将时间序列因果模型拓展到连续时间，提出可变观测下轨迹不变的新标准。
Towards Continuous-time Causal Foundation Models
- 用SDE建模连续时间因果机制，设计分层集成方法
- 细网格积分显著优于粗略积分，8/8实验中表现更优
- 适合药代动力学与物理系统等需时间敏感建模场景
将离散时间因果先验-数据拟合网络扩展至连续时间，需以随机微分方程（SDE）表达机制。若仅在观测间隔处积分一次，轨迹分布会依赖观测时间，先验仍为披着SDE外衣的离散马尔可夫模型。本文提出精确连续性标准——轨迹律对观测时序不变，并建立三层次分类体系（离散；朴素观测网格积分；细网格积分并解耦观测），并在具有奥恩斯坦-乌伦贝克或小型MLP非线性漂移的随机有向无环图上实现顶层构造。在包含线性和非线性先验的2×2编码器×积分器消融实验中，细网格积分在8/8单元中优于朴素方法（符号一致性p<1/256），且随着评估网格细化，差距扩大；细积分下编码器轴无影响，而朴素方法则表现出时间感知领先。我们开源了先验模型及初步零样本协议，应用于药代动力学和物理系统数据。
原文摘要 · Abstract (English)
Extending discrete-time causal Prior-data Fitted Networks for time series to continuous time invites writing the mechanism as a stochastic differential equation (SDE) -- but if the SDE is integrated \emph{once per observation gap}, the trajectory law depends on when it is observed, and the prior remains a discrete-time Markov model in SDE clothing. We propose a precise continuity criterion -- trajectory-law invariance to the observation schedule -- together with a three-tier taxonomy (discrete; naive observation-grid integration; fine-grid integration with decoupled observation) and a construction realising the top tier on a random DAG with OU or small-MLP nonlinear drifts, irregular observation schedules, and hard / soft / time-varying interventions. A $2 \times 2$ encoder $\times$ integrator ablation, run independently on a linear and a nonlinear prior, finds fine-grid integration beats naive on 8/8 cells (sign-consistency $p < 1/256$) with the gap growing as the eval grid refines; the encoder axis is null with fine integration but time-aware-leading with naive. We release the prior and a preliminary zero-shot protocol on pharmacokinetic and physical-system data.
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