混合量子预测模型中几何学习的实证表征
Empirical Characterization of Learning Geometry in Hybrid Quantum Forecasting Models
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中文总结 AI 辅助
该研究对比混合量子预测模型与经典基线，通过NTK分析其学习动态，发现二者泛化能力相当但学习轨迹不同，混合模型参数量更少且多数频率条件下收敛更快。
中文摘要 AI 辅助
我们通过与结构对齐的经典基线模型对比，表征了紧凑混合量子预测模型的学习动态。使用具有受控谱复杂度和数据可用性的平稳谐波混合与非平稳线性调频基准，我们通过核目标对齐、核漂移、谱集中和训练损失分析了经验神经正切核（NTK）动态。经典模型表现出更强的早期目标对齐，而混合模型通常形成的核谱集中程度更低、核漂移更小。尽管存在这些不同的优化几何结构，两种架构在评估的所有 regime 中都达到了相似的保留样本性能。值得注意的是，混合模型使用125个可训练参数，而经典基线为281个，且在18种频率条件中有15种更早达到验证集选定的检查点。傅里叶增强的经典基线无法重现观察到的训练行为，而受控的重复编码消融实验表明，重复编码会系统性地改变优化和核几何结构。这些结果表明，相当的泛化能力可来自显著不同的学习轨迹，且单个NTK诊断指标并非验证集收敛的单调预测因子。该研究未宣称通用量子优势，而是识别出仅由端点精度所掩盖的、依赖于架构的学习行为。
英文摘要
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.
发表机构
- CINVESTAV Guadalajara（墨西哥国立理工学院瓜达拉哈拉分校）
- Cinvestav Unidad Tamaulipas（墨西哥国立理工学院塔毛利帕斯分校）
机构由 AI 辅助整理，请以论文原文为准。
