用神经算子建模连续时间因果关系，支持不规则观测与反馈环。
Orca: Neural Operators for Causal Reasoning in Continuous Time
- 节点和机制均为时间函数，通过神经算子学习动态因果关系。
- 可处理不规则时间观测与反馈循环，实现反事实推断。
- 适合医疗、气候等连续演化系统的因果分析，代码开源。
结构化因果模型是干预与反事实推理的标准语言，但通常描述静态变量（仅测量一次），且不允许循环依赖。而我们关心的系统，如病人、气候与经济，往往在时间上连续演化、以不规则间隔观测，并包含反馈回路。我们提出，神经算子学习为该场景下的因果推理提供了自然基础，构建了名为Orca的框架：因果图中每个节点是时间函数，每个机制是函数空间间的可学习映射。我们扩展现有神经算子架构以表达因果机制——机制将父节点函数作为输入，计算目标节点函数值，遵守时间方向，并将潜在外生噪声视为可推断并用于反事实的函数。我们形式化了该模型类，并在合成连续时间示例上展示了反事实推理能力。代码已公开于 https://github.com/gerritgr/orca。
原文摘要 · Abstract (English)
Structural causal models are the standard language for reasoning about interventions and counterfactuals, but they describe static variables, typically measured once, and usually forbid cyclic dependencies. Many systems we care about, such as patients, climates, and economies, instead evolve continuously in time, are observed at irregular time points, and contain feedback loops. We argue that neural operator learning provides a natural foundation for causal reasoning in this setting, and propose Orca, a framework in which each node of the causal graph is a function of time and each mechanism is a learned map between function spaces. We extend existing neural operator architectures to express causal mechanisms: a mechanism computes the function value of a node from its parent nodes by taking several parent functions as input, respects the arrow of time, and treats latent exogenous noise as a function that can be inferred and reused for counterfactuals. We formalize the model class and demonstrate counterfactual reasoning on synthetic continuous-time examples. Code is available at https://github.com/gerritgr/orca
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