Flexible mapping of abstract domains by grid cells via self-supervised extraction and projection of generalized velocity signals

To sidestep the computational cost of learning representations for each high-dimensional sensory input, the brain extracts self-consistent, low-dimensional descriptions of displacements across abstract spaces, leveraging the spatial velocity integration of grid cells to efficiently build maps of different domains.Our neural network model for abstract velocity extraction factorizes the content of these abstract domains from displacements within the domains to generate content-independent and self-consistent, low-dimensional velocity estimates. Crucially, it uses a self-supervised geometric consistency constraint that requires displacements along closed loop trajectories to sum to zero, an integration that is itself performed by the downstream grid cell circuit over learning. This process results in high fidelity estimates of velocities and allowed transitions in abstract domains, a crucial prerequisite for efficient map generation in these high-dimensional environments. We also show how our method outperforms traditional dimensionality reduction and deep-learning based motion extraction networks on the same set of tasks.This is the first neural network model to explain how grid cells can flexibly represent different abstract spaces and makes the novel prediction that they should do so while maintaining their population correlation and manifold structure across domains.