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Fully-inductive Node Classification on Arbitrary Graphs
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Introduces fully-inductive node classification on arbitrary graphs and proposes GraphAny, which combines analytically solved LinearGNNs with an entropy-normalized distance-feature inductive attention module, trained on a single graph.
Problem
Node classification models generalize across graph structures only when feature and label spaces match training; no model handles new graphs with arbitrary feature dimensions and label spaces without retraining.
Approach
LinearGNN gives closed-form predictions via pseudo-inverse of propagated features (no gradient training), and multiple LinearGNN predictions are fused by an MLP attention over permutation-invariant, entropy-normalized pairwise distance features, so the only trainable part is independent of feature and label dimensions.
Key results
- GraphAny trained on Wisconsin with 120 labeled nodes achieves 67.26% average accuracy over 31 graphs (67.31% on 27 held-out graphs), slightly above GCN (66.55%) and GAT (67.03%) trained per dataset.
- GraphAny is 2.95x faster in total wall time than GCN across 31 graphs (6.37 vs 18.80 min).
- LinearSGC2 reaches 64.41% total average, about 2.1% below GCN on average, with no training.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train GraphAny on Wisconsin using 120 labeled nodes instead of training a separate transductive model per test graph | GraphAny · Held Out Avg. (27 graphs) | accuracy (%) | Helped |
| Normalize distance features to a fixed entropy rather than using unnormalized distances (ablation) | GraphAny inductive attention · Inductive node classification | test performance | Helped |
| Use unnormalized Euclidean distance or Jensen-Shannon divergence features instead of entropy-normalized features (ablation) | GraphAny inductive attention · Transductive node classification | test performance | Helped |
| Vary the fixed entropy value H (ablation) | GraphAny inductive attention · Inductive and transductive settings | performance | No clear effect |
| Use graph-level attention instead of node-level attention (ablation) | GraphAny · Inductive and transductive node classification | test performance | Hurt |
| Use transductive vector attention instead of distance-feature inductive attention (ablation) | GraphAny · Inductive node classification | test performance | Hurt |
| Add low-pass LinearSGC1 and LinearSGC2 channels (ablation) | GraphAny-LinearGNN · 31 graphs | test accuracy | Helped |
| Add higher-order Chebyshev convolution channels (ablation) | GraphAny-Chebyshev · 31 graphs | test accuracy | Hurt |
| Add more local personalized PageRank channels (ablation) | GraphAny-PPR · 31 graphs | test accuracy | Helped |
| Use learned attention to combine channels rather than averaging them with MeanAgg (ablation) | GraphAny · 31 graphs | test accuracy | Helped |
Surprising findings
- Transductive attention (fixed attention vector) performed worse than a single LinearSGC2 model, while node-level inductive attention generalized.
- A GraphAny model trained on only 120 labeled nodes of Wisconsin matches or beats per-dataset trained GCN and GAT on average.
Limitations
- LinearGNNs alone are not expected to outperform transductive models; GraphAny is only slightly better than or below ACM-GCN (1-2% gap).
- Attention module is trained on a small set of labeled nodes from a single or few training graphs; generalization evidence limited to node classification.
- Baselines like GCN/GAT are not strictly fully inductive; comparisons rely on per-dataset tuning and no existing fully-inductive baseline exists.
Experimental setup
Datasets: Cora Wisconsin Arxiv Products PyG datasets DGL datasets OGB datasets
Benchmarks: Cora Wisconsin Arxiv Products 31 node classification datasets ACM-GNN comparison on 27 graphs
Metrics: test accuracy wall time Hits@2
Baselines: MLP GCN GAT LabelProp LinearSGC1 LinearSGC2 ACM-GNN
Builds on: SGC GCN label propagation Chebyshev filters
Closest papers by meaning
- GraphUniverse: Enabling Systematic Evaluation of Inductive Generalization (ICLR 2026 · similarity 0.88)
- Subgraph Invariant Learning Towards Large-Scale Graph Node Classification (AAAI 2025 · similarity 0.87)
- Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models (NeurIPS 2025 · similarity 0.87)
- Node Identifiers: Compact, Discrete Representations for Efficient Graph Learning (ICLR 2025 · similarity 0.86)
- Label-free Node Classification on Graphs with Large Language Models (LLMs) (ICLR 2024 · similarity 0.86)
- An Efficient Subgraph-Inferring Framework for Large-Scale Heterogeneous Graphs (AAAI 2024 · similarity 0.86)
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