The topology and geometry of neural representations

拓扑(电路) 计算机科学 代表(政治) 相似性(几何) 稳健性(进化) 人口 人工智能 人工神经网络 模式识别(心理学) 数学 图像(数学) 社会学 人口学 组合数学 基因 政治 化学 法学 生物化学 政治学
作者
Baihan Lin,Nikolaus Kriegeskorte
出处
期刊:Proceedings of the National Academy of Sciences of the United States of America [National Academy of Sciences]
卷期号:121 (42) 被引量:3
标识
DOI:10.1073/pnas.2317881121
摘要

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, an extension of representational similarity analysis that uses a family of geotopological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. We evaluate this 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.
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