Similarity of Neural Network Representations Revisited

TL;DR

This paper revisits methods for comparing neural network representations, highlighting limitations of CCA and introducing CKA as a more reliable similarity measure that can compare representations across different initializations.

Contribution

The paper introduces the centered kernel alignment (CKA) as a new similarity measure that overcomes CCA's limitations and effectively compares neural network representations.

Findings

CKA is equivalent to a form of centered kernel alignment.

CKA can reliably identify correspondences between differently initialized networks.

CCA cannot measure meaningful similarities for high-dimensional representations.

Abstract

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.