Subedi & Tewari Prove Zero-Shot Super-Resolution Is Not Guaranteed

A new paper by Unique Subedi and Ambuj Tewari (arXiv:2606.00296) tackles the theoretical foundations of zero-shot super-resolution in neural operators—a phenomenon where models trained on coarse grids accurately predict on finer grids without retraining. Despite strong empirical reports, the authors show that this capability is not universal. They prove that even in a benign setting where input functions are available over the entire continuum and the ground truth is a simple rank-one linear operator, zero-shot super-resolution is information-theoretically impossible. This result formally shatters the assumption that neural operators can always generalize across resolutions.

On the positive side, the researchers identify Hölder smoothness of the output functions as a sufficient condition for zero-shot super-resolution, and they derive corresponding generalization bounds that quantify when and how well it works. Experimental results validate the theoretical failure modes, showing that models fail exactly under conditions predicted by theory. This work provides crucial guardrails for practitioners relying on super-resolution capabilities in scientific machine learning (e.g., PDE surrogates, climate modeling) and highlights the need for careful validation rather than blind trust in empirical performance.