Summary
Estimating how changing one thing affects another is important in fields like medicine or economics. Some AI models try to learn this by practicing on many made-up examples but depend heavily on the starting assumptions they are given, called priors. The researchers show that using knowledge from large language models, which can suggest likely cause-and-effect diagrams, helps improve these AI estimates in a reliable way. They designed a method to pick the best prior automatically instead of guessing, leading to much better performance and clearer reasons why it helps. This approach turns an uncertain trial-and-error process into a dependable selection method.
causal effect estimationinterventionprior-data fitted networkssynthetic causal taskspriorslarge language modelscausal graphsamortized inferenceclosed-loop selectiongeneralization
Abstract
Causal effect estimation asks how an outcome would change under an intervention, and medicine, economics, and public policy all treat it as a foundational task. Prior-data fitted networks (PFNs) amortize the task: a model trained on large numbers of programmatically generated synthetic causal tasks reads a new problem's observational data into context and returns an interventional-effect estimate in a single forward pass. The capability of such models is largely determined by the synthetic training prior, which is currently designed by hand, a bottleneck acknowledged by both Do-PFN and CausalPFN. Large language models (LLMs) can now ``draw'' plausible causal graphs for a given domain, suggesting that LLM-distilled graphs could serve as prior material. Whether injecting such graphs helps at all, where any gain comes from, and when injection helps. Practice has so far relied on manual trial and error. We propose a \emph{closed-loop prior selection framework} that casts prior injection as a budget-constrained optimization over a candidate prior pool. Candidates undergo cheap post-training and are scored by a composite metric dominated by real-domain generalization; the winner then receives full training and paired statistical validation. On a 7.34M-parameter Do-PFN, the framework's winner attains a formally significant $2.75\times$ gain on the primary evaluation domain, and its error falls below that of the uninjected official base. Generalization on an adjacent monitoring domain improves significantly, and no monitored capability degrades. Mechanism experiments show that the gain depends on the semantic content of the distilled graph rather than its structural diversity alone does not produce it (directional evidence). With this framework and this regularity in hand, the use of LLM causal priors stops being manual trial and error and becomes an empirically verifiable selection problem.