Resolve hidden-sector corrections at exponential load

Determine whether the Gaussian hidden-neuron fluctuation corrections in Model B—the exponent shift from β/τ_h to β/τ_h+N/2 and the additive pattern shift—can be absorbed into a redefinition of the reference measure while leaving the rate-level phase diagram unchanged.

Background

The leading analysis of Model B uses the adiabatic partition function. Gaussian fluctuations around the hidden softmax saddle generate an exponent shift and an additive shift involving the sum of all stored patterns. Because the number of patterns is exponential in the visible dimension, these corrections are not perturbatively small.

The paper identifies their treatment as a structural open question: resolving it would clarify whether the leading phase diagram is robust and how softmax normalization affects the thermodynamics beyond leading order.