Deconfounded Representation Similarity for Comparison of Neural Networks

Tianyu Cui, Yogesh Kumar, Pekka Marttinen, Samuel Kaski

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Similarity metrics such as representational similarity analysis (RSA) and centered kernel alignment (CKA) have been used to understand neural networks by comparing their layer-wise representations. However, these metrics are confounded by the population structure of data items in the input space, leading to inconsistent conclusions about the \emph{functional} similarity between neural networks, such as spuriously high similarity of completely random neural networks and inconsistent domain relations in transfer learning. We introduce a simple and generally applicable fix to adjust for the confounder with covariate adjustment regression, which improves the ability of CKA and RSA to reveal functional similarity and also retains the intuitive invariance properties of the original similarity measures. We show that deconfounding the similarity metrics increases the resolution of detecting functionally similar neural networks across domains. Moreover, in real-world applications, deconfounding improves the consistency between CKA and domain similarity in transfer learning, and increases the correlation between CKA and model out-of-distribution accuracy similarity.
Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 35 (NeurIPS 2022)
PublisherMorgan Kaufmann Publishers
Number of pages14
ISBN (Print)9781713871088
Publication statusPublished - 31 Oct 2022
EventConference on Neural Information Processing Systems -
Duration: 28 Nov 20229 Dec 2022


ConferenceConference on Neural Information Processing Systems


  • Deep Neural Networks
  • representation similarity
  • functional similarity
  • covariate adjustment regression

Research Beacons, Institutes and Platforms

  • Institute for Data Science and AI
  • Digital Futures
  • Sustainable Futures


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