arXiv:2511.10018cs.LGquant-ph2025-11

用量子干涉思想提升模型交互建模能力,可精准控制协同与抵消效应。

Interaction as Interference: A Quantum-Inspired Aggregation Approach

  • 借鉴量子力学中的相干叠加,引入干涉交叉项实现可控交互建模。
  • 在合成数据上超越主流基线,在真实数据上保持竞争力且稳定提升性能。
  • 适合关注交互机制可解释性与模型校准的从业者,尤其在小样本场景中优势明显。

传统方法将交互视为人工构造的乘积项或灵活模型中的涌现模式,难以控制协同或拮抗的产生机制。本文提出一种量子启发视角:依据玻恩规则(概率为幅值平方),相干聚合先求和复幅值再平方,产生干涉交叉项;而非相干代理则直接对平方模长求和,消除该交叉项。在最小线性幅值模型中,此交叉项等价于2×2因子设计中的标准潜在结果交互对比Δ_{INT},使相对相位具备机制层面调控协同与拮抗的能力。我们构建轻量级干涉核分类器(IKC),并引入两个诊断指标:相干增益(相干与非相干代理的对数似然增益)与干涉信息(诱导的KL差距)。相位扫描实验验证了其可逆性。在高交互合成任务(XOR)中,IKC在配对、预算匹配条件下优于强基线;在真实表格数据集(Adult与Bank Marketing)上总体表现竞争,但通常略逊于最强大的基线。固定参数后,从非相干切换至相干聚合始终改善负对数似然、Brier评分与期望校准误差,两数据集均呈现正相干增益。

原文摘要 · Abstract (English)

Classical approaches often treat interaction as engineered product terms or as emergent patterns in flexible models, offering little control over how synergy or antagonism arises. We take a quantum-inspired view: following the Born rule (probability as squared amplitude), \emph{coherent} aggregation sums complex amplitudes before squaring, creating an interference cross-term, whereas an \emph{incoherent} proxy sums squared magnitudes and removes it. In a minimal linear-amplitude model, this cross-term equals the standard potential-outcome interaction contrast \(Δ_{\mathrm{INT}}\) in a \(2\times 2\) factorial design, giving relative phase a direct, mechanism-level control over synergy versus antagonism. We instantiate this idea in a lightweight \emph{Interference Kernel Classifier} (IKC) and introduce two diagnostics: \emph{Coherent Gain} (log-likelihood gain of coherent over the incoherent proxy) and \emph{Interference Information} (the induced Kullback-Leibler gap). A controlled phase sweep recovers the identity. On a high-interaction synthetic task (XOR), IKC outperforms strong baselines under paired, budget-matched comparisons; on real tabular data (\emph{Adult} and \emph{Bank Marketing}) it is competitive overall but typically trails the most capacity-rich baseline in paired differences. Holding learned parameters fixed, toggling aggregation from incoherent to coherent consistently improves negative log-likelihood, Brier score, and expected calibration error, with positive Coherent Gain on both datasets.

交互建模量子启发模型校准可解释性

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