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How Much Can Transfer? BRIDGE: Bounded Multi-Domain Graph Foundation Model with Generalization Guarantees
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Proposes BRIDGE, a multi-domain graph foundation model that pre-trains with domain-invariant dimension- and semantic-wise aligners, prompts with a self-supervised MoE, and adds a spectral Lipschitz-based generalization-bound regularizer for few-shot node and graph classification.
Problem
Pretrain-then-prompt graph foundation models lack theoretical grounding for why they transfer and how much knowledge can move from source to target graph domains, especially in few-shot settings with heterogeneous feature dimensions and semantics.
Approach
Align heterogeneous multi-domain graph features with domain-invariant aligners during pre-training, initialize graph prompts through a lightweight self-supervised MoE that assembles source aligners, and regularize fine-tuning with a spectral, Lipschitz-based upper bound on target generalization error.
Key results
- One-shot node classification: BRIDGE averages about 3.41% gain over 15 baselines; e.g., 68.55% on Reddit vs 64.87% for ProNoG.
- One-shot graph classification: BRIDGE reaches 75.76% on Reddit vs 73.14% for MDGPT and 3.25% average improvement.
- Five-shot graph classification with LLM-generated node descriptions reaches 86.87% on Reddit (BRIDGE + LLM) vs 84.42% without LLM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add semantic-wise aligner As (ablation) | BRIDGE · CiteSeer node classification, one-shot | accuracy: 40.2 -> 42.2 | Helped |
| Use selective MoE routing instead of average routing (ablation) | BRIDGE · CiteSeer node classification, one-shot | accuracy: 39.9 -> 42.2 | Helped |
| Add spectral regularizer Rspec (ablation) | BRIDGE · CiteSeer node classification, five-shot | accuracy: 54.5 -> 60.2 | Helped |
| Add LLM-generated textual node features | BRIDGE · Reddit cross-domain, zero-shot node classification | accuracy: 55.72% -> 57.16% | Helped |
| Add LLM-generated textual node features | BRIDGE · Reddit cross-domain, five-shot graph classification | accuracy: 84.42% -> 86.87% | Helped |
| Increase the number of variant embedding augmentations to K = 3 | BRIDGE · Computers graph classification, five-shot | accuracy: 65.0% | Helped |
| Increase spectral regularizer weight to γ = 0.1 | BRIDGE · Computers graph classification, five-shot | accuracy: 65.6% | Helped |
Surprising findings
- In very low-shot settings BRIDGE slightly lags some baselines such as ProNoG before its spectral regularizer takes effect.
Limitations
- Few-shot warm-up: lags some baselines at very low shot counts.
- Theoretical bound relies on Lipschitz assumptions and spectral approximations that are not tight in practice.
- Evaluation limited to six datasets from three domains and to node and graph classification.
Experimental setup
Datasets: Cora CiteSeer PubMed Photo Computers Reddit
Benchmarks: Cora CiteSeer PubMed Photo Computers Reddit
Metrics: accuracy
Baselines: GCN GAT GCC DGI InfoGraph GraphCL DSSL GraphACL GPPT GraphPrompt GraphPrompt+ GPF
Builds on: GraphPrompt GCOPE MDGPT ProNoG GPF
Closest papers by meaning
- Multi-Domain Graph Foundation Models: Robust Knowledge Transfer via Topology Alignment (ICML 2025 · similarity 0.90)
- GraphBridge: Towards Arbitrary Transfer Learning in GNNs (ICLR 2025 · similarity 0.90)
- Contextual Structure Knowledge Transfer for Graph Neural Networks (AAAI 2025 · similarity 0.89)
- Unified Graph Neural Networks Pre-training for Multi-domain Graphs (AAAI 2025 · similarity 0.88)
- GraphKeeper: Graph Domain-Incremental Learning via Knowledge Disentanglement and Preservation (NeurIPS 2025 · similarity 0.88)
- EvoluNet: Advancing Dynamic Non-IID Transfer Learning on Graphs (ICML 2024 · similarity 0.87)
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