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Learning Divergence Fields for Shift-Robust Graph Representations
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Proposes GLIND, a geometric diffusion model with stochastic, variationally inferred divergence fields and a causal deconfounded regularizer, instantiated as GCN/GAT/Transformer-style layers for out-of-distribution generalization on interdependent data.
Problem
Generalization under distribution shift for interdependent data (graphs or implicit geometries), where the proximity structure differs between training and testing domains.
Approach
Generalizes diffusion-equation message passing with stochastic diffusivity sampled from a variational multinomial over K hypotheses, and derives a step-wise re-weighted KL regularizer (model-free prior via a pseudo-dataset mixture of posteriors) from deconfounded causal learning to favor stable input-output relations across domains.
Key results
- On Arxiv 2018-2020 test split, GLIND-gcn and GLIND-gat reach 57.06% and 59.71% accuracy, reported as 23.8% and 26.6% improvements over the runner-ups.
- On DPPIN, GLIND-Trans attains the lowest RMSE in all seven test domains, with an average 21.6% RMSE reduction over the runner-up.
- On CIFAR and STL with unobserved geometry, GLIND variants outperform ERM and OOD baselines (e.g., GLIND-gcn 79.24% on CIFAR at 150 degrees vs. 72.30% ERM-GCN).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Glind-GCN instead of the strongest GCN baseline | GCN · Arxiv 2018-2020 | accuracy: 46.09 ± 0.58 -> 57.06 ± 1.21 | Helped |
| Use Glind-GAT instead of the strongest GAT baseline | GAT · Arxiv 2018-2020 | accuracy: 47.17 ± 0.84 -> 59.71 ± 0.53 | Helped |
| Use Glind-Trans instead of the runner-up | DIFFormer · DPPIN test domains | RMSE: 21.6% | Helped |
| Remove the residual link (ablation) | Glind · STL | accuracy | Hurt |
| Remove self-loop feature aggregation (ablation) | Glind · STL | accuracy | Hurt |
| Set the number of branches to K=1 (ablation) | Glind · STL | accuracy | Hurt |
| Remove the KL regularization term (ablation) | Glind · STL | accuracy | Hurt |
| Replace the pseudo-posterior mixture prior with the average variational posterior (ablation) | Glind · STL | accuracy | Hurt |
| Vary the diffusivity hypothesis count K (ablation) | Glind-GCN · Arxiv | accuracy | Mixed |
Limitations
- Stochastic branching and pseudo-dataset prior add hyperparameters (K, T, tau) that need grid search
- Evaluation limited to a small set of datasets and synthetic kNN geometries for image data
Experimental setup
Datasets: Twitch Arxiv DPPIN STL-10 CIFAR-10
Benchmarks: Arxiv Twitch DPPIN STL-10 CIFAR-10
Metrics: accuracy ROC-AUC RMSE
Baselines: ERM IRM GroupDRO DANN Mixup EERM
Builds on: DIFFormer GCN GAT EERM
Closest papers by meaning
- Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold (NeurIPS 2026 · similarity 0.88)
- SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusion (ICML 2025 · similarity 0.87)
- A Generalized Neural Diffusion Framework on Graphs (AAAI 2024 · similarity 0.87)
- Quantifying Distributional Invariance in Causal Subgraph for IRM-Free Graph Generalization (NeurIPS 2025 · similarity 0.87)
- Out-of-Distribution Generalization on Graphs via Progressive Inference (AAAI 2025 · similarity 0.87)
- On Divergence Measures for Training GFlowNets (NeurIPS 2024 · similarity 0.87)
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