Applicability of the free-probability variational method to TAP complexity for the Ising perceptron

Determine whether the free-probability/variational approach that evaluates the random-determinant term in Kac–Rice computations can be carried out for the TAP free energy landscape of the Ising perceptron to establish annealed topological trivialization.

Background

For several models, annealed topological trivialization has been obtained by analyzing random determinants via free probability and associated variational formulas for the limiting spectral measure.

The authors discuss that this pathway, although successful elsewhere (e.g., multi-species spherical spin glasses), is highly model-dependent and requires tools such as vector Dyson equations; it is currently unclear if this program can be executed for the Ising perceptron’s TAP landscape.