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Implicit Subgraph Neural Network
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Proposes ISNN, the first implicit subgraph neural network that runs an EIGNN-style implicit model on a hybrid graph of nodes and label-aware subgraph supernodes, trained with a provably convergent penalty-based bilevel algorithm that replaces inner gradient descent with fixed-point iteration.
Problem
Subgraph classification requires capturing subgraph-level properties and long-range dependencies between and within subgraphs, which existing pooling-based and rigid-definition subgraph GNNs fail to model; naive implicit models are unstable on subgraph tasks.
Approach
Augment the graph with supernodes representing subgraphs (membership edges plus label-aware subgraph-subgraph edges inferred from pretrained embeddings), apply an implicit (EIGNN-based) model to this hybrid graph, and train it as a bilevel problem where the inner loop uses fixed-point iteration (no inner gradients) thanks to non-expansive constraints.
Key results
- ISNN reaches 0.731 micro-F1 on PPI-BP vs 0.636 for the best prior baseline (SSNP), and 0.646 on HPO-METAB vs 0.598 (GLASS).
- ISNN achieves 0.924 AUROC on PPI-BP vs 0.835 for GLASS.
- On EM-USER ISNN gets 0.914 F1 vs 0.888 for SSNP, while on HPO-NEURO it is second-best in F1 (0.688 vs 0.682 for SSNP on F1 ordering; GLASS 0.675) and AUROC (0.896 vs 0.867 SSNP).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ISNN instead of the strongest baseline | Subgraph classification · PPI-BP | Micro-F1: 0.636±0.007 -> 0.731±0.026 | Helped |
| Use ISNN instead of the strongest baseline | Subgraph classification · HPO-METAB | Micro-F1: 0.598±0.014 -> 0.646±0.014 | Helped |
| Use ISNN instead of the strongest baseline | Subgraph classification · HPO-NEURO | Micro-F1: 0.682±0.004 -> 0.688±0.004 | Helped |
| Use ISNN instead of the strongest baseline | Subgraph classification · EM-USER | Micro-F1: 0.888±0.005 -> 0.914±0.009 | Helped |
| Use ISNN instead of the strongest baseline | Subgraph classification · PPI-BP | AUROC: 0.835±0.002 -> 0.924±0.012 | Helped |
| Use ISNN instead of the strongest baseline | Subgraph classification · HPO-METAB | AUROC: 0.891±0.002 -> 0.919±0.002 | Helped |
| Use ISNN instead of the strongest baseline | Subgraph classification · HPO-NEURO | AUROC: 0.868±0.004 -> 0.896±0.002 | Helped |
| Use ISNN instead of the strongest baseline | Subgraph classification · EM-USER | AUROC: 0.960±0.004 -> 0.959±0.005 | Hurt |
| Use position-based subgraph-level edges rather than the other constructions (ablation) | ISNN · HPO-METAB | F1: 0.586±0.021 | No clear effect |
| Use structure-based subgraph-level edges (ablation) | ISNN · HPO-METAB | F1: 0.598±0.021 | No clear effect |
| Use neighborhood-based subgraph-level construction (ablation) | ISNN · HPO-METAB | F1: 0.595±0.021 | No clear effect |
| Assign random subgraph-level edge weights (ablation) | ISNN · HPO-METAB | F1: 0.589±0.028 | No clear effect |
Surprising findings
- Ablation shows randomly assigned subgraph-subgraph edge weights perform about as well as position, neighborhood, or structure-based subgraph graphs (HPO-METAB F1 0.589 random vs 0.586-0.598 for others).
- Training naive IGNN or EIGNN on subgraph tasks is unstable and performs poorly (e.g., IGNN-plain F1 0.215 on HPO-NEURO).
Limitations
- Gains on HPO-NEURO are limited because label-to-integer conversion for multi-label data does not capture subgraph relations well.
- Subgraph-level edge construction variants (position, neighborhood, structure, random) show no significant differences, so the claimed benefit of subgraph-level structure is not clearly established.
- Performance is sensitive to the penalty parameter gamma; larger gamma degrades results.
Experimental setup
Datasets: PPI-BP HPO-METAB HPO-NEURO EM-USER
Benchmarks: PPI-BP HPO-METAB HPO-NEURO EM-USER
Metrics: micro-F1 AUROC runtime
Baselines: Sub2Vec GLASS SubGNN SSNP GCN-plain IGNN-plain EIGNN-plain SoftIGNN SoftEIGNN MLP
Builds on: EIGNN V-PBGD SubGNN GLASS SSNP
Closest papers by meaning
- Translating Subgraphs to Nodes Makes Simple GNNs Strong and Efficient for Subgraph Representation Learning (ICML 2024 · similarity 0.89)
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