Connect equilibrium escape barriers to retrieval dynamics

Derive the genuine relaxation dynamics, nucleation prefactors, and multistep retrieval dynamics of attention networks corresponding to the equilibrium barrier and escape ladders obtained for Model B.

Background

The paper derives an equilibrium reaction-coordinate description of retrieval loss in Model B, including a barrier and two quantized escape ladders associated with distinct defections and co-defections.

It does not establish how these equilibrium quantities govern actual dynamical relaxation, nucleation rates, or the multistep retrieval process in attention networks. A dynamical theory is therefore needed to connect the phase-diagram analysis to observed retrieval lifetimes and trajectories.

References

Establishing the relevant competing branches, barriers, and transition dynamics lies beyond the local conditional theory developed here and is left for future work.

— A Function-Space Approach to the Statistical Mechanics of Learning Dynamics  (2609.09589 - Zhang et al., 9 Sep 2026) in Section 6, Discussion and Future Work

Connecting them to genuine relaxation dynamics, nucleation prefactors, and the multi-step retrieval dynamics of attention networks is left for future work.

— 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”