Validate learned high-dimensional deployment of Settling

Establish whether learned high-dimensional implementations of Settling preserve useful validity-aware basin geometry and gradient alignment, thereby validating the equilibrium-selection mechanism beyond the analytic geometric diagnostic.

Background

The paper analytically studies Settling using a mean-seeking proposal and an explicitly constructed consistency energy in a geometric trajectory environment. This controlled setting isolates the inference mechanism but does not test whether learned proposal networks and learned consistency critics can reproduce the same behavior on realistic, high-dimensional data.

The unresolved empirical problem is to evaluate a complete learned deployment, including representation quality, negative-state construction, energy misspecification, spurious equilibria, basin coverage, inference-time computation, and comparisons with both mean-seeking and mode-preserving baselines. The paper identifies local gradient alignment and stable basin geometry as the key conditions that would need to transfer.