Similarity of Neural Network Representations Revisited

Simon Kornblith, Mohammad Norouzi, Honglak Lee, Geoffrey Hinton
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:3519-3529, 2019.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-kornblith19a, title = {Similarity of Neural Network Representations Revisited}, author = {Kornblith, Simon and Norouzi, Mohammad and Lee, Honglak and Hinton, Geoffrey}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {3519--3529}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/kornblith19a/kornblith19a.pdf}, url = {https://proceedings.mlr.press/v97/kornblith19a.html}, 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.} }
Endnote
%0 Conference Paper %T Similarity of Neural Network Representations Revisited %A Simon Kornblith %A Mohammad Norouzi %A Honglak Lee %A Geoffrey Hinton %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-kornblith19a %I PMLR %P 3519--3529 %U https://proceedings.mlr.press/v97/kornblith19a.html %V 97 %X 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.
APA
Kornblith, S., Norouzi, M., Lee, H. & Hinton, G.. (2019). Similarity of Neural Network Representations Revisited. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:3519-3529 Available from https://proceedings.mlr.press/v97/kornblith19a.html.

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