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Making Classic GNNs Strong Baselines Across Varying Homophily: A Smoothness–Generalization Perspective

NeurIPS 2025 · Graph learning › GNN architectures · approach: GNN generalization theory · 1 citations (OpenAlex)

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Proposes Inceptive Graph Neural Networks (IGNN), three minimal design principles (separative transformation, inceptive aggregation, neighborhood relationship learning) on classic GCN-style message passing, to resolve a theorized smoothness-generalization dilemma and achieve robust performance across varying homophily.

Problem

Classic GNNs face a smoothness-generalization trade-off as depth grows, hurting performance on high-order homophilic neighborhoods and heterophilic graphs with varying homophily; existing methods handle homophily and heterophily separately.

Approach

Theoretically links oversmoothing (distance to the information-less subspace) and Lipschitz-constant-based generalization in GCN message passing, then argues that separate per-hop transformations, concatenated/inceptive multi-hop aggregation, and learned hop relationships decouple smoothness from generalization, with c-IGNN as the best variant.

Key results

• c-IGNN achieves the best average rank (A.R. 1.3) across 11 main benchmark datasets, e.g., 38.51% on Actor and 97.24% on BlogCatalog, outperforming 30 baselines.
• On large datasets, c-IGNN reports 73.26% on ogbn-arxiv and 82.04% on ogbn-products, with r-IGNN reaching 82.74% on Pokec.
• Ablation shows that the full combination of SN, IN and NR (c-IGNN) gives the best average rank of 1.0 versus 2.6 for r-IGNN and 3.0 for SIGN.

Measured effects reported in the paper

Surprising findings

• Classic homophilic inceptive GNNs (e.g., SIGN, IncepGCN) outperform many recent heterophily-specific GNNs when hyperparameters are tuned, suggesting the key limitation is the dilemma rather than homophily assumptions.

Limitations

• Language/word graphs (e.g., roman-empire) where transformers excel are left to future work
• Theory relies on linearized GCN simplifications (removing intermediate nonlinearities) and Lipschitz-based generalization proxies
• Experiments use random 48/32/20 splits chosen by the authors, which may differ from standard benchmarks

Experimental setup

Datasets: Actor BlogCatalog Flickr Roman-empire Squirrel-filtered Chameleon-filtered Amazon-ratings PubMed Photo WikiCS ogbn-arxiv Pokec

Benchmarks: Actor BlogCatalog Flickr Roman-empire Squirrel-filtered Chameleon-filtered Amazon-ratings PubMed Photo WikiCS ogbn-arxiv Pokec

Metrics: accuracy average rank

Baselines: MLP SGC GCN GAT GraphSAGE APPNP JKNet IncepGCN SIGN MixHop FAGCN DAGNN

Builds on: GCN SIGN GCNII GPRGNN APPNP

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