Curvature-Aware Deep Learning for Vector Boson Fusion: Differential Geometry, Physics-Inspired Features, and Quantum Method Limitations

Particle physics classification often assumes flat geometry, ignoring the curved statistical structure of collision data. We present a geometric framework for Vector Boson Fusion Higgs classification that combines physics-inspired observables with product manifold neural networks. The method unifies Euclidean, hyperbolic, and spherical representations to capture nonlinear correlations among kinematic features. Geometric embedding yields measurable improvements over flat baselines, demonstrating that curvature-aware architectures recover information lost in standard approaches. The study highlights how incorporating geometric structure enhances discrimination power in high-energy collision data.