Grounding High Dimensional Representation Similarity by Comparing Decodability and Network Performance

To understand and interpret neural networks, representation similarity metrics have been used to compare learned representations between and across networks. Recent experiments have compared these similarity metrics to find the best performing and the most robust metrics, noting that classic baselines perform surprisingly well. These experiments are mostly constrained to studying relatively low-dimensional representations because of the computational cost of prominent representation similarity metrics. We extend previous work to test representation similarity metrics on larger convolutional networks processing larger images. In order to make this work possible, we employ reformulated representation similarity metrics for use on very high-dimensional representations. Using these reformulated similarity metrics, we test how well each metric captures changes to representations induced by ablations in two popular convolutional networks. In order to ground the effects of changes to representations in function, we use linear decoding probes and network performance measures. These measures of function allow us to test how well similarity metrics capture changes in decodable information versus changes in network performance. Linear decoding methods index available information in the representation, while network performance measures index the information used by the network. We show that all the tested representation similarity metrics significantly predict changes in network function and decodability. Within these metrics, on average, Procrustes and CKA outperform regularized CCA-based methods. All metrics predict decodability changes significantly better than they do network function. Procrustes and CKA do not outperform regularized CCA-based metrics for all network and functionality measure combinations. We add to the growing literature on representational similarity metrics to facilitate the improvement of current metrics for network interpretability.