What Representational Similarity Measures Imply about Decodable Information
This work provides a unifying interpretation for researchers in neuroscience and machine learning, though it is incremental as it reframes existing measures rather than introducing new ones.
The paper tackles the problem of interpreting neural representational similarity measures by showing that measures like CKA and CCA can be equivalently motivated from a decoding perspective, quantifying the alignment between optimal linear readouts across tasks, and demonstrates a tight link between representation geometry and linear decodability.
Neural responses encode information that is useful for a variety of downstream tasks. A common approach to understand these systems is to build regression models or ``decoders'' that reconstruct features of the stimulus from neural responses. Popular neural network similarity measures like centered kernel alignment (CKA), canonical correlation analysis (CCA), and Procrustes shape distance, do not explicitly leverage this perspective and instead highlight geometric invariances to orthogonal or affine transformations when comparing representations. Here, we show that many of these measures can, in fact, be equivalently motivated from a decoding perspective. Specifically, measures like CKA and CCA quantify the average alignment between optimal linear readouts across a distribution of decoding tasks. We also show that the Procrustes shape distance upper bounds the distance between optimal linear readouts and that the converse holds for representations with low participation ratio. Overall, our work demonstrates a tight link between the geometry of neural representations and the ability to linearly decode information. This perspective suggests new ways of measuring similarity between neural systems and also provides novel, unifying interpretations of existing measures.