Rethinking Causal Prior-Fitted Networks under Unobserved Confounding: Identifiability and Randomized Evidence

Prior-Fitted Networks (PFNs) amortize the cost of causal effect estimation across tasks, enabling one-pass in-context prediction on new datasets without task-specific optimization. Yet efficient amortized inference does not by itself ensure causal identifiability: accurate effect estimation also depends on whether the observed context contains sufficient information to determine the causal target. Existing identifiability guarantees for causal PFNs rely on unconfounded settings such as strong ignorability, leaving what can be identified from PFN contexts unresolved under unobserved confounding, where the same context distribution may be compatible with different causal effects. We formalize this through context identifiability: when all compatible mechanisms agree on the target effect, ideal posterior inference recovers it asymptotically; otherwise, an irreducible bias remains that cannot in general be eliminated by more data or more accurate approximation. This framework further shows that broader causal priors can preserve ambiguity and that instrumental-variable identification still depends on additional structural assumptions. We therefore consider limited randomized evidence alongside confounded observational data and show that retaining source labels can restore identification of the target effect. Guided by this result, we propose Randomization-Aware PFN (RA-PFN), which adapts a pretrained causal PFN through mixed-source prior fitting, source embeddings, and randomization-aware attention while preserving one-pass inference. Across three public benchmarks, RA-PFN achieves the lowest causal effect estimation errors under unobserved confounding with limited randomized evidence, while retaining the inference-efficiency advantage of PFN-based estimation without downstream fitting.