用数学框架重新定义因果知识的相对性，让机器更懂因果关系的本质。
The Relativity of Causal Knowledge
- 基于范畴论构建因果模型的函子范畴，揭示其概率结构的凸性。
- 通过层理论实现因果知识在网络中的传递与一致性校验。
- 为多主体协作的因果推理提供数学基础，适合研究可信AI的学者。
人工智能的发展暴露出纯预测系统之局限，亟需转向因果与协作推理。受格罗滕迪克数学革命启发，本文提出因果知识的相对性：结构因果模型（SCMs）本质上是嵌入于关系网络中的不完美、主观表征。借助范畴论，我们将SCMs组织为函子范畴，并证明其观测与干预概率度量自然形成凸结构，从而可用凸空间编码未干预的SCMs。进一步利用层理论，构建因果知识的层与余层结构，实现网络中因果知识的传递，同时保持干预一致性与主体视角。最终，给出相对因果知识的严格数学定义。
原文摘要 · Abstract (English)
Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the relativity of causal knowledge, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the network sheaf and cosheaf of causal knowledge. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of relative causal knowledge.
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