Justin F. Howard

Non-Euclidean Toroidal Topography in Large Language Models: Compact Riemannian Manifold Embeddings, Geodesic Attention, and 3D Photonic Co-Simulation Verification

Conventional Transformer neural networks embed token representations within flat Euclidean latent spaces RD . Despite their empirical utility, Euclidean geometries ex- hibit severe isotropic distance concentration in high dimen- sions, lack periodic boundary-free inductive bias,...