Similarity of Neural Network Models: A Survey of Functional and Representational Measures

Measuring similarity of neural networks has become an issue of great importance and research interest to understand and utilize differences of neural networks. While there are several perspectives on how neural networks can be similar, we specifically focus on two complementing perspectives, i.e., (i) representational similarity, which considers how activations of intermediate neural layers differ, and (ii) functional similarity, which considers how models differ in their outputs. In this survey, we provide a comprehensive overview of these two families of similarity measures for neural network models. In addition to providing detailed descriptions of existing measures, we summarize and discuss results on the properties and relationships of these measures, and point to open research problems. Further, we provide practical recommendations that can guide researchers as well as practitioners in applying the measures. We hope our work lays a foundation for our community to engage in more systematic research on the properties, nature and applicability of similarity measures for neural network models.