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Poster
Grounding Representation Similarity Through Statistical Testing
Frances Ding · Jean-Stanislas Denain · Jacob Steinhardt

Thu Dec 09 04:30 PM -- 06:00 PM (PST) @
in Poster Session 7 »

To understand neural network behavior, recent works quantitatively compare different networks' learned representations using canonical correlation analysis (CCA), centered kernel alignment (CKA), and other dissimilarity measures. Unfortunately, these widely used measures often disagree on fundamental observations, such as whether deep networks differing only in random initialization learn similar representations. These disagreements raise the question: which, if any, of these dissimilarity measures should we believe? We provide a framework to ground this question through a concrete test: measures should have \emph{sensitivity} to changes that affect functional behavior, and \emph{specificity} against changes that do not. We quantify this through a variety of functional behaviors including probing accuracy and robustness to distribution shift, and examine changes such as varying random initialization and deleting principal components. We find that current metrics exhibit different weaknesses, note that a classical baseline performs surprisingly well, and highlight settings where all metrics appear to fail, thus providing a challenge set for further improvement.

Keywords: Deep Learning · Robustness · Representation Learning

Author Information

Frances Ding (University of California Berkeley)
Jean-Stanislas Denain (University of California Berkeley)
Jacob Steinhardt (UC Berkeley)

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