In-Context Full Conformal Prediction: Validity and Efficiency

In-context learning enables pretrained models to adapt to new tasks without parameter updates, but rigorous uncertainty quantification for in-context predictions remains poorly understood. Conformal prediction provides finite-sample distribution-free coverage, yet full conformal prediction can be computationally expensive because it may require candidate-dependent model refitting. We develop an in-context full conformal procedure that replaces these refitting steps with forward evaluations of a fixed pretrained predictor. Under exchangeability and a natural context-order invariance condition, we establish finite-sample marginal coverage. We further characterize the statistical efficiency of the resulting prediction sets, showing that it depends jointly on prediction risk and prompt stability. As a concrete nonparametric instantiation, we show that standard softmax Transformers can approximate Gaussian local polynomial regression and achieve the minimax-optimal prediction rate over Hölder classes. Empirically, we show that replacing candidate-wise refitting with forward evaluations of a frozen in-context predictor substantially reduces online computation while maintaining comparable empirical coverage and set length. Together, these results establish in-context learning as a computationally efficient approach to full conformal prediction with pretrained predictors.