Very glad of this new collaborative work "Herglotz-NET: Implicit Neural Representation of Spherical Data with Harmonic Positional Encoding" with ThΓ©o Hanon, Nicolas Mil-Homens Cavaco, John Kiely, Laurent Jacques https://arxiv.org/html/2502.13777v1
In this work, we propose Herglotz-NET (HNET), a novel INR architecture that employs a harmonic positional encoding based on complex Herglotz mappings. This encoding yields a well-posed representation on the sphere with interpretable and robust spectral properties. Moreover, we present a unified expressivity analysis showing that any spherical-based INR satisfying a mild condition exhibits a predictable spectral expansion that scales with network depth. Our results establish HNET as a scalable and flexible framework for accurate modeling of spherical data.
