Lorentz-Manifold Transformers: A Geometric–Dynamical Framework for Hierarchical Representation Learning

Neural sequence models face a fundamental tension between representational capacityand geometric constraints. We present the Lorentz-Manifold Transformer (LMT), integrat-ing hyperbolic geometry (Lorentz model) with oscillatory dynamics (Hyperbolic ArtificialKuramoto Oscillatory Neurons, H-AKOrN) to address the Geometric Capacity Bottle-neck. The LMT establishes mathematical guarantees for topological preservation through:(1) manifold capacity bounds proving exponential advantage (αcH /αcR = Ω(er )), (2) geomet-ric frustration as a proxy for representational misalignment, and (3) Gromov-Wassersteinstructural risk. Computational complexity (