Similarity of Neural Network Representations Revisited


Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical correlation analysis (CCA). We show that CCA belongs to a family of statistics for measuring multivariate similarity, but that neither CCA nor any other statistic that is invariant to invertible linear transformation can measure meaningful similarities between representations of higher dimension than the number of data points. We introduce a similarity index that measures the relationship between representational similarity matrices and does not suffer from this limitation. This similarity index is equivalent to centered kernel alignment (CKA) and is also closely connected to CCA. Unlike CCA, CKA can reliably identify correspondences between representations in networks trained from different initializations.

Jan 14, 2020 12:00 PM
Iman Mirzadeh
Iman Mirzadeh
Graduate Alumni

Iman Mirzadeh, PhD, Computer Science (Artificial Intelligence), Washington State University (2018-2022)