DRESS：一种连续框架用于结构图细化
DRESS: A Continuous Framework for Structural Graph Refinement
AI总结：
DRESS是一种无参数的连续框架，通过迭代优化图边结构相似性生成稳定指纹，提升图结构表达能力，并在强正则图基准中实现有效区分。
摘要：
我们介绍了DRESS，一种确定性、无参数的框架，通过迭代细化图中边的结构相似性来生成一个规范指纹：通过非线性动力系统收敛到其唯一固定点得到的实值边向量。该指纹通过构造是同构不变的，数值上是稳定的（严格有界、精度保持且数学上合理），计算速度快且可以并行处理：DRESS的总运行时间是O(I·m·d_max)，其中I是迭代次数，m是边数，d_max是最大度数，且通过Birkhoff收缩保证收敛。我们扩展了原始方程到Motif-DRESS（任意结构动机）和Generalized-DRESS（抽象聚合模板），并引入Δ-DRESS，通过在每个顶点删除子图上运行DRESS来提升表达能力。Δ-DRESS实验证明能够将7983个图在全面的强正则图基准中分离，且在测试的CFI实例（k=0,1,2,3）中，k-删除（Δ^k-DRESS）实验证明能够达到(k+2)-WL边界。
英文摘要：
We introduce DRESS, a deterministic, parameter-free framework that iteratively refines the structural similarity of edges in a graph to produce a canonical fingerprint: a real-valued edge vector, obtained by converging a non-linear dynamical system to its unique fixed point. The fingerprint is isomorphism-invariant by construction, numerically stable (strictly bounded, precision-preserving, and mathematically well-posed), fast and embarrassingly parallel to compute: DRESS total runtime is $\mathcal{O}(I \cdot m \cdot d_{\max})$ for $I$ iterations to convergence, and convergence is guaranteed by Birkhoff contraction. We generalize the original equation to Motif-DRESS (arbitrary structural motifs) and Generalized-DRESS (abstract aggregation template), and introduce $Δ$-DRESS, which runs DRESS on each vertex-deleted subgraph to boost expressiveness. $Δ$-DRESS empirically separates all 7,983 graphs in a comprehensive Strongly Regular Graph benchmark, and on the tested CFI instances ($k = 0,1,2,3$), $k$-deletion ($Δ^k$-DRESS) empirically matches the $(k{+}2)$-WL boundary.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
