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Life sciences · Preprint
arXiv · September 10, 2026
Posted before peer review. The findings may change or fail to hold.
HERALD is a gradient-free graph condensation method that adjusts node scoring and feature selection based on measured graph heterophily. The method is evaluated on eight benchmark datasets across homophilic and heterophilic settings against unspecified comparators, reported to match or outperform state-of-the-art on heterophilic graphs while remaining competitive on homophilic ones, but effect sizes and statistical comparisons are not provided in this abstract.
Benchmark comparison study. Benchmark graph datasets in homophilic and heterophilic settings used for node-classification tasks.. Intervention: HERALD graph condensation framework with heterophily-adaptive node scoring and feature selection. Compared with: State-of-the-art graph condensation methods (unspecified); BONSAI used for storage budget parity comparison.
HERALD tested on eight benchmark datasets spanning homophilic and heterophilic settings Method evaluated across four GNN architectures Reports matching or outperforming state-of-the-art condensers on heterophilic graphs with competitive performance on homophilic graphs
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Unrefereed arXiv preprint presenting a novel algorithmic framework for graph condensation with experimental validation on benchmark datasets; not yet peer-reviewed.
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Graph condensation aims to produce a small surrogate graph that preserves the downstream node-classification performance of a much larger original graph. Existing methods rely on Weisfeiler-Lehman neighbourhood aggregation or gradient-based distribution matching, both of which assume that adjacent nodes share the same label, an assumption that breaks down under heterophily. We propose HERALD (High-fidelity Exemplar Retrieval with Adaptive Landmark Distillation), a gradient-free graph condensation framework that adapts the node scoring and feature selection in the condensation pipeline to the graph's measured heterophily. HERALD selects features via a joint Fisher-discriminability and activation-density criterion that down-weights aggregated representations on heterophilic graphs, and scores nodes by a weighted combination of prototype representativeness, decision-boundary proximity, and Local Intrinsic Dimensionality (LID), where the weights are driven by a smooth sigmoid function of the heterophily ratio. Nodes are then assembled into a condensed subgraph through score-ordered BFS expansion, Personalised PageRank pruning, and class rebalancing, all at an identical storage budget to BONSAI, enabling direct comparison. Experiments on eight benchmark datasets spanning homophilic and heterophilic settings show that HERALD matches or outperforms state-of-the-art condensers on heterophilic graphs and remains competitive on homophilic ones across four GNN architectures.
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