AI 中文总结
针对非凸有效集下条件均值坍缩问题，提出基于均衡的推断算子Settling，分离提议生成、一致性评估与均衡选择，在几何诊断中表现优于基线，成功率高达99/100。
AI 中文摘要
许多学习系统即使在可行输出形成不连通或非凸集合时，也仅返回单点估计。在平方损失下，一个模糊的条件分布因此可能具有无效的贝叶斯最优条件均值。我们将这种失败形式化为条件均值坍缩，并引入Settling，一种基于均衡的推断算子，它将提议生成、一致性评估和测试时均衡选择分离开来。该算子将均值寻求提议视为初始化，并将其精炼至局部稳定配置；在给定初始化的条件下，精炼是确定性的。我们建立了精确梯度下降、局部收敛性以及与学习的一致性批评者相关的不精确梯度鲁棒性条件。在一个可复现的100上下文几何诊断中，均值寻求基线在0/100上下文中成功，随机去噪在100/100中成功，而Settling在99/100中成功，同时产生显著更低的轨迹粗糙度。一项1,200次运行的敏感性研究在障碍抖动范围高达0.20时获得97-100%的成功率，在从0.05到0.50的一次性初始化扰动范围内获得94-100%的成功率。跨领域面板仍为机制说明；学习的高维验证仍是一个开放的实证检验。
英文摘要
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, and an inexact-gradient robustness condition relevant to learned consistency critics. In a reproducible 100-context geometric diagnostic, the mean-seeking baseline succeeds in 0/100 contexts, stochastic denoising in 100/100, and Settling in 99/100 while producing substantially lower trajectory roughness. A 1,200-run sensitivity study yields 97-100% success across obstacle-jitter ranges up to 0.20 and 94-100% across one-time initialization perturbations from 0.05 to 0.50. Cross-domain panels remain mechanism illustrations; learned high-dimensional validation remains an open empirical test.
