发表机构
Old Dominion University; University of Texas at El Paso（老道明大学; 德克萨斯大学埃尔帕索分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究自适应增长量子分类器中电路深度与训练数据规模的联合优化，复现Q-FLAIR机制并在MNIST数据集实验，发现训练集规模与电路规模无确定关系，泛化差距与Caro边界相关性弱，为联合优化留下待解决问题。
AI 中文摘要
构建量子模型存在一个权衡问题：电路应具备多高的复杂度，以及需要多少训练数据才能满足需求。Caro等人的研究表明，具有更少可训练门的模型需要更少的训练数据即可实现良好的泛化性能。Q-FLAIR是一种量子特征映射电路，它可以按门的数量逐步增长，一旦进一步增长无法降低训练损失就会停止。本文探讨上述两项研究结果是否能结合形成可预测的缩放定律，具体研究两个问题：随着训练数据规模增长，Q-FLAIR自身的停止规则会选择更大还是更小的电路？由此产生的泛化行为是否与Caro等人的边界相匹配？本文忠实复现了Q-FLAIR的增长机制，包括其解析重构过程和精确停止规则，并在全分辨率（784像素）的MNIST 3和5分类任务上进行实验，训练集规模N设置为2000至10000的五个不同值，随后对每个生成的电路进行微调，以测量Caro等人提出的有效门数量K。研究发现，训练集规模与Q-FLAIR收敛到的电路规模之间不存在可预测的关系；电路规模和测试准确率均随N呈非单调变化，且不同随机种子带来的差异几乎与N之间的任何趋势一样大；在15次运行中有14次，经验泛化差距从未超过Caro等人的边界，因此该边界在这些运行中作为有效保证成立，但该差距与边界值的相关性仅为0.12，表明K无法解释观察到的大部分变化。为何有效保证能与如此弱的预测能力共存仍是一个悬而未决的问题，回答该问题可能是在实践中实现电路深度与训练数据规模联合优化的必要前提。
英文摘要
Building a quantum model involves a tradeoff: how complex the circuit should be, and how much training data it needs. Caro et al. show that models with fewer trainable gates need less training data to generalize well. Q-FLAIR shows that a quantum feature-map circuit can be grown gate-by-gate, stopping once further growth stops improving the training loss. We ask whether these two results combine into a predictable scaling law. Does Q-FLAIR's own stopping rule pick larger or smaller circuits as training data grows? Does the resulting generalization behavior track Caro et al.'s bound? We reimplement Q-FLAIR's growth mechanism faithfully, including its analytic reconstruction and exact stopping rule. We run it on full-resolution (784-pixel) MNIST 3-vs-5 classification, at five training-set sizes from N = 2000 to 10000. We then fine-tune each resulting circuit, so we can measure Caro et al.'s notion of active gates, K. We find no predictable relationship between training-set size and the circuit size Q-FLAIR converges to. Circuit size and test accuracy both vary non-monotonically with N, and seed-to-seed variance is nearly as large as any trend across N. The empirical generalization gap never exceeds Caro et al.'s bound in 14 of 15 runs, so the bound holds as a valid guarantee in those runs. But the gap correlates only weakly with the bound's value (r = 0.12). This shows that K does not explain most of the variation we observe. Why a valid guarantee can coexist with such weak predictive power remains an open question, and answering it may be necessary before circuit depth and training data size can be jointly optimized in practice.
Journal refNeurIPS 2026 Workshop SaTQuML: Secure and Trustworthy Quantum Machine Learning, NeurIPS 2026 Workshop
