Spectral Discovery of Continuous Symmetries via Generalized Fourier Transforms
Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on learned augmentation schemes. We propose a fundamentally different perspective based on spectral structure. We introduce a framework for discovering continuous one-parameter subgroups using the Generalized Fourier Transform (GFT). Our central observation is that invariance to a subgroup induces structured sparsity in the spectral decomposition of a function across irreducible representations. Instead of optimizing over generators, we detect symmetries by ide...
| Authors | Pavan Karjol, Kumar Shubham, Prathosh AP |
|---|---|
| Primary category | cs.LG |
| Published | 7 March 2026 |
| Last updated at source | 7 March 2026 |
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