Papers › Similarity of Neural Network Representations Revisited

Similarity of Neural Network Representations Revisited

1 May 2019ICML 2019 2019 5arXiv:1905.00414archive 2025-07-28

Simon Kornblith, Mohammad Norouzi, Honglak Lee, Geoffrey Hinton

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.

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Syntology Ran 25 of 28 code samples harvested from 9 repositories linked to this paper; 3 have no recorded run. Of those that ran: 9 ran · honoured contract; 5 ran · our draft was wrong; 9 ran · fixture could not drive it; 2 ran with no contract checked.

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IBM/NeuronAlignment mentioned on GitHubpytorch report
benjamin-mlr/first-align-then-predict mentioned on GitHubpytorch report
jayroxis/CKA-similarity mentioned on GitHubpytorch report
kexueyi/discover_infant_vis mentioned on GitHubpytorch report
ristoale97/centered-kernel-alignment mentioned on GitHubpytorch report
pwc-1/Paper-9 mindspore report

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CKA jayroxis/CKA-similarity/CKA.py community (archive-listed) ran no licence file found · pointer only · d871d94be50b9e08 · report
CKA lemonadec/Relevance-between-Accuracy-under-Black-box-Attack-and-the-Similarity-between-Networks/similarity.py community (archive-listed) ran · our draft was wrong fingerprinted no licence file found · pointer only · ee46af7585e6a68f · report
ModelInfo ristoale97/centered-kernel-alignment/ckatorch/cka.py community (archive-listed) ran · metamorphic tier: deterministic MIT (permissive) · 1926e59186ecc073 · report
centering yl2488/CKA-Centered-Kernel-Alignment/CKA.py community (archive-listed) ran · honoured contract fingerprinted MIT (permissive) · 5c273c526536356d · report
cka_batch ristoale97/centered-kernel-alignment/ckatorch/cka.py community (archive-listed) ran · fixture could not drive it fingerprinted MIT (permissive) · 7dc891b50b8982a5 · report
compute_CKA_similarity kexueyi/discover_infant_vis/src/utils/cka_utils.py community (archive-listed) ran · honoured contract fingerprinted no licence file found · pointer only · 377bcf14c19d449e · report
compute_ccas yl2488/CKA-Centered-Kernel-Alignment/cca_core.py community (archive-listed) ran · fixture could not drive it fingerprinted MIT (permissive) · 01472465bed8b268 · report
compute_ccas uchicago-sandlab/robust_representation_similarity/similarity_metrics/cca_core.py community (archive-listed) ran · fixture could not drive it fingerprinted no licence file found · pointer only · 9e9090cf436b48e6 · report
compute_corr IBM/NeuronAlignment/utils/crosscorrelation.py community (archive-listed) ran · our draft was wrong Apache-2.0 (permissive) · 9737d6197d04f626 · report
create_zero_dict uchicago-sandlab/robust_representation_similarity/similarity_metrics/cca_core.py community (archive-listed) ran · our draft was wrong fingerprinted no licence file found · pointer only · 290ba45d53d47533 · report
get_activations IBM/NeuronAlignment/utils/crosscorrelation.py community (archive-listed) ran · our draft was wrong Apache-2.0 (permissive) · ca7973c5cf3fa73e · report
get_zscore IBM/NeuronAlignment/utils/crosscorrelation.py community (archive-listed) ran · our draft was wrong Apache-2.0 (permissive) · d49541af704a1ba1 · report
hsic1 ristoale97/centered-kernel-alignment/ckatorch/cka.py community (archive-listed) ran · fixture could not drive it fingerprinted MIT (permissive) · 9b1aad174038093c · report
kernel_CKA yuanli2333/CKA-Centered-Kernel-Alignment/CKA.py community (archive-listed) ran · honoured contract fingerprinted MIT (permissive) · 395716aee7f73b45 · report
kernel_HSIC yl2488/CKA-Centered-Kernel-Alignment/CKA.py community (archive-listed) ran · honoured contract fingerprinted MIT (permissive) · c633017bfba675e4 · report
linear_CKA benjamin-mlr/first-align-then-predict/hidden_similarity/cka.py community (archive-listed) ran · honoured contract fingerprinted no licence file found · pointer only · 98db9cd60f9666cc · report
linear_HSIC benjamin-mlr/first-align-then-predict/hidden_similarity/cka.py community (archive-listed) ran · honoured contract fingerprinted no licence file found · pointer only · 9bcdcb150b92d09a · report
positivedef_matrix_sqrt yl2488/CKA-Centered-Kernel-Alignment/cca_core.py community (archive-listed) ran · honoured contract fingerprinted MIT (permissive) · ea98389a1755bb3f · report
positivedef_matrix_sqrt uchicago-sandlab/robust_representation_similarity/similarity_metrics/cca_core.py community (archive-listed) ran · honoured contract fingerprinted no licence file found · pointer only · 3bd8381fd601f386 · report
rbf yl2488/CKA-Centered-Kernel-Alignment/CKA.py community (archive-listed) ran · honoured contract fingerprinted MIT (permissive) · 0f137cab706f1953 · report
remove_small yl2488/CKA-Centered-Kernel-Alignment/cca_core.py community (archive-listed) ran · fixture could not drive it MIT (permissive) · ffcbd13c7094948e · report
remove_small uchicago-sandlab/robust_representation_similarity/similarity_metrics/cca_core.py community (archive-listed) ran · fixture could not drive it no licence file found · pointer only · f6ad5c8be57f992d · report
sum_threshold uchicago-sandlab/robust_representation_similarity/similarity_metrics/cca_core.py community (archive-listed) ran · fixture could not drive it fingerprinted no licence file found · pointer only · 1d8a61b6c896525a · report
CKA ristoale97/centered-kernel-alignment/ckatorch/cka.py community (archive-listed) unverified MIT (permissive) · a86b6c3e6909ec10 · report
get_cca_similarity uchicago-sandlab/robust_representation_similarity/similarity_metrics/cca_core.py community (archive-listed) unverified no licence file found · pointer only · fbc3e2408fc37570 · report
plot_cka ristoale97/centered-kernel-alignment/ckatorch/cka.py community (archive-listed) unverified MIT (permissive) · 3f6aa279cc980040 · report
center_gram identical code first harvested elsewhere ran · fixture could not drive it fingerprinted licence of this copy not recorded · 7a3daac7c3a534a6 · report
cka identical code first harvested elsewhere ran · fixture could not drive it licence of this copy not recorded · e9f80de46ff7dcd7 · report

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