Towards Continuous-time Causal Foundation Models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913168592207872 |
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| author | Thumm, Dennis Wiedemann, Ruben Chen, Ying |
| author_facet | Thumm, Dennis Wiedemann, Ruben Chen, Ying |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28880 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards Continuous-time Causal Foundation Models Thumm, Dennis Wiedemann, Ruben Chen, Ying Machine Learning Data Analysis, Statistics and Probability Methodology 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. |
| title | Towards Continuous-time Causal Foundation Models |
| topic | Machine Learning Data Analysis, Statistics and Probability Methodology |
| url | https://arxiv.org/abs/2605.28880 |