Similarity of Neural Network Representations Revisited
This work addresses a fundamental issue in neural network interpretability for researchers, providing a more robust tool for analyzing model similarities, though it is incremental as it builds on prior representation comparison methods.
The paper tackled the problem of comparing neural network representations by showing that existing methods like CCA fail under high-dimensional data, and introduced a new similarity index (CKA) that reliably identifies correspondences between networks trained from different initializations.
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.