Jason Kim – Cornell University
Wednesday, May 20, 2026
Zoom opens: 10:30AM EDT
Seminar begins: 10:45AM EDT
Modeling the Geometry of Thought with Curvature Regularized Neural Networks
When a mouse perceives a hawk's shadow, it may have only seconds to decide where to run, yet the safest refuge is often neither visible nor nearby. To survive, it must search its mental model of the world, or cognitive map, quickly enough to choose among many possibilities, and accurately enough to avoid dead ends and hazards along the way. This scenario highlights a core design problem: our cognitive map must preserve fine local structure for reliable action, yet remain globally searchable so that distant, useful solutions can be found efficiently in both space and time. In this talk, I will discuss how to use a novel geometry-aware autoencoder to model the geometric structure of the cognitive map from longitudinal calcium imaging from thousands of hippocampal CA1 neurons in mice as they learn a memory-guided navigation task. We find that the hippocampus achieves both local fidelity and global searchability through small-world network structure in the space of neural representations, and find evidence that they are engaged during offline processing. This functional organization, with implications for both neuroscience and artificial intelligence, sheds light on how hippocampal representations may be optimized for a fundamental challenge faced by intelligent systems: efficiently searching through accurate internal models of the world.