Curves in Context: Zero-Shot Regression of Functional Data

Scalar-on-function prediction—mapping an observed curve to a scalar response— is a central task of functional data analysis (FDA). Practice remains dominated by dataset-specific pipelines whose ingredients (basis, smoothing, model family, hyperparameters) must be reselected for every new problem and are tied to a fixed observation grid. We introduce FunPFN, a foundation model for scalar-on-function regression. FunPFN is pretrained once, purely on synthetic episodes drawn from a generative prior over functional tasks, and then predicts on a new dataset in a single forward pass: the training set is supplied as an in-context support set and the model returns a Gaussian predictive distribution for every query curve, with no gradient updates and no hyperparameter tuning. Its encoder combines a Fourier neural operator (FNO) trunk and a support-standardized spectral readout, making predictions discretization-invariant by construction. Across ten simulation scenarios, FunPFN achieves the best average rank among fourteen methods (1.7), significantly ahead of all twelve tuned baselines (Friedman test, Holm post-hoc); the runner-up, TabPFN applied to the discretized curves (4.7), is not separated by this test, yet its normalized excess risk is 1.5 to 4.6 times that of FunPFN in every scenario. On twelve real benchmark tasks, FunPFN ranks second overall while operating over 200 times faster than TabPFN (0.025s vs. 5.983s).