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# Topological ensemble detection with differentiable yoking

*Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations*, PMLR 197:354-369, 2023.

#### Abstract

Modern neural recordings comprise thousands of neurons recorded at millisecond precision. An important step in analyzing these recordings is to identify

*neural ensembles*— subsets of neurons that represent a subsystem of specific functionality A famous example in the mammalian brain is that of the grid cells, which separate into ensembles of different spatial resolution. Recent work demonstrated that recordings from individual ensembles exhibit the topological signature of a torus. This is obscured, however, in combined recordings from multiple ensembles. Inspired by this observation, we introduce a topological ensemble detection algorithm that is capable of unsupervised identification of neural ensembles based on their topological signatures. This identification is achieved by optimizing a loss function that captures the assumed topological signature of the ensemble and opens up exciting possibilities, e.g., searching for cell ensembles in prefrontal cortex, which may represent cognitive maps on more conceptual spaces than grid cells.