Optimizing Neural Manifold Dynamics for Learning

With billions on neurons in the brain, their activity needs to be organized to allow for coherent action. Neural activity is formally very high-dimensional. However, emerging evidence from diverse segments of the nervous system suggests that the activity patterns of neural populations possess an underlying low-dimensional structure that can be described with a curved and expanding map. This award will study these maps, and how they change with learning. The observation that brain requires descriptions in terms of curved and nonlinear maps also make it necessary to generalize classic results developed in 1980s on the capacity of collections of neurons to store memories. The Principal Investigator (PI) will work on generalizing these classic results to understand whether the capacity of neural networks is greater than what was thought previously. The developed algorithms will make it possible to generate new machine learning algorithms with a wide range of applications in brain-machine including national defense, medical research, and social communication. The PI will analyze low-dimensional manifolds that describe neural activity in various species and brain areas, including the fly and rodent brains and spanning various sensory and higher-order integration brain regions. The manifolds will be characterized by their curvature and dimensionality, and the investigators will examine how these parameters change with learning. To aid manifold reconstruction, the investigators will develop novel metric and non-metric manifold learning methods. Based on their previous findings, the investigators will generalize classic results on the memory capacity of neural networks to tackle the case of curved manifolds. Special emphasis will be placed on hyperbolic manifolds due to recent evidence supporting their relevance in the latent structure of neural responses. The outreach program is designed to harness the inherent interest people have in maintaining learning and enhancing brain function. Engagement will include outreach to K-12 schools in San Diego and summer programs to foster the growth of future physicists. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.