Spaces and sequences in the hippocampus: a homological perspective.

Topological techniques have become a popular tool for studying information flows in neural networks. In particular, simplicial homology theory is used to analyze how cognitive representations of space emerge from large conglomerates of independent neuronal contributions. Meanwhile, a growing number of studies suggest that many cognitive functions are sustained by serial patterns of activity. Here, we investigate stashes of such patterns using Significance statement: This study employs path homology theory to examine serial patterns of neuronal activity in the hippocampus, a critical region for learning and memory. While the traditional, simplicial homology approaches used to model cognitive maps, path homology provides a universal framework for analyzing the ordinal arrangement of neuronal sequences without presupposing their nature or function. The findings reveal that a limited number of distinct sequence classes, supported by combinations of short activity motifs, form a stable ordinal schema over timescales corresponding to periods of spatial learning. Notably, the ordinal maps derived from these sequences do not capture topological affinities, highlighting that spatial and sequential analyses address distinct but complementary dimensions of neural information processing.