Grounding Representation Similarity with Statistical Testing
This work addresses a foundational issue for researchers in interpretability and representation learning, though it is incremental in refining evaluation methods.
The paper tackles the problem of disagreement among representation similarity measures in neural networks by proposing a framework to evaluate them based on sensitivity to functional changes and specificity against irrelevant ones, finding that current metrics have weaknesses and a classical baseline performs well.
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 sensitivity to changes that affect functional behavior, and 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.