(R)evolving Geometry of Condensed Generalized States in the Hippocampal Cognitive Map

The hippocampus represents essential aspects of an animal's experiences and actions through consistent patterns of neural activity typically referred to as a cognitive map. How such maps emerge from millions of neurons remains one of the most fascinating problems in neuroscience. Recently, pioneering studies have attempted to use large datasets of neural activity and dimensionality reduction techniques to reliably model these maps. Such techniques, however, tend to overfit the data by modeling the idiosyncrasies rather than capturing the overarching trends. Here, we show that a novel technique using differential geometry to selectively control all distortions associated with overfitting, Γ-autoencoder, builds interpretable and quantitative models of cognitive maps. We apply this method to activity from thousands of hippocampal neurons across many days in mice learning to collect rewards under two task conditions on looped linear tracks. We show that the 3 most salient model coordinates correspond to position (space), trial (time), and task belief. The resulting cognitive map has a cylindrical topology for each task condition. For a given trial, a specific position elicits a consistent pattern of firing. In subsequent trials this pattern rotates along the track position (cylinder circumference), and drifts along the trial direction (cylinder axis). We show that rotation and drift allow for condensation of firing patterns from multiple points on the track in previous trials onto a pattern of activity associates with a current position on the track. This condensation enables the formation of temporally expanded representations analogous to a context window in transformer architectures in artificial neural networks.