可行流匹配用于图重构：基于采样内原始-对偶引导
Feasible Flow Matching for Graph Reconstruction via Within-Sampling Primal-Dual Guidance
浏览论文内容
中文总结 AI 辅助
针对带结构侧信息的图重构问题，提出CPD-PIFM方法，通过沿轨迹演化的拉格朗日乘子引导采样，在不重训下提升可行性11-26个百分点，并保持置换等变性与竞争力。
中文摘要 AI 辅助
从部分观测进行图重构通常带有结构侧信息，如度界、三角形计数或边密度带。先验信息流匹配（PIFM）通过将局部先验向图分布传输来重构图，但缺乏机制来整合这些侧信息。我们提出约束原始-对偶PIFM（CPD-PIFM），该方法用拉格朗日乘子增强采样器，这些乘子沿每条轨迹演化。乘子对预测端点处的约束违反作出响应，并引导后续采样步骤而无需重新训练。我们证明该采样器继承了PIFM的置换等变性，并将其期望终端松弛度界定为由步数的平方根倒数衰减的项加上两个近似项。在三个链接预测基准和九种数据集与约束组合上，CPD-PIFM将可行性提高了11-26个百分点，并且在无需为每个约束选择单独乘子的情况下，与固定引导保持竞争力。
英文摘要
Graph reconstruction from partial observations often comes with structural side information, such as degree bounds, triangle counts, or an edge-density band. Prior-Informed Flow Matching (PIFM) reconstructs graphs by transporting a local prior toward the graph distribution, but it provides no mechanism to incorporate this side information. We put forth Constrained Primal-Dual PIFM (CPD-PIFM), which augments the sampler with Lagrange multipliers that evolve along each trajectory. The multipliers respond to constraint violations at a predicted endpoint and guide subsequent sampling steps without retraining. We prove that the sampler inherits PIFM's permutation equivariance and bound its expected terminal slack by a term that decays as the inverse square root of the number of steps, plus two approximation terms. On three link-prediction benchmarks and nine combinations of datasets and constraints, CPD-PIFM raises feasibility by 11-26 percentage points and remains competitive with fixed guidance without selecting a separate multiplier for each constraint.
