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DeepSN: A Sheaf Neural Framework for Influence Maximization

Asela Hevapathige, Qing Wang, Ahad N. Zehmakan

TL;DR

This work tackles influence maximization by marrying a diffusion process defined on sheaves with reaction dynamics, yielding a learning-based diffusion model that captures complex influence patterns. The two-phase DeepSN framework first learns influence propagation with a novel Sheaf GNN and then reduces seed-search complexity via a subgraph-based objective, guided by learned connectivity from sheaf coefficients. Empirically, DeepSN outperforms strong baselines across IC, LT, and SIS on both real and synthetic networks, with notable improvements under non-progressive SIS dynamics and clear gains from the reaction terms and subgraph strategy. The approach advances practical IM by enabling data-driven, topology-aware diffusion modeling and scalable seed selection, with potential impact on viral marketing, information spread, and network interventions.

Abstract

Influence maximization is key topic in data mining, with broad applications in social network analysis and viral marketing. In recent years, researchers have increasingly turned to machine learning techniques to address this problem. They have developed methods to learn the underlying diffusion processes in a data-driven manner, which enhances the generalizability of the solution, and have designed optimization objectives to identify the optimal seed set. Nonetheless, two fundamental gaps remain unsolved: (1) Graph Neural Networks (GNNs) are increasingly used to learn diffusion models, but in their traditional form, they often fail to capture the complex dynamics of influence diffusion, (2) Designing optimization objectives is challenging due to combinatorial explosion when solving this problem. To address these challenges, we propose a novel framework, DeepSN. Our framework employs sheaf neural diffusion to learn diverse influence patterns in a data-driven, end-to-end manner, providing enhanced separability in capturing diffusion characteristics. We also propose an optimization technique that accounts for overlapping influence between vertices, which helps to reduce the search space and identify the optimal seed set effectively and efficiently. Finally, we conduct extensive experiments on both synthetic and real-world datasets to demonstrate the effectiveness of our framework.

DeepSN: A Sheaf Neural Framework for Influence Maximization

TL;DR

This work tackles influence maximization by marrying a diffusion process defined on sheaves with reaction dynamics, yielding a learning-based diffusion model that captures complex influence patterns. The two-phase DeepSN framework first learns influence propagation with a novel Sheaf GNN and then reduces seed-search complexity via a subgraph-based objective, guided by learned connectivity from sheaf coefficients. Empirically, DeepSN outperforms strong baselines across IC, LT, and SIS on both real and synthetic networks, with notable improvements under non-progressive SIS dynamics and clear gains from the reaction terms and subgraph strategy. The approach advances practical IM by enabling data-driven, topology-aware diffusion modeling and scalable seed selection, with potential impact on viral marketing, information spread, and network interventions.

Abstract

Influence maximization is key topic in data mining, with broad applications in social network analysis and viral marketing. In recent years, researchers have increasingly turned to machine learning techniques to address this problem. They have developed methods to learn the underlying diffusion processes in a data-driven manner, which enhances the generalizability of the solution, and have designed optimization objectives to identify the optimal seed set. Nonetheless, two fundamental gaps remain unsolved: (1) Graph Neural Networks (GNNs) are increasingly used to learn diffusion models, but in their traditional form, they often fail to capture the complex dynamics of influence diffusion, (2) Designing optimization objectives is challenging due to combinatorial explosion when solving this problem. To address these challenges, we propose a novel framework, DeepSN. Our framework employs sheaf neural diffusion to learn diverse influence patterns in a data-driven, end-to-end manner, providing enhanced separability in capturing diffusion characteristics. We also propose an optimization technique that accounts for overlapping influence between vertices, which helps to reduce the search space and identify the optimal seed set effectively and efficiently. Finally, we conduct extensive experiments on both synthetic and real-world datasets to demonstrate the effectiveness of our framework.

Paper Structure

This paper contains 37 sections, 12 theorems, 36 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Influence Maximization Methods
  4. Diffusion GNNs
  5. Problem Formulation
  6. Influence Maximization
  7. Our Work
  8. Learning to Estimate Influence
  9. Topological Sheaf Diffusion
  10. Sheaf Reaction Diffusion
  11. Reaction Operators
  12. Pointwise Dynamics
  13. Coupled Dynamics
  14. Stability of Reaction Diffusion
  15. Sheaf GNN Training
  16. ...and 22 more sections

Key Result

Lemma 1

Let $\lambda_{\text{min}}$ denote the smallest eigenvalue of $L_\mathcal{F}$. $\hat{L}_\mathcal{F}$ is positive definite if and only if $\epsilon > -\lambda_{\text{min}}$.

Figures (4)

  • Figure 1: The DeepSN framework consists of two phases: (a) learning to estimate influence with sheaf GNN; b) optimizing seed selection using the subgraphs, IM model, and trained sheaf GNN.
  • Figure 2: Performance of DeepSN for influence estimation in terms of MAE (Mean Absolute Error), compared to baseline methods. Results under IC model are provided in the appendix.
  • Figure 3: Impact of layer depth and feature dimension on DeepSN's performance
  • Figure 4: Performance of DeepSN for influence estimation under IC model.

Theorems & Definitions (23)

  • Definition 1: Influence Maximization Problem
  • Definition 2: Cellular Sheaf
  • Definition 3: Non-linear Sheaf Laplacian
  • Lemma 1
  • Remark 1
  • Lemma 2
  • Lemma 3
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • ...and 13 more