This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use cases that result in more efficient models for analyzing point clouds, graphs, and meshes. Moreover, I outline a vision for how topological concepts could be used in the future, comprising (1) the learning of functions on topological spaces, (2) the building of hybrid models that imbue neural networks with knowledge about the topological information in data, and (3) the analysis of qualitative properties of neural networks. With current research already addressing some of these aspects, this article thus serves as an introduction and invitation to this nascent area of research.

翻译：本文综述性文章阐述了拓扑学概念如何能够丰富机器学习研究。以几何拓扑不变量——欧拉特征变换（ECT）作为贯穿案例，本文展示了多个应用场景，这些场景为分析点云、图结构和网格数据提供了更高效的模型。此外，本文展望了拓扑概念在未来可能的发展方向，包括：（1）拓扑空间上函数的学习；（2）构建混合模型，使神经网络能够融合数据中的拓扑信息；（3）神经网络定性特性的分析。当前研究已涉及其中若干方面，因此本文旨在为这一新兴研究领域提供导引并发出研究邀约。