What Representational Similarity Measures Imply about Decodable Information

Constructing well-motivated methodologies for quantifying similarity between high-dimensional neural representations is an active research in computational neuroscience. Such similarity measures have implications for understanding variability in neural computations across individuals and species [1], as well as for comparisons between biological systems and computational models [2]. One common approach to understand these systems is to build regression models or “decoders” that reconstruct features of the stimulus from neural responses. Here, we leverage this idea to quantify the similarity of different neural systems. Our approach is distinct from typical motivations behind representational (dis)similarity measures like representational similarity analysis (RSA), centered kernel alignment (CKA), canonical correlation analysis (CCA), and Procrustes shape distance, which highlight geometric intuition and invariances to orthogonal or affine transformations. However, we show that CKA, CCA, and other measures can be equivalently motivated from similarity in decoding patterns. Specifically, these measures can be understood to 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 intrinsic dimensionality. Overall, our work demonstrates a tight link between the geometry of neural representations and the ability to linearly decode information, suggests new ways of measuring similarity between neural systems and provides novel, unifying interpretations of existing measures.