Robust Graph Condensation via Classification Complexity Mitigation

TL;DR

This work tackles GC robustness when the original graph is corrupted by adopting a geometry-focused approach: MRGC enforces that the GC-produced condensed graph resides on a smooth, low-dimensional graph data manifold to preserve GC’s intrinsic classification-complexity reduction under universal attacks. It introduces three modules—Intrinsic Dimension Manifold Regularization, Curvature-Aware Manifold Smoothing, and Class-Wise Manifold Decoupling—to reduce intrinsic dimension, smooth decision boundaries, and decouple class manifolds, respectively. Theoretical insights show GC lowers intrinsic dimension while attacks raise it, justifying the regularization strategy, and extensive experiments across five datasets demonstrate MRGC’s superior robustness against structure, feature, and label perturbations compared to strong GC baselines and RobGC. The approach offers practical impact by enhancing GC reliability for efficient GNN training in adversarial environments, with future work extending to graph-level tasks and broader robustness scenarios.

Abstract

Graph condensation (GC) has gained significant attention for its ability to synthesize smaller yet informative graphs. However, existing studies often overlook the robustness of GC in scenarios where the original graph is corrupted. In such cases, we observe that the performance of GC deteriorates significantly, while existing robust graph learning technologies offer only limited effectiveness. Through both empirical investigation and theoretical analysis, we reveal that GC is inherently an intrinsic-dimension-reducing process, synthesizing a condensed graph with lower classification complexity. Although this property is critical for effective GC performance, it remains highly vulnerable to adversarial perturbations. To tackle this vulnerability and improve GC robustness, we adopt the geometry perspective of graph data manifold and propose a novel Manifold-constrained Robust Graph Condensation framework named MRGC. Specifically, we introduce three graph data manifold learning modules that guide the condensed graph to lie within a smooth, low-dimensional manifold with minimal class ambiguity, thereby preserving the classification complexity reduction capability of GC and ensuring robust performance under universal adversarial attacks. Extensive experiments demonstrate the robustness of \ModelName\ across diverse attack scenarios.

Figures (7)

• Figure 1: Examples in Cora chen2021understanding dataset (ratio=2.6%): (a) GCond performance under attacks. (b) The robust GNN is adapted for GC under attacks, with (+M) indicating MedianGCN is the GC backbone and (*M) denoting its use in the condensed graph. (c) Classification complexity evaluation, where (*) means the original graph is under attack during GC. Details can be found in Appendix \ref{['apendix_exp']}.
• Figure 2: The framework of MRGC, which introduces three complementary graph manifold learning modules into the GC process: constraining the intrinsic dimension, smoothing classification boundaries via manifold curvature limits, and encouraging class manifold decoupling. These modules address the increase in classification complexity within the condensed graph induced by attacks.
• Figure 3: Ablation study.
• Figure 4: Classification complexity("*" indicates attack).
• Figure 6: Explanation of the Quadratic Hypersurface Fitting Process in Section \ref{['sec_curvature']}

Theorems & Definitions (10)

• Theorem 1
• Theorem 2
• Proposition 1
• Theorem 3
• proof
• Corollary 1
• Theorem 4
• proof
• Proposition 2
• proof