This article provides a concise overview of some of the recent advances in the application of rough path theory to machine learning. Controlled differential equations (CDEs) are discussed as the key mathematical model to describe the interaction of a stream with a physical control system. A collection of iterated integrals known as the signature naturally arises in the description of the response produced by such interactions. The signature comes equipped with a variety of powerful properties rendering it an ideal feature map for streamed data. We summarise recent advances in the symbiosis between deep learning and CDEs, studying the link with RNNs and culminating with the Neural CDE model. We concluded with a discussion on signature kernel methods.

翻译：本文简要概述了粗糙路径理论在机器学习应用中的一些最新进展。讨论了受控微分方程（CDE）作为描述数据流与物理控制系统相互作用的关键数学模型。在描述此类相互作用产生的响应时，自然出现了一组被称为“签名”（signature）的迭代积分。签名具有多种强大性质，使其成为流数据的理想特征映射。我们总结了深度学习与CDE之间共生关系的最新进展，研究了其与RNN的联系，并最终以神经受控微分方程（Neural CDE）模型作为高潮。最后，我们讨论了签名核方法。