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DeepSN: A Sheaf Neural Framework for Influence Maximization
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Proposes DeepSN, a sheaf reaction-diffusion GNN that learns influence diffusion and a Louvain-subgraph-based seed selection, evaluated on IM under IC, LT and SIS models.
Problem
Influence maximization is hard due to exponential seed-set search and complex, non-progressive diffusion dynamics that standard GNNs (oversmoothing) fail to capture.
Approach
Models influence propagation as a sheaf diffusion-reaction process with learnable sheaf coefficients and pointwise/coupled reaction terms, and selects seeds within Louvain-partitioned subgraphs of a learned weighted graph to shrink the search space.
Key results
- On Cora-ML under LT with 20% seeds, DeepSN reaches 95.3% influence spread versus 94.1 for DeepIM (best baseline in that column).
- Under SIS on Cora-ML at 1% seeds, DeepSN_SP reaches 16.8 vs 7.1 for DeepIM.
- Influence-estimation MAE for DeepSN is reported as lower than GCN, GAT, GraphSAGE and DSN across most IC, LT and SIS settings.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add pointwise and coupled reaction components (ablation) | DeepSN · Cora-ML, 1% seeds | average total influence (%): 9.7 -> 11.5 | Helped |
| add pointwise and coupled reaction components (ablation) | DeepSN · Cora-ML, 5% seeds | average total influence (%): 20.5 -> 25.6 | Helped |
| add pointwise and coupled reaction components (ablation) | DeepSN · Cora-ML, 10% seeds | average total influence (%): 32.8 -> 40.9 | Helped |
| add pointwise and coupled reaction components (ablation) | DeepSN · Cora-ML, 20% seeds | average total influence (%): 49.8 -> 52.8 | Helped |
| add pointwise dynamics (ablation) | DeepSN · Cora-ML, 10% seeds | average total influence (%): 34.0 -> 40.9 | Helped |
| add coupled dynamics (ablation) | DeepSN · Cora-ML, 10% seeds | average total influence (%): 37.9 -> 40.9 | Helped |
| use subgraph-based optimization instead of optimizing seeds over the entire network (ablation) | DeepSN · Cora-ML (SIS), 10% seeds | average total influence (%): 25.3 -> 34.2 | Helped |
| use sheaf coefficients instead of adjacency for subgraph division (ablation) | DeepSN · Cora-ML (SIS), 10% seeds | average total influence (%): 26.0 -> 34.2 | Helped |
| use the learned IM component instead of CELF (ablation) | DeepSN · Cora-ML (SIS), 10% seeds | average total influence (%): 30.6 -> 34.2 | Helped |
| use DeepSN instead of DeepIM | Influence maximization · Cora-ML (SIS), 10% seeds | influence spread: 21.9 -> 34.2 | Helped |
| use DeepSN instead of DeepIM | Influence maximization · Cora-ML (LT), 10% seeds | influence spread: 83.5 -> 68.2 | Hurt |
Surprising findings
- DeepSN underperforms or ties baselines on several settings, e.g. Cora-ML IC 5% (25.6 vs 28.1 for DeepIM) and Power Grid LT at 20% where DeepIM is higher.
Limitations
- Supports only two-state diffusion models; multi-state models are future work.
- DeepIM and other baselines outperform DeepSN in several settings (e.g. LT on Jazz/Random at some budgets).
Experimental setup
Datasets: Jazz Network Science Cora-ML Power Grid Random Digg
Benchmarks: Jazz Network Science Cora-ML Power Grid Random Digg
Metrics: average influence spread (%) MAE for influence estimation
Baselines: IMM OPIM SubSIM IMINFECTOR ToupleGDD PIANO DeepIM GCN GAT GraphSAGE DSN
Builds on: sheaf diffusion GNN (DSN) Louvain algorithm IMM CELF
Closest papers by meaning
- REM: A Scalable Reinforced Multi-Expert Framework for Multiplex Influence Maximization (AAAI 2025 · similarity 0.87)
- DiffIM: Differentiable Influence Minimization with Surrogate Modeling and Continuous Relaxation (AAAI 2025 · similarity 0.87)
- A Generalized Neural Diffusion Framework on Graphs (AAAI 2024 · similarity 0.86)
- Hyperparametric Robust and Dynamic Influence Maximization (AAAI 2025 · similarity 0.86)
- DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Models (ICLR 2024 · similarity 0.85)
- Influence Functions for Edge Edits in Non-Convex Graph Neural Networks (NeurIPS 2025 · similarity 0.85)
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