A central question for neuroscience is how to characterize brain representations of perceptual and cognitive content. An ideal characterization should distinguish different functional regions with robustness to noise and idiosyncrasies of individual brains that do not correspond to computational differences. Previous studies have characterized brain representations by their representational geometry, which is defined by the representational dissimilarity matrix (RDM), a summary statistic that abstracts from the roles of individual neurons (or responses channels) and characterizes the discriminability of stimuli. Here we explore a further step of abstraction: from the geometry to the topology of brain representations. We propose topological representational similarity analysis (tRSA), an extension of representational similarity analysis (RSA) that uses a family of geo-topological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. We evaluate this new family of statistics in terms of the sensitivity and specificity for model selection using both simulations and functional MRI (fMRI) data. In the simulations, the ground truth is a data-generating layer representation in a neural network model and the models are the same and other layers in different model instances (trained from different random seeds). In fMRI, the ground truth is a visual area and the models are the same and other areas measured in different subjects. Results show that topology-sensitive characterizations of population codes are robust to noise and interindividual variability and maintain excellent sensitivity to the unique representational signatures of different neural network layers and brain regions.

翻译：神经科学的一个核心问题是如何刻画大脑对感知和认知内容的表征。理想的刻画应能区分不同功能区域，并对噪声及个体大脑中不代表计算差异的特异性具有鲁棒性。以往研究通过表征几何来刻画大脑表征，这由表征相异矩阵（RDM）定义，该汇总统计量抽象了单个神经元（或响应通道）的作用，并刻画了刺激的可区分性。在此，我们探索进一步抽象：从大脑表征的几何到拓扑。我们提出拓扑表征相似性分析（tRSA），这是表征相似性分析（RSA）的扩展，它使用一族几何拓扑汇总统计量，在弱化几何的同时，将RDM推广以刻画拓扑。我们通过模拟实验和功能磁共振成像（fMRI）数据，评估了这族新统计量在模型选择中的敏感性和特异性。在模拟中，真实情况是神经网络模型中的数据生成层表征，而模型是不同模型实例（通过不同随机种子训练）的同一层及其他层。在fMRI中，真实情况是一个视觉区域，而模型是不同受试者中测量的同一区域及其他区域。结果表明，对群体编码的拓扑敏感刻画对噪声和个体间变异性具有鲁棒性，并能出色地保持对不同神经网络层和脑区独特表征特征的敏感性。