Title: Can Operator Learning Achieve Zero-Shot Super-Resolution?

Abstract: It is frequently observed that neural operators demonstrate zero-shot super-resolution capabilities, a trait where models trained on low-resolution grids maintain predictive accuracy on high-resolution test data without the need for further training. Although this behavior is well-supported by empirical results, its theoretical underpinnings have yet to be fully clarified. This study offers a rigorous theoretical analysis of zero-shot super-resolution within the context of operator learning. We initially demonstrate that, theoretically, zero-shot super-resolution may be information-theoretically unattainable, even in favorable scenarios where input functions are defined across the entire continuum and the ground truth consists of a straightforward rank-one linear operator. Subsequently, we establish that the Hölder smoothness of output functions serves as a sufficient condition for achieving zero-shot super-resolution, alongside deriving relevant generalization bounds. Lastly, our experimental findings corroborate these identified failure modes.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC