Characterizing the structural properties of neural networks is crucial yet poorly understood, and there are no well-established similarity measures between networks. In this work, we observe that neural networks can be represented as abstract simplicial complex and analyzed using their topological 'fingerprints' via Persistent Homology (PH). We then describe a PH-based representation proposed for characterizing and measuring similarity of neural networks. We empirically show the effectiveness of this representation as a descriptor of different architectures in several datasets. This approach based on Topological Data Analysis is a step towards better understanding neural networks and serves as a useful similarity measure.
翻译:确定神经网络的结构特性至关重要,但人们对此了解甚少,而且各网络之间没有既定的类似措施。在这项工作中,我们发现神经网络可以作为抽象的简易综合体来代表,并通过持久性同理学(PH)用它们的地形“指印”进行分析。我们然后描述了为确定和衡量神经网络的相似性而提出的以PH为基础的代表。我们从经验上表明了这种代表作为若干数据集中不同结构的描述符的有效性。基于地形数据分析的这一方法是更好地了解神经网络的一个步骤,也是有用的类似性衡量标准。