Centred Kernel Alignment (CKA) has recently emerged as a popular metric to compare activations from biological and artificial neural networks (ANNs) in order to quantify the alignment between internal representations derived from stimuli sets (e.g. images, text, video) that are presented to both systems. In this paper we highlight issues that the community should take into account if using CKA as an alignment metric with neural data. Neural data are in the low-data high-dimensionality domain, which is one of the cases where (biased) CKA results in high similarity scores even for pairs of random matrices. Using fMRI and MEG data from the THINGS project, we show that if biased CKA is applied to representations of different sizes in the low-data high-dimensionality domain, they are not directly comparable due to biased CKA's sensitivity to differing feature-sample ratios and not stimuli-driven responses. This situation can arise both when comparing a pre-selected area of interest (e.g. ROI) to multiple ANN layers, as well as when determining to which ANN layer multiple regions of interest (ROIs) / sensor groups of different dimensionality are most similar. We show that biased CKA can be artificially driven to its maximum value when using independent random data of different sample-feature ratios. We further show that shuffling sample-feature pairs of real neural data does not drastically alter biased CKA similarity in comparison to unshuffled data, indicating an undesirable lack of sensitivity to stimuli-driven neural responses. Positive alignment of true stimuli-driven responses is only achieved by using debiased CKA. Lastly, we report findings that suggest biased CKA is sensitive to the inherent structure of neural data, only differing from shuffled data when debiased CKA detects stimuli-driven alignment.

翻译：中心核对齐（CKA）近期成为比较生物与人工神经网络（ANN）激活的流行指标，用于量化两种系统接收刺激集（如图像、文本、视频）后产生的内部表征之间的对齐程度。本文重点指出，若将CKA作为神经数据对齐度量使用时，学界应当注意若干问题。神经数据属于"低数据-高维度"范畴，在此类情形下，（有偏）CKA即使面对随机矩阵对也会产生高相似度评分。基于THINGS项目的fMRI与MEG数据，我们证明：当有偏CKA应用于低数据-高维度域中不同规模表征时，由于该度量对特征-样本比率差异（而非刺激驱动响应）敏感，这些表征将失去直接可比性。这种情形既可能出现在比较预设感兴趣区域（如ROI）与多个ANN层时，也可能出现在确定不同维度的多个感兴趣区域（ROI）/传感器组与哪个ANN层最相似时。我们证实，当使用不同样本-特征比率的独立随机数据时，有偏CKA可被人为推至最大值。进一步研究发现，将真实神经数据的样本-特征对打乱后，有偏CKA相似度与未打乱数据相比未发生显著变化，表明其对刺激驱动神经响应缺乏敏感性。只有采用无偏CKA才能获得真正的刺激驱动响应正对齐。最后，我们报告发现：有偏CKA对神经数据固有结构敏感，且仅在无偏CKA检测到刺激驱动对齐时才会表现出与打乱数据的差异。