Normalizing Flows on Tori and Spheres
Normalizing Flows on Tori and Spheres
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发表时间：
2020-02
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通讯作者：
Danilo Jimenez Rezende;G. Papamakarios;S. Racanière;M. S. Albergo;G. Kanwar;P. Shanahan;Kyle Cranmer
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作者：
Danilo Jimenez Rezende;G. Papamakarios;S. Racanière;M. S. Albergo;G. Kanwar;P. Shanahan;Kyle Cranmer
归一化流是在高维空间中构建表达性分布的一种强大工具。到目前为止，大部分文献都集中在欧几里得空间上学习流。然而，一些问题，比如涉及角度的问题，是在具有更复杂几何结构的空间（如环面或球面）上定义的。在本文中，我们提出并比较了在这类空间上具有表达性且数值稳定的流。我们的流是根据空间的维度递归构建的，从圆、闭区间或球面上的流开始。
Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles, are defined on spaces with more complex geometries, such as tori or spheres. In this paper, we propose and compare expressive and numerically stable flows on such spaces. Our flows are built recursively on the dimension of the space, starting from flows on circles, closed intervals or spheres.