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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2510.04762 |
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| _version_ | 1866908577887682560 |
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| author | Glüsenkamp, Thorsten |
| author_facet | Glüsenkamp, Thorsten |
| contents | A generic D-dimensional Gaussian can be conditioned or projected onto the D-1 unit sphere, thereby leading to the well-known Fisher-Bingham (FB) or Angular Gaussian (AG) distribution families, respectively. These are some of the most fundamental distributions on the sphere, yet cannot straightforwardly be written as a normalizing flow except in two special cases: the von-Mises Fisher in D=3 and the central angular Gaussian in any D. In this paper, we describe how to generalize these special cases to a family of normalizing flows that behave similarly to the full FB or AG family in any D. We call them "zoom-linear-project" (ZLP)-Fisher flows. Unlike a normal Fisher-Bingham distribution, their composition allows to gradually add complexity as needed. Furthermore, they can naturally handle conditional density estimation with target distributions that vary by orders of magnitude in scale - a setting that is important in astronomical applications but that existing flows often struggle with. A particularly useful member of the new family is the Kent analogue that can cheaply upgrade any flow in this situation to yield better performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04762 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fisher-Bingham-like normalizing flows on the sphere Glüsenkamp, Thorsten Machine Learning Instrumentation and Methods for Astrophysics Artificial Intelligence A generic D-dimensional Gaussian can be conditioned or projected onto the D-1 unit sphere, thereby leading to the well-known Fisher-Bingham (FB) or Angular Gaussian (AG) distribution families, respectively. These are some of the most fundamental distributions on the sphere, yet cannot straightforwardly be written as a normalizing flow except in two special cases: the von-Mises Fisher in D=3 and the central angular Gaussian in any D. In this paper, we describe how to generalize these special cases to a family of normalizing flows that behave similarly to the full FB or AG family in any D. We call them "zoom-linear-project" (ZLP)-Fisher flows. Unlike a normal Fisher-Bingham distribution, their composition allows to gradually add complexity as needed. Furthermore, they can naturally handle conditional density estimation with target distributions that vary by orders of magnitude in scale - a setting that is important in astronomical applications but that existing flows often struggle with. A particularly useful member of the new family is the Kent analogue that can cheaply upgrade any flow in this situation to yield better performance. |
| title | Fisher-Bingham-like normalizing flows on the sphere |
| topic | Machine Learning Instrumentation and Methods for Astrophysics Artificial Intelligence |
| url | https://arxiv.org/abs/2510.04762 |