横向场伊辛模型在图学习中的表达能力研究
On the Expressive Power of the Transverse-Field Ising Model for Graph Learning
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- Pasqal（帕斯卡尔）
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中文总结 AI 辅助
该研究提出受量子启发的图对Transformer QDAGer，将量子动力学特征注入注意力机制，用于学习NP难的图编辑距离，实验证明其动力学特征比经典结构特征的归纳偏置更强。
中文摘要 AI 辅助
我们研究由图索引伊辛哈密顿量诱导的量子演化，将其作为图学习的结构信号来源。图自同构保留哈密顿量的对称性，这些对称性约束量子演化，从而将随时间变化的局域测量转化为图结构的有效探测手段。利用这一思路，我们提出QDAGer，一种受量子启发的图对Transformer，它将节点占据度时间序列及关联两点相关子的量子动力学特征直接注入注意力机制。我们将QDAGer应用于学习图编辑距离（GED）这一NP难相似度度量，采用直接的置换不变嵌入差异或基于对齐的代理损失。在不同编辑代价设置下的多个GED基准实验表明，所提出的动力学特征在相同训练协议下比经典结构替代特征提供更强的归纳偏置。此外，我们报告了消融实验，在保持架构固定的情况下，将动力学信号替换为标准随机游走和热核特征，结果表明性能提升源于注入的动力学，而非仅模型容量。
英文摘要
We study the quantum evolution induced by graph-indexed Ising Hamiltonians as a source of structural signal for graph learning. Graph automorphisms preserve symmetries of the Hamiltonian, and these symmetries constrain the quantum evolution in a way that turns time-dependent local measurements into informative probes of graph structure. Leveraging this idea, we introduce QDAGer, a quantum-inspired graph-pair Transformer that injects quantum-dynamical features from time series of node occupations and connected two-point correlators directly into the attention mechanism. We apply QDAGer to learning Graph Edit Distance (GED), an NP-hard similarity measure, using either a direct permutation-invariant embedding discrepancy or an alignment-based surrogate loss. Experiments on multiple GED benchmarks under different edit cost settings show that the proposed dynamical features provide a stronger inductive bias than classical structural alternatives under the same training protocol. In addition, we report ablations where the dynamical signal is replaced by standard random-walk and heat-kernel features while keeping the architecture fixed, highlighting that the gain comes from the injected dynamics rather than model capacity alone.
