Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Learning Network Dismantling Without Handcrafted Inputs

Haozhe Tian, Pietro Ferraro, Robert Shorten, Mahdi Jalili, Homayoun Hamedmoghadam

TL;DR

This work tackles network dismantling, an NP-hard problem, by learning a purely data-driven dismantling policy that operates on adjacency information alone. The proposed model, MIND, employs an all-ones, multi-head attention encoder (MIND-AM) and a history-aware mechanism (MIND-MP) to capture structural roles without handcrafted features, coupled with an omni-node in the decoder for global state awareness. A diversified synthetic training pipeline with degree-preserving rewiring and entropy-regularized RL (SAC) enables strong generalization to large real networks, achieving state-of-the-art dismantling performance with linear-time complexity. The approach reduces reliance on hand-engineered inputs, demonstrates scalability to networks with millions of nodes, and offers potential applicability to a broad class of graph-inference problems.

Abstract

The application of message-passing Graph Neural Networks has been a breakthrough for important network science problems. However, the competitive performance often relies on using handcrafted structural features as inputs, which increases computational cost and introduces bias into the otherwise purely data-driven network representations. Here, we eliminate the need for handcrafted features by introducing an attention mechanism and utilizing message-iteration profiles, in addition to an effective algorithmic approach to generate a structurally diverse training set of small synthetic networks. Thereby, we build an expressive message-passing framework and use it to efficiently solve the NP-hard problem of Network Dismantling, virtually equivalent to vital node identification, with significant real-world applications. Trained solely on diversified synthetic networks, our proposed model -- MIND: Message Iteration Network Dismantler -- generalizes to large, unseen real networks with millions of nodes, outperforming state-of-the-art network dismantling methods. Increased efficiency and generalizability of the proposed model can be leveraged beyond dismantling in a range of complex network problems.

Learning Network Dismantling Without Handcrafted Inputs

TL;DR

This work tackles network dismantling, an NP-hard problem, by learning a purely data-driven dismantling policy that operates on adjacency information alone. The proposed model, MIND, employs an all-ones, multi-head attention encoder (MIND-AM) and a history-aware mechanism (MIND-MP) to capture structural roles without handcrafted features, coupled with an omni-node in the decoder for global state awareness. A diversified synthetic training pipeline with degree-preserving rewiring and entropy-regularized RL (SAC) enables strong generalization to large real networks, achieving state-of-the-art dismantling performance with linear-time complexity. The approach reduces reliance on hand-engineered inputs, demonstrates scalability to networks with millions of nodes, and offers potential applicability to a broad class of graph-inference problems.

Abstract

The application of message-passing Graph Neural Networks has been a breakthrough for important network science problems. However, the competitive performance often relies on using handcrafted structural features as inputs, which increases computational cost and introduces bias into the otherwise purely data-driven network representations. Here, we eliminate the need for handcrafted features by introducing an attention mechanism and utilizing message-iteration profiles, in addition to an effective algorithmic approach to generate a structurally diverse training set of small synthetic networks. Thereby, we build an expressive message-passing framework and use it to efficiently solve the NP-hard problem of Network Dismantling, virtually equivalent to vital node identification, with significant real-world applications. Trained solely on diversified synthetic networks, our proposed model -- MIND: Message Iteration Network Dismantler -- generalizes to large, unseen real networks with millions of nodes, outperforming state-of-the-art network dismantling methods. Increased efficiency and generalizability of the proposed model can be leveraged beyond dismantling in a range of complex network problems.

Paper Structure

This paper contains 31 sections, 2 theorems, 31 equations, 6 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Reinforcement Learning
  4. Graph Neural Networks
  5. Network Dismantling via Machine Learning
  6. Network Dismantling as an RL Problem
  7. Methodology
  8. GNN Encoder
  9. All-to-One Attention Mechanism
  10. Message Iteration Profiles
  11. NN Decoder
  12. Systematically Diversified Training Networks
  13. Entropy-Regularized Policy Learning
  14. Experiments
  15. Result on Real Networks
  16. ...and 16 more sections

Key Result

Theorem 1

Assume $A_\alpha$ and $W$ are both diagonalizable with respective primary eigenvectors $u_1 \in \mathbb{R}^N$ and $v_1 \in \mathbb{R}^F$, whose corresponding eigenvalues are $\lambda_1$ and $\mu_1$, such that $|\lambda_1| > |\lambda_n|$ and $|\mu_1| > |\mu_n|$ for all $n \ne 1$. Then, for any initia In particular, node embeddings $e_i^{(k)}$ converge to a scalar multiple of $v_1^\top$: i.e., all

Figures (6)

  • Figure 1: (a) The original social network from the FilmTrust project guo2016novel with 610 nodes. (b) The dismantled network by MIND, down to a 10% relative Largest Connected Component (LCC) size. (c) Relative LCC size versus the fraction of nodes removed, comparing MIND with two state-of-the-art methods. (The 5 largest components are color-coded in network plots.)
  • Figure 2: Dismantling performance of MIND and the baseline methods on (a) biological, (b) social, (c) information, and (d) technological networks. The scatter plots display the AUC of dismantling for all methods normalized relative to that of MIND at 100 (AUC above 100 denotes worse performance than MIND). The bar plots summarize the overall performance of the methods in each network domain, with shorter bars corresponding to lower average AUC and thus stronger dismantling performance.
  • Figure 3: Dismantling performance of MIND and the baseline methods on synthetic networks (ER, CM, and SBM) of varying sizes. The scatter plot compares the dismantling performance of all methods normalized for each network relative to MIND, and the bar plot summarizes the overall performance. The AUCs are averaged over 10 realizations.
  • Figure 4: (a) Relative LCC size during the dismantling of an ER network with $1$ k nodes. We compare the node dismantling sequence derived (by PCA) from a set of heuristics with those generated by (b) GDM and (c) MIND; Spearman rank correlation coefficient $R$ and the regression (solid line) with confidence interval (shaded area) are shown on the plots. The heuristic removal sequence is derived from the principal component of GDM’s input node features.
  • Figure 5: The validation AUC during training (mean$\pm$std). MIND is compared against: i) GATv2; ii) GCN; iii) MIND without MIND-AM (the all-to-one attention mechanism); and iv) MIND without MIND-MP (the message-profile over iterations).
  • ...and 1 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Lemma 1
  • proof