Amortized Survival Distribution Estimation via In-Context Learning

Survival analysis models time-to-event (TTE) outcomes in the presence of *censoring*. Most survival models require dataset-specific fitting, whereas prior-fitted networks (PFNs) enable in-context prediction on new datasets without gradient-based adaptation. However, existing survival PFNs provide limited theoretical guidance for the design of their pretraining objective, *context-size* distribution, and synthetic *prior*. We introduce TTE-PFN, an amortized in-context estimator that maps a labeled *right-censored context* and unlabeled *query* covariates to predictive *event-* and *censoring-time distributions* in a single forward pass. TTE-PFN combines *oracle-distillation* supervision from *analytic* conditional distributions, randomized *context sizes*, and a diverse *prior* over survival data-generating processes. We first show that the *oracle-distillation* and matched *sampled-label* objectives share the same *posterior*-predictive population minimizer, but the latter incurs additional positive-semidefinite gradient covariance, which *oracle distillation* removes to facilitate faster and more stable optimization. We further establish *posterior*-predictive optimality across all represented *context sizes* and derive an excess-risk bound decomposing predictive error into *amortization*, *prior coverage*, and *posterior concentration*. Across 115 survival datasets and seven metrics that span *predictive accuracy*, *concordance*, and *calibration*, TTE-PFN achieves the best aggregate rank against 28 competing methods and ranks first on the *predictive accuracy* metrics. TTE-PFN also has the lowest runtime in our evaluation protocol, requiring only $0.052$ seconds to predict $1,000$ individuals.