用耦合核建模可能世界间的因果关系,解决传统预测无法处理反事实不确定性的问题。
WorldKernel: A World Model is the Coupling Kernel of Admissible Possible Worlds

- 将世界模型视为可接受世界间的正定耦合核,显式编码反事实关联。
- 在28%的模型中,强预测器对反事实耦合失效,而该方法能给出可证的区间边界。
- 适合因果推理、反事实分析与不确定性量化研究者阅读。
普遍假设认为,只要有足够的观测和干预数据,强大的预测器就足以应对。我们报告了一种与此相悖的失败模式:在数百个结构化因果模型中,强预测器与贝叶斯基线在可识别量上均表现良好,但在不可识别量(反事实世界间的耦合)上,预测器坍缩为单点,其中28%的模型其结果无任何有效模型能产生,而真实值是一个不可缩小的可接受区间。该差距是结构性的:预测无法表示反事实耦合的不确定性。本文将世界模型定义为可接受世界间的一个正定耦合核 K(T,T'),其对角线为普通后验(即预测器恢复的内容),非对角线则为预测器无法表达的跨世界耦合,所有反事实推理都依赖于此。本文系统阐述该非对角线部分的理论。该结构真实存在:两个后验相同的状态在跨世界查询上仍可能不同,而非对角线正是修复反事实的关键。该核可被约束:正定性提供边际分布所缺乏的部分可识别信息,可多项式时间界定反事实响应,而精确响应程序在计算上不可行。逻辑结构进一步收紧边界,最多提升三分之一,并传播至从未直接涉及的耦合。该核可通过针对性约束(由不可行性学习所得)快速获取,效率远超非针对性方法。其完整重构等价于可接受世界的近似计数,在Sly-Sun阈值以下可解,以上则不可近似;本文不宣称突破最坏情况复杂度。
原文摘要 · Abstract (English)
A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.
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