Normalizing Flows on Quotient Manifolds via Boundary Quotients
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916046046232576 |
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| author | Ghanem, William Cai, Benjamin |
| author_facet | Ghanem, William Cai, Benjamin |
| contents | We introduce boundary quotients and present a framework for learning densities on manifolds that arise as boundary quotients of simpler domains. We show that this framework can be used to construct normalizing flows on quotient manifolds $N/G$, where a discrete group $G$ acts on $N$. We instantiate this construction for genus-$g$ surfaces $Σ_g$. When $G$ is finite, we show applicability to symmetry aware learning; we demonstrate this on cyclic quotients of the 3-sphere. Experiments on lens spaces show that simple pre-quotient RealNVP models can achieve strong results while being substantially cheaper to evaluate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22882 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normalizing Flows on Quotient Manifolds via Boundary Quotients Ghanem, William Cai, Benjamin Machine Learning Probability We introduce boundary quotients and present a framework for learning densities on manifolds that arise as boundary quotients of simpler domains. We show that this framework can be used to construct normalizing flows on quotient manifolds $N/G$, where a discrete group $G$ acts on $N$. We instantiate this construction for genus-$g$ surfaces $Σ_g$. When $G$ is finite, we show applicability to symmetry aware learning; we demonstrate this on cyclic quotients of the 3-sphere. Experiments on lens spaces show that simple pre-quotient RealNVP models can achieve strong results while being substantially cheaper to evaluate. |
| title | Normalizing Flows on Quotient Manifolds via Boundary Quotients |
| topic | Machine Learning Probability |
| url | https://arxiv.org/abs/2511.22882 |