This paper contributes to the challenge of learning a function on streamed multimodal data through evaluation. The core of the result of our paper is the combination of two quite different approaches to this problem. One comes from the mathematically principled technology of signatures and log-signatures as representations for streamed data, while the other draws on the techniques of recurrent neural networks (RNN). The ability of the former to manage high sample rate streams and the latter to manage large scale nonlinear interactions allows hybrid algorithms that are easy to code, quicker to train, and of lower complexity for a given accuracy. We illustrate the approach by approximating the unknown functional as a controlled differential equation. Linear functionals on solutions of controlled differential equations are the natural universal class of functions on data streams. They are mathematically very explicit and interpretable, allow quantitative arguments, and yet are able to approximate any continuous function on streams arbitrarily well. They form the basis of rough path theory. Stochastic differential equations are examples of controlled differential equations where the controlling stream is a stochastic process. Following this approach, we give a hybrid Logsig-RNN algorithm that learns functionals on streamed data with outstanding performance.

本研究提出了一种结合基于signature和log-signature的方法和循环神经网络的混合算法来学习流数据的功能逼近，其具有渐进复杂度低、训练速度快、精度高等优点，并在各数据集上得到了出色的准确性和鲁棒性。

使用具有log signature功能的RNN学习随机微分方程