对比图压缩的两种方法，发现保信号多样性与保传播一致性难兼顾。
Does Graph Compression Preserve Signal Propagation?
- 比较粗化与稀疏化对图信号传播的影响，采用三类互补指标量化。
- 稀疏化保信号多样性但传播轨迹偏离原图，粗化更忠实但加剧过平滑。
- 揭示传播保真度与信号多样性是两个冲突目标，需联合评估。
图压缩能降低图学习的计算开销，但其对信号传播的影响尚未充分研究。现有工作通过下游任务性能或结构保真度评估压缩效果，却未直接反映传播动态的变化。我们研究了两种基础压缩范式——粗化与稀疏化，探究它们是否保持原始图的传播行为。在五个数据集、多种压缩率和传播深度下，通过三种互补指标测量信号行为。结果表明，两类压缩存在持续张力：稀疏化保留更高信号多样性并缓解过平滑，但其传播轨迹逐步偏离原图；粗化更忠实地保留传播行为，但伴随更强的平滑效应与秩崩溃。这些发现表明，保信号多样性和保传播保真度是两个独立且在压缩中相互矛盾的目标，凸显了需同时考虑这两个维度的评估协议的重要性。代码与结果见：https://github.com/KawshikBanerjee/Compression-Propagation-Duality。
原文摘要 · Abstract (English)
Graph compression reduces the computational cost of graph learning, but its effect on signal propagation remains largely underexplored. Existing work evaluates compression through downstream task performance or structural preservation, neither of which directly captures how propagation dynamics change after compression. We study two fundamental compression paradigms, coarsening and sparsification, and ask whether they preserve the propagation behavior of the original graph. Across five datasets, varying compression rates, and propagation depths, we measure signal behavior through three complementary metrics. Our results reveal a consistent tension between the two compression families. Sparsification retains higher signal diversity and mitigates oversmoothing, but its propagation trajectory progressively diverges from that of the original graph. Coarsening more faithfully preserves propagation behavior, but at the cost of stronger smoothing and rank collapse. These findings demonstrate that two propagation-centric objectives, preserving signal diversity and preserving propagation fidelity, are distinct and empirically at odds under graph compression, highlighting the need for evaluation protocols that jointly consider both dimensions. The code and results are available at: https://github.com/KawshikBanerjee/Compression-Propagation-Duality
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