Comparing Neural Network Representations with Bayesian Prior Predictive Distributions

How best to compare internal representations of neural networks remains a highly relevant unresolved question in both machine learning and neuroscience, even though numerous similarity measures have been proposed. Here, we propose and extensively evaluate a new measure based on a Bayesian perspective on linear readouts called BayesCompare. BayesCompare compares the prior predictive distributions of linear readouts from the representations using metrics or divergences for probability distributions. We evaluate BayesCompare with a suite of experiments using 6 popular architectures trained on ImageNet-1k, comparing BayesCompare against a wide range of existing methods, including Representational Similarity Analysis (RSA) and Centered Kernel Alignment (CKA). First, we quantify each method's ability to retrieve the corresponding layer from 5 instances of the same architecture. All methods are able to retrieve layers to some extent, but some metrics within BayesCompare improve layer retrieval over existing methods. Second, we confirm that BayesCompare preserves the gradual change between representations throughout the network resulting from incremental operations of layers, to a similar extent as the existing methods. Third, we measure the methods' consistency under different random image sets and set sizes. All BayesCompare metrics provide highly reliable results even with only 50 input images, whereas RSA shows the lowest consistency. We also analyze the effects of rank transformation and assess the agreement between all metrics. BayesCompare metrics are closely aligned with each other, but distinct from existing methods, suggesting that BayesCompare captures a different aspect of representational similarity. Overall, these results establish BayesCompare as an effective way of measuring representational similarity while being easy and fast to compute and give strong guidance on which variants one should use. We provide a Python package to apply BayesCompare.