arXiv:2605.01319quant-phcs.LG2026-05

解析量子模型训练中梯度消失的根源,揭示不同机制的贡献比例。

Decomposing Gradient Suppression in Barren Plateaus: Activity, Sign Organization, and Coupling

论文配图:Decomposing Gradient Suppression in Barren Plateaus: Activity, Sign Organization, and Coupling
图 1 · 摘自论文原文
  • 分解梯度方差为活动性、符号组织和耦合三部分,精确量化各成分作用
  • HEA中96.5%-98.9%的梯度抑制来自活动性衰减,组织与耦合无系统性变化
  • HVA中活动性与组织随系统规模增长,均显著影响梯度消失,适合研究复杂量子优化

传统上,贫瘠平原(BPs)被描述为梯度方差抑制,但这一整体表征无法揭示哈密顿量各项对梯度信号损失的贡献。本文提出一项逐项解析框架,将梯度二阶矩精确分解为预抵消活动性、符号组织及其统计耦合。基于条件随机符号模型(保留各项幅值,符号独立对称),提供组织与耦合的基准参考。应用于硬件高效变分形式(HEA)与哈密顿量变分形式(HVA)在横向与纵向伊辛模型上的实验显示:对HEA而言,有限尺寸下的二阶矩抑制几乎完全由活动性衰减导致,占比达96.5%-98.9%,而组织无系统性缩放,耦合与随机符号基准一致;对HVA,活动性与组织随系统规模增长,且贡献相当。偏差校正后的平均梯度检查在所有条件下接近零,表明结果近似适用于梯度方差。微观符号对齐分析进一步发现,HVA呈现局域结构化的符号组织,而HEA仅存在微弱残余符号结构且未形成净组织。这些模式在两类哈密顿量下均重现,实现了超越整体统计的梯度抑制逐项刻画。

原文摘要 · Abstract (English)

Barren plateaus (BPs) are conventionally characterized by suppressed gradient variance, but this aggregate description does not reveal how the loss of gradient signal is composed across Hamiltonian terms. We introduce a term-resolved framework that decomposes the second moment of the gradient exactly into pre-cancellation activity, sign organization, and their statistical coupling. A conditional random-sign model, which preserves termwise magnitudes while treating signs as independent and symmetric, provides exact references for organization and coupling. We apply the framework to a hardware-efficient ansatz (HEA) and a Hamiltonian variational ansatz (HVA) for the transverse-field and longitudinal-field Ising models. For the HEA, finite-size suppression of the second moment is carried almost entirely by decaying activity, accounting for 96.5-98.9% of the fitted log-slope across tested depths in both Hamiltonians, while organization shows no systematic scaling and coupling remains consistent with its random-sign reference. For the HVA, activity and organization instead grow with system size and contribute comparably to the second-moment scaling. A bias-corrected mean-gradient check is consistent with zero in every tested condition, so these results carry over approximately to the gradient variance. Microscopic sign-alignment analysis further shows sector-structured organization in the HVA, whereas the HEA exhibits only weak residual sign structure that does not accumulate into net signed organization. These patterns are reproduced across both Hamiltonians, providing a term-resolved characterization of BP-relevant gradient suppression beyond aggregate gradient statistics.

量子机器学习梯度消失变分量子算法伊辛模型

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