Establish stability beyond one-step freezing

Establish the stability of the Model-B sector decomposition against fluctuations between sectors and determine whether the predicted Ruelle statistics of attention weights hold in the frozen phase.

Background

The finite-temperature analysis treats freezing within each attention sector and obtains a one-step replica-symmetry-breaking-like description, including a prediction of Ruelle point-process statistics for the frozen-phase attention weights.

The paper leaves unresolved the stability of this construction to fluctuations between sectors, analogous to an Almeida–Thouless test, as well as the validity of the predicted attention-weight statistics.

References

Within each sector the freezing prescription is exact (#1{append:model_b_copy_representation}), but fluctuations between sectors (an analogue of the AT condition) and the predicted Ruelle statistics of the F-phase attention weights remain unexamined.

— Phases in a class of associative memories via hidden neurons  (2609.10976 - Ota et al., 10 Sep 2026) in Appendix, Section Complete phase diagram, subsection “Remarks and open problems”