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Poster D in Poster Session D: Wednesday, August 5, 2:00 – 3:45 pm, Kimmel Center, Shorin & Rosenthal Rooms

Geometric regularization of representation spaces enables efficient application of cognitive operators

Paul Liebenow¹, Johann Bauer², Joseph Scott German¹, Angela J. Yu³; ¹Technische Universität Darmstadt, ²City University, ³University of California, San Diego

Presenter: Paul Liebenow

Humans solve many cognitive tasks by applying operators to internal representations rather than directly manipulating sensory input. A central challenge for artificial agents is to reach human-level generalization on abstract problems. One idea is to learn latent representation spaces whose geometric structure supports the efficient learning, application and generalization of operators . We refer to this kind of operator as a cognitive operator. In this work, we study how the curvature of representation spaces influences the learnability and accuracy of cognitive operators corresponding to structured environmental transformations. Focusing on the mental rotation task, we model an agent using an encoder whose latent space serves as an internal representation. Drawing on tools from differential geometry, we formalize environmental transformations as Lie group actions and cognitive operators as vector fields on a latent manifold. Motivated by curvature-dependent error bounds for differential equations on Riemannian manifolds, we propose a set of curvature-regularization objectives that encourage locally linear, low-curvature latent geometries. Experimental results on synthetic mental rotation stimuli show that curvature-regularized latent spaces yield more accurate operator learning performance. Together, these findings highlight the importance of latent geometry for bridging representation learning and cognitive computation, and provide a principled framework for learning cognitive operators in neural systems.

Topic Area: Methods, Tools, Theory & Neural Coding