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This article introduces torch-harmonics, a new library enabling differentiable machine learning on spherical domains through specialized transforms and attention mechanisms. By providing rotationally-aware building blocks like spherical transformers, it directly addresses the growing need for ML tools that respect topological constraints in fields ranging from cosmology to geophysics. The work represents a significant advancement in applying deep learning architectures to non-Euclidean data structures.
A library for differentiable signal processing and machine learning on the sphere
arXiv:2609.39737v1 Announce Type: new Abstract: The two-dimensional sphere embedded in three-dimensional Euclidean space S2, plays a central role in a variety of scientific and engineering domains, including geophysics, planetary science, geodesy, atmospheric physics, quantum chemistry, cosmology, and virtual reality, among many others. As machine learning increasingly permeates these fields, the demand grows for robust tools that process and model functions on the sphere, while respecting the inherent topological and symmetry properties of the domain. We present torch-harmonics, a comprehensive library that offers efficient, differentiable implementations of advanced signal processing and machine learning (ML) methods for spherical data. These include the spherical harmonic transform (SHT), the spherical analogue of the Fourier transform, vector spherical harmonics, discrete-continuous and spectral convolutions, as well as both global and neighborhood spherical attention mechanisms. Beyond traditional representations, torch-harmonics provides the building blocks for state-of-the-art spherical ML architectures such as spherical transformers in order to enable scalable, rotationally-aware learning and inference in modern scientific and engineering applications.
Abstract:The two-dimensional sphere embedded in three-dimensional Euclidean space S2, plays a central role in a variety of scientific and engineering domains, including geophysics, planetary science, geodesy, atmospheric physics, quantum chemistry, cosmology, and virtual reality, among many others. As machine learning increasingly permeates these fields, the demand grows for robust tools that process and model functions on the sphere, while respecting the inherent topological and symmetry properties of the domain. We present torch-harmonics, a comprehensive library that offers efficient, differentiable implementations of advanced signal processing and machine learning (ML) methods for spherical data. These include the spherical harmonic transform (SHT), the spherical analogue of the Fourier transform, vector spherical harmonics, discrete-continuous and spectral convolutions, as well as both global and neighborhood spherical attention mechanisms. Beyond traditional representations, torch-harmonics provides the building blocks for state-of-the-art spherical ML architectures such as spherical transformers in order to enable scalable, rotationally-aware learning and inference in modern scientific and engineering applications.
Machine Learning (cs.LG); Atmospheric and Oceanic Physics (physics.ao-ph); Geophysics (physics.geo-ph)
arXiv:2609.39737 [cs.LG]
(or arXiv:2609.39737v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.39737 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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