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Settling: Equilibrium Inference for Non-Convex Validity Sets

arXiv · AI, language, vision and robotics · article · Sep 9, 2026 · UTC

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 ini

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