Empirical Characterization of Learning Geometry in Hybrid Quantum Forecasting Models

2026-08-19

AI Summary

研究通过比较混合量子预测模型与经典基线模型，分析了它们在学习几何上的差异及优化过程中的表现，尽管两者最终性能相似，但展现了不同的学习轨迹。

Abstract

We characterize the learning dynamics of a compact hybrid quantum forecasting model through comparison with a structurally aligned classical baseline. Using stationary harmonic-mixture and nonstationary chirp benchmarks with controlled spectral complexity and data availability, we analyze empirical Neural Tangent Kernel dynamics through kernel-target alignment, kernel drift, spectral concentration, and training loss. The classical model exhibits stronger early target alignment, whereas the hybrid model generally develops a less concentrated kernel spectrum and smaller kernel drift. Despite these distinct optimization geometries, both architectures attain similar held-out performance across the evaluated regimes. Notably, the hybrid model uses 125 trainable parameters compared with 281 for the classical baseline and reaches its validation-selected checkpoint earlier in 15 of 18 frequency conditions. A Fourier-augmented classical baseline does not reproduce the observed training behavior, while a controlled re-uploading ablation shows that repeated encoding systematically modifies both optimization and kernel geometry. These results demonstrate that comparable generalization can emerge from substantially different learning trajectories and that individual NTK diagnostics do not provide monotonic predictors of validation convergence. Rather than claiming a general quantum advantage, the study identifies architecture-dependent learning behavior that is masked by endpoint accuracy alone.

Problem

• Learning Geometry
• Hybrid Quantum Models
• Classical Baselines
• Optimization Dynamics
• Generalization

Innovation

• hybrid quantum forecasting model
• Neural Tangent Kernel dynamics
• kernel-target alignment
• spectral concentration
• re-uploading ablation