Settling: Equilibrium Inference for Non-Convex Validity Sets
Many learning systems return a single point estimate even when admissible outputs form disconnected or non-convex sets. Under squared loss, an ambiguous conditional distribution can therefore have a Bayes-optimal conditional mean that is invalid. We formalize this failure as conditional mean collapse and introduce Settling, an equilibrium-based inference operator that separates proposal generation, consistency evaluation, and test-time equilibrium selection. The operator treats a mean-seeking proposal as an initialization and refines it toward a locally stable configuration; conditional on initialization, refinement is deterministic. We establish exact-gradient descent, local convergence,...
| Authors | Lyes Saad Saoud |
|---|---|
| Primary category | cs.LG |
| Published | 9 September 2026 |
| Last updated at source | 9 September 2026 |
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