Hybrid Quantum Models Show Unique Learning Geometry.

This research investigates the learning behavior of compact hybrid quantum forecasting models by comparing them against classical counterparts with similar structures. The study focuses on understanding the empirical Neural Tangent Kernel (NTK) dynamics, analyzing aspects like kernel-target alignment, kernel drift, and spectral concentration during training. Key findings indicate that classical models initially show stronger target alignment. However, hybrid quantum models generally develop a less concentrated kernel spectrum and exhibit smaller kernel drift over time. Despite these differences in optimization geometry, both model types achieve comparable held-out performance across various spectral complexities and data availability conditions. Notably, the hybrid model achieved similar accuracy with significantly fewer trainable parameters (125 vs. 281 for the classical baseline) and often reached its validation checkpoint earlier. The study concludes that comparable generalization can arise from substantially different learning trajectories, and individual NTK diagnostics alone are not monotonic predictors of validation convergence, highlighting unique architecture-dependent learning behaviors in hybrid quantum models.