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.

References

Cross-domain panels remain mechanism illustrations; learned high-dimensional validation remains an open empirical test.

— Settling: Equilibrium Inference for Non-Convex Validity Sets  (2609.09682 - Saoud, 9 Sep 2026) in Abstract; Section 6, paragraph 'Transfer to learned high-dimensional systems'; Section 7, Conclusion

The GELU sweep uses a reduced 7-point grid rather than the full 15 (Appendix~\ref{app:compute_budget}), and this alone could plausibly produce a less clean fit simply from pooling over fewer entanglement conditions. We consider this unlikely to be the primary explanation, since the ReLU classifier was validated on data from the same style of reduced grid elsewhere without a comparable increase in component count, but we have not run the GELU sweep at the full 15 points to rule this out directly, and treat it as an open question rather than a settled one.

— Hidden not Deleted: How Networks Suppress Entangled Features  (2609.27593 - Samanta et al., 23 Sep 2026) in Appendix, Section “Robustness: Full Results and Ruling Out Alternatives,” subsection “Candidate explanations for the GELU basin structure”