Title:

Solving the Mysteries of Place Cells and Grid Cells by Representation Learning

Abstract:

The 2014 Nobel Prize in Physiology or Medicine recognized the discovery of place cells and grid cells in the mammalian brain. Each place cell fires at a single specific location, whereas each grid cell fires at multiple locations forming a hexagonal grid pattern. Yet the computational principles underlying these phenomena have remained mysterious. We show both emerge from representation learning through geometric optimization. Grid cells learn embeddings that preserve local distances through conformal isometry, forming a coordinate system. We prove hexagonal patterns are optimal: hexagonal flat tori uniquely minimize deviation from local distance preservation by distributing curvature isotropically through six-fold symmetry. Building upon this coordinate system, place cells learn embeddings that preserve spatial adjacency relations defined by transition kernels of heat diffusion with reflecting boundary conditions, thereby forming a cognitive map. Specifically, inner products between embeddings reconstruct transition probabilities, causing localized firing patterns to emerge automatically from non-negative matrix factorization constraints. This reveals how the brain solves navigation by transforming spatial reasoning into optimization on learned geometric representations.

Bio:

Ying Nian Wu is a professor in the Department of Statistics and Data Science at UCLA. He earned his A.M. and Ph.D. in statistics from Harvard University in 1994 and 1996, respectively. From 1997 to 1999, he served as an assistant professor in the Department of Statistics at the University of Michigan before joining UCLA in 1999. He became a full professor in 2006, and he was an Amazon Scholar 2020-2025. Wu’s research spans generative AI, computer vision, computational neuroscience, and bioinformatics.