The topology and geometry of neural representations

Significance Characterizing the representations encoded in patterns of neural activity is key to understanding brain computation. Representational similarity analysis uses the geometry of neural population response patterns to compare representations between brains and models. We propose topological representational similarity analysis (tRSA) to also characterize the topology, providing a more robust signature of a region’s computational function. tRSA compresses uninformative variation in small and large representational distances to focus on the critical intermediate scale. Analyzing functional MRI data and simulations, we show tRSA matches standard representational similarity analysis at identifying corresponding brain regions and model layers, while focusing on the core topological features distinguishing representations. Considering topology alongside geometry enables a comprehensive understanding of the information represented in population codes.