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。理想的刻画方式应能以对噪声的鲁棒性，以及对个体大脑中与计算差异无关的特异性，来区分不同功能区域。以往研究通过表征几何来刻画大脑表征，该几何由表征相异矩阵（RDM）定义，这是一种从单个神经元（或响应通道）的作用中抽象出来的汇总统计量，用于表征刺激的可分辨性。在此，我们探索了进一步抽象：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，将RDM泛化以在弱化几何的同时表征拓扑。我们通过模拟实验和功能性磁共振成像（fMRI）数据，评估了这一新统计量族在模型选择中的敏感性和特异性。在模拟实验中，真实数据来源于神经网络模型中的某一数据生成层表征，而模型则是不同模型实例（从不同随机种子训练获得）中的同一层和其他层。在fMRI中，真实数据来源于某一视觉区域，而模型则是不同受试者中测得的同一区域和其他区域。结果表明，对种群编码的拓扑敏感性刻画，能够稳健应对噪声和个体间变异性，同时保持对不同神经网络层和脑区独特表征特征的优秀敏感性。