Recent approaches for arbitrary-scale single image super-resolution (ASSR) have used local neural fields to represent continuous signals that can be sampled at different rates. However, in such formulation, the point-wise query of field values does not naturally match the point spread function (PSF) of a given pixel. In this work we present a novel way to design neural fields such that points can be queried with a Gaussian PSF, which serves as anti-aliasing when moving across resolutions for ASSR. We achieve this using a novel activation function derived from Fourier theory and the heat equation. This comes at no additional cost: querying a point with a Gaussian PSF in our framework does not affect computational cost, unlike filtering in the image domain. Coupled with a hypernetwork, our method not only provides theoretically guaranteed anti-aliasing, but also sets a new bar for ASSR while also being more parameter-efficient than previous methods.

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