A library for differentiable signal processing and machine learning on the sphere
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.
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BibTeX
@misc{kurth2026library,
title = {{A library for differentiable signal processing and machine learning on the sphere}},
author = {Thorsten Kurth and Max Rietmann and Mauro Bisson and Andrea Paris and Alberto Carpentieri and Jean Kossaifi and Anima Anandkumar and Christian Hundt and Boris Bonev},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39737},
eprint = {2609.39737},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39737},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A library for differentiable signal processing and machine learning on the sphere
AU - Thorsten Kurth
AU - Max Rietmann
AU - Mauro Bisson
AU - Andrea Paris
AU - Alberto Carpentieri
AU - Jean Kossaifi
AU - Anima Anandkumar
AU - Christian Hundt
AU - Boris Bonev
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39737
UR - https://arxiv.org/abs/2609.39737
AB - 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.
ER -