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arXiv 2202.02763cs.LGmath.PRstat.ML
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基于黎曼分数的生成式建模

Riemannian Score-Based Generative Modelling

ENS(巴黎高等师范学院);CNRS(法国国家科学研究中心);PSL University(巴黎文理研究大学);University of Oxford(牛津大学)

Valentin De Bortoli, Emile Mathieu, Michael Hutchinson, James Thornton, Yee Whye Teh, Arnaud Doucet

摘要:

基于得分的生成模型(SGM)是一类功能强大的生成模型,具有显著的经验性能。基于分数的生成建模(SGM)包括一个“噪声”阶段,其中扩散被用来逐渐添加高斯噪声到数据中,以及一个生成模型,它需要一个“去噪”过程,通过近似扩散的时间反演来定义。现有的SGM假设数据支持在欧几里得空间上,即具有平坦几何形状的流形。在许多领域,如机器人,地球科学或蛋白质建模,数据往往是自然描述的分布生活在黎曼流形和目前的SGM技术是不合适的。我们在这里介绍黎曼基于得分的生成模型(RSGMs),一类生成模型扩展SGMs到黎曼流形。我们展示了我们的方法在各种流形上,特别是地球和气候科学球形数据。

英文摘要:

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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