Drivers of high similarity scores and criteria for a “good” score

Determine the factors that drive high similarity scores and specify criteria for what constitutes a “good” similarity score when comparing model representations to neural data using measures such as Centered Kernel Alignment (CKA), angular Procrustes distance, Normalized Bures Similarity (NBS), and linear or ridge regression.

Background

Representational similarity measures are widely used to compare artificial models with neural data, yet the interpretation of their scores is ambiguous. The paper motivates this by noting uncertainty about both what drives high similarity scores and what thresholds should be considered good, then introduces a methodology to differentiate through these measures and empirically probe their behavior.

Clarifying the determinants of high scores and establishing interpretable criteria for score quality is essential for meaningful model–brain alignment claims, since different measures may emphasize different aspects of the data (e.g., high-variance principal components).

References

However, it is currently unclear what drives high similarity scores and even what constitutes a “good” score.

— Differentiable Optimization of Similarity Scores Between Models and Brains  (2407.07059 - Cloos et al., 2024) in Abstract

We observe an anomalous dip in CKA similarity for Flood-S1 at the 25\% and 50\% pretraining-data fractions (0.733 and 0.726, respectively, versus 0.807 at 10\% and 0.855 at 75\%). We do not have a confident explanation for this non-monotonicity and report it as an open observation rather than speculate on its cause.

— Data-Efficient ConvNeXt Pretraining for High-Resolution Sentinel-1 GRD SAR Representation Learning  (2610.21993 - Natsume et al., 15 Oct 2026) in Section 4.7, “Representation Analysis” (Section~\ref{sec:cka})