{"ID":2835337,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.22882","arxiv_id":"2511.22882","title":"Normalizing Flows on Quotient Manifolds via Boundary Quotients","abstract":"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.","short_abstract":"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 fo...","url_abs":"https://arxiv.org/abs/2511.22882","url_pdf":"https://arxiv.org/pdf/2511.22882v3","authors":"[\"William Ghanem\",\"Benjamin Cai\"]","published":"2025-11-28T05:12:27Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.PR\"]","methods":"[]","has_code":false}