量子混合模型用更少参数实现与经典模型相当的预测性能。
Empirical Characterization of Learning Geometry in Hybrid Quantum Forecasting Models

- 对比经典模型,量子混合模型优化路径不同但效果相近。
- 仅125个参数,训练更快且在15/18条件下提前收敛。
- 适合关注量子模型训练机制与泛化能力的研究者。
通过与结构对齐的经典基线对比,我们分析了紧凑型混合量子预测模型的学习动态。采用具有可控谱复杂性和数据量的平稳谐波混合与非平稳啁啾基准,基于核目标对齐、核漂移、谱集中度和训练损失等指标,实证研究了神经正切核(NTK)行为。经典模型早期目标对齐更强,而混合模型通常具有更分散的核谱和更小的核漂移。尽管优化几何显著不同,两者在评估范围内达到相似的保留性能。值得注意的是,混合模型仅使用125个可训练参数,相比经典基线(281参数)更少,并在18种频率条件中的15种下更早达到验证选择的检查点。傅里叶增强的经典基线无法复现观察到的训练行为,控制性重编码消融实验表明重复编码系统性改变优化与核几何。结果表明,相似泛化能力可来自截然不同的学习轨迹,单一NTK诊断无法单调预测验证收敛。研究揭示了架构依赖的学习行为,该行为被终点精度所掩盖。
原文摘要 · Abstract (English)
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.
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