Inducing Fourier Geometry: A Smoothness Prior Imposes Approximate Translation Equivariance in Multimodal Stellar Embeddings
Learned representations often contain geometric structure induced by symmetries in the underlying data. We ask whether a known continuous parameter space can instead be used to \emph{induce} such structure when the corresponding symmetry is only approximate. We introduce a graph-Laplacian smoothness prior that encourages representations to vary smoothly over a physical parameter space without specifying a representation geometry; in the continuum limit it selects Laplacian eigenfunctions and therefore predicts the Fourier-like geometry associated with translation symmetry. On multimodal stellar representations spanning six astronomical surveys, the prior induces Toeplitz Gram structure an...
| Authors | Ilay Kamai, Alex M. Bronstein, Hagai B. Perets |
|---|---|
| Primary category | cs.LG |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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