Neural Representation Geometry
Overview
Neural representation geometry asks how learned features are organized by distances, directions, neighborhoods, manifolds, and topology, and how this structure supports prediction, memory, transfer, or behavior. Researchers compare models and brains using methods such as CKA, Procrustes alignment, and relative representations, and characterize spaces with covariance spectra, intrinsic-dimension estimates, persistent homology, and Riemannian geometry; sparse autoencoders and interventions probe feature structure and causal roles. Work spans vision and language models, contrastive embeddings, world models, and neural recordings, with evaluations including retrieval, out-of-distribution transfer, compositional generalization, and brain alignment. A central tension is that measured geometry can change under function-preserving coordinate transformations, while similarity or geometric patterns alone do not establish shared computation, causal importance, or better performance; robust, task-aware measures remain an open need.
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