论文标题
基于持久的机器学习操作员
Persistence-based operators in machine learning
论文作者
论文摘要
人工神经网络可以学习复杂的，显着的数据功能，以实现给定的任务。在频谱的另一端，数学基础的方法（例如拓扑数据分析）使用户可以设计分析管道完全了解数据约束和对称性。我们介绍了一类基于持久性的神经网络层。基于持久性的层使用户可以轻松地注入有关数据尊重的对称性（模棱两可）的知识，配备了可学习的权重，并且可以由最新的神经体系结构组成。
Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries (equivariance) respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.
