Extend the class-H phase diagrams beyond the adiabatic limit

Determine the phase diagrams of the higher-order class-H associative memories for finite hidden-to-visible inverse-temperature ratio, including the genuinely two-temperature regime and its equal-temperature restricted-Boltzmann-machine limit.

Background

For Models A and C with k>2 and for Model B, the analysis takes the adiabatic limit in which hidden neurons are enslaved to the visible configuration. At finite hidden-sector temperature, the model becomes a genuinely two-temperature system, and the paper does not analyze the interpolation away from this limit.

The unresolved problem is to characterize the phases and retrieval behavior at finite β/τ_h, including the equal-temperature endpoint corresponding to a bipartite Gibbs measure.