提出新型球面归一化流，可灵活建模复杂球面分布。
Fisher-Bingham-like normalizing flows on the sphere
- 基于缩放-线性-投影机制构建球面流，扩展经典分布到任意维度
- 支持渐进式增加复杂度，能处理量级差异大的条件密度估计
- 适用于天体物理等高动态范围场景，尤其适合升级现有模型
D维高斯分布可通过条件化或投影转化为D-1维单位球上的分布，形成经典的Fisher-Bingham（FB）或角高斯（AG）分布族。这些是球面上最基本的分布，但除两个特例外——三维空间中的von-Mises-Fisher分布和任意维的中心角高斯分布——通常无法直接表示为归一化流。本文提出一种通用方法，将这两个特例推广为一类在任意维度下行为类似全量FB或AG分布的归一化流，称为“缩放-线性-投影”（ZLP）-Fisher流。该结构允许按需逐步增加复杂度，且能自然处理目标分布量级相差悬殊的条件密度估计问题，这在天体应用中至关重要。新族中一个特别有用的成员是肯特（Kent）类近似，可低成本提升此类场景下的模型性能。
原文摘要 · Abstract (English)
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.
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