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[2602.14997] Spectral Convolution on Orbifolds for Geometric Deep Learning
Summary
This paper introduces spectral convolution on orbifolds, expanding geometric deep learning (GDL) techniques to non-Euclidean data structures, with applications illustrated in music theory.
Why It Matters
The research addresses the growing need for machine learning methods that can handle complex data structures beyond traditional Euclidean spaces. By introducing spectral convolution on orbifolds, it opens new avenues for applying GDL in various fields, including music theory, enhancing the versatility of machine learning models.
Key Takeaways
- Spectral convolution can be adapted for orbifolds, enhancing GDL capabilities.
- The paper provides a theoretical framework for applying GDL to complex data structures.
- An example from music theory illustrates practical applications of the proposed methods.
- This research contributes to the understanding of non-Euclidean data in machine learning.
- The findings could influence future developments in geometric deep learning techniques.
Computer Science > Machine Learning arXiv:2602.14997 (cs) [Submitted on 16 Feb 2026] Title:Spectral Convolution on Orbifolds for Geometric Deep Learning Authors:Tim Mangliers, Bernhard Mössner, Benjamin Himpel View a PDF of the paper titled Spectral Convolution on Orbifolds for Geometric Deep Learning, by Tim Mangliers and 2 other authors View PDF HTML (experimental) Abstract:Geometric deep learning (GDL) deals with supervised learning on data domains that go beyond Euclidean structure, such as data with graph or manifold structure. Due to the demand that arises from application-related data, there is a need to identify further topological and geometric structures with which these use cases can be made accessible to machine learning. There are various techniques, such as spectral convolution, that form the basic building blocks for some convolutional neural network-like architectures on non-Euclidean data. In this paper, the concept of spectral convolution on orbifolds is introduced. This provides a building block for making learning on orbifold structured data accessible using GDL. The theory discussed is illustrated using an example from music theory. Comments: Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI) Cite as: arXiv:2602.14997 [cs.LG] (or arXiv:2602.14997v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2602.14997 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Benjamin Himpel [vie...