Papers › Similarity of Neural Network Representations Revisited
Similarity of Neural Network Representations Revisited
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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Code
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.
By repository: community (archive-listed): 26 samples from 9 repositories, 23 ran; 2 identical to code first harvested elsewhere. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.
14 repositories listed; official and paper-mentioned ones first.
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28 samples harvested; 25 ran; 9 honoured the contract we drafted; 3 have no recorded run. Read from Syntology's graph 2026-09-25; that is when this build read the record, not when the samples ran.
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Harvested from 9 repositories linked to this paper, official or community; each sample names its own and says which. Some samples are identical code Syntology first harvested from another repository; for those, this paper's copy is not located and its licence is not recorded. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.
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