Estimating Neural Representation Alignment from Sparsely Sampled Inputs and Features

Abstract: In both artificial and biological systems, the centered kernel alignment (CKA) has become a widely used tool for quantifying neural representation similarity. While current CKA estimators typically correct for the effects of finite stimuli sampling, the effects of sampling a subset of neurons are overlooked, introducing notable bias in standard experimental scenarios. Here, we provide a theoretical analysis showing how this bias is affected by the representation geometry. We then introduce a novel estimator that corrects for both input and feature sampling. We use our method for evaluating both brain-to-brain and model-to-brain alignments and show that it delivers reliable comparisons even with very sparsely sampled neurons. We perform within-animal and across-animal comparisons on electrophysiological data from visual cortical areas V1, V4, and IT data, and use these as benchmarks to evaluate model-to-brain alignment. We also apply our method to reveal how object representations become progressively disentangled across layers in both biological and artificial systems. These findings underscore the importance of correcting feature-sampling biases in CKA and demonstrate that our bias-corrected estimator provides a more faithful measure of representation alignment. The improved estimates increase our understanding of how neural activity is structured across both biological and artificial systems.