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.

本研究介绍了一种称为 Riemannian Score-based Generative Models （RSGMs）的生成模型，采用一种新的方法将 SGMs 扩展到黎曼流形，尤其在地球和气候科学球形数据方面进行了演示。

黎曼分数基生成建模

Riemannian Score-Based Generative Modelling

As an effective strategy, data augmentation (DA) alleviates data scarcity
scenarios where deep learning techniques may fail. It is widely applied in
computer vision then introduced to natural language processing and achieves
improvements in many tasks. One of the main focuses of the DA methods is to
improve the diversity of training data, thereby helping the model to better
generalize to unseen testing data. In this survey, we frame DA methods into
three categories based on the diversity of augmented data, including
paraphrasing, noising, and sampling. Our paper sets out to analyze DA methods
in detail according to the above categories. Further, we also introduce their
applications in NLP tasks as well as the challenges. Some helpful resources are
provided in the appendix.

本文综述了数据增强的三个类别：释义、加噪和采样，以及在 NLP 中的应用和挑战。