers support random-access retrieval that PAL cannot perform without auxiliary state.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Sequence Modeling moved forward this cycle; last verified May 2026. Public score 3.0/10.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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A novel sequence modeling architecture inspired by hysteresis that offers improved efficiency for tasks with long episodic memory.
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Sequence Modeling
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