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.

本研究解决了神经响应如何有效传达信息的理解问题，尤其是通过构建回归模型或解码器来重建刺激特征。我们提出，许多流行的相似性度量可以从解码的角度来解释，特别是中心核对齐（CKA）和典型相关分析（CCA）能够量化最优线性解码器之间的对齐度。这一发现为神经系统相似性的衡量提供了新的思路，并对现有度量的理解提供了统一的解释。

可解码信息的表示相似性度量的意义