Representational Learning and Grid Cells

Ying Nian Wu, UCLA Department of Statistics and Data Science

Wegmans Hall 1400

A key perspective of deep learning is representation learning, where concepts or entities are embedded in latent spaces and are represented by latent vectors whose elements can be interpreted as activities of neurons. In this talk, I will discuss our recent work on representational models of grid cells. The grid cells in the mammalian entorhinal cortex exhibit striking hexagon firing patterns when the agent (e.g., a rat or a human) navigates in the 2D open field. I will explain that the grid cells collectively form a vector representation of the 2D self-position, and the 2D self-motion is represented by the transformation of the vector. We identify a group representation condition and an isotropic scaling condition for the transformation, and show that these two conditions lead to locally conformal embedding and the hexagon grid patterns.

Ying Nian Wu is currently a professor in the Department of Statistics and Data Science, UCLA. He received his A.M. degree and Ph.D. degree in statistics from Harvard University in 1994 and 1996 respectively. He was an assistant professor in the Department of Statistics, University of Michigan from 1997 to 1999. He joined UCLA in 1999. He has been a full professor since 2006. He has been an Amazon scholar since 2020. Wu’s research areas include generative modeling, computer vision, computational neuroscience, and bioinformatics.