用量子相位建模语义层次，提升概念尺度与文本方向的捕捉能力。
QuantumPhaseNet: A Gauge-Covariant Geometric and Quantum-Spectral Theory of Semantic Concept Hierarchies with Prototype Validation of a Classical Quantum-Inspired Model
- 将语义状态视为复数振幅，通过协变相位率定义概念尺度
- 在合成数据上实现0.852的层次相关性与0.953的判别准确率
- 适合研究语义结构建模与经典量子启发式方法的评估
我们提出 QuantumPhaseNet，一种基于规范协变几何与量子谱理论的 Transformer 扩展。上下文相关的语义状态被建模为复数振幅；协变相位速率生成语义波长，作为概念尺度的代理；低频图模式定义文档级论述方向。理论部分建立了局部规范不变性、量子模块的幺正性、WavePhase Attention 的有界性与条件稳定性，以及可校准的幻觉风险模型。我们在第14.1节实现了全离线验证工作室，并在内置合成设置（n=240，观测噪声0.22，电路噪声0.08，五组随机种子）下评估了五个研究问题。RQ1：波长-层次斯皮尔曼相关达0.852（基线0.707），方向准确率87.3%，AUC 0.953。RQ2：论述对齐0.933（基线0.589），漂移前平均段落数41.2（基线16.2）。RQ3：AUROC 0.881（余弦0.765，相位打乱0.536）。RQ4：错误检测AUROC 0.854（熵0.634），Brier 0.150，ECE 0.098。RQ5未显示量子优势：目标概率和端到端效率分别为25.5%和0.107，而切比雪夫经典近似为70.7%和0.707。结果提供经典量子启发组件的初步合成证据，但缺乏外部有效性或无条件量子加速。
原文摘要 · Abstract (English)
We present QuantumPhaseNet, a gauge-covariant geometric and quantum-spectral extension of Transformer representations. Context-dependent semantic states are modeled as complex amplitudes; a covariant phase rate induces a semantic wavelength used as a proxy for conceptual scale; and low-frequency graph modes define a document-level discourse direction. The theoretical part establishes local gauge invariance, unitarity of the quantum block, boundedness and conditional stability of WavePhase Attention, and a calibratable hallucination-risk formulation. We also implemented a fully offline Validation Studio for the classical quantum-inspired pipeline in Section 14.1 and evaluated the five research questions in Section 16.1 on its built-in synthetic setting (n=240, observation noise 0.22, circuit noise 0.08, five seeds). RQ1 yielded a wavelength-hierarchy Spearman correlation of 0.852 versus 0.707 for the baseline, 87.3% direction accuracy, and AUC 0.953. RQ2 achieved discourse alignment 0.933 versus 0.589 and 41.2 versus 16.2 paragraphs before drift. RQ3 achieved AUROC 0.881 versus cosine 0.765 and phase-shuffle 0.536. RQ4 achieved error-detection AUROC 0.854 versus entropy 0.634, with Brier 0.150 and ECE 0.098. RQ5 did not show quantum advantage: target probability and end-to-end cost efficiency were 25.5% and 0.107, compared with 70.7% and 0.707 for the Chebyshev classical approximation. These results provide initial synthetic evidence for the classical quantum-inspired components, but not external validity or unconditional quantum speedup.
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