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Lying Graph Convolution: Learning to Lie for Node Classification Tasks

Daniele Castellana

TL;DR

This work addresses node classification across graphs with varying homophily by introducing Lying-GCN, an adaptive propagation scheme inspired by opinion dynamics where nodes may lie about their private embeddings when sharing messages. The method defines per-edge, per-channel lying weights that modulate messages, resulting in an asymmetric diffusion process whose dynamics are analyzed via a spectral view of the operator E = \tilde{L}^{sym} ⊙ (Z+I) and the resulting complex eigenvalues that induce early oscillations. Empirically, Lying-GCN improves performance on heterophilic graphs and remains competitive on homophilic graphs, with Lying-GCNII delivering robust results in deeper architectures and often matching or surpassing state-of-the-art baselines. The work highlights that adaptively modulated diffusion per channel can address heterophily without sacrificing homophily performance, offering a complementary tool alongside existing techniques like GCNII and attention-based methods.

Abstract

In the context of machine learning for graphs, many researchers have empirically observed that Deep Graph Networks (DGNs) perform favourably on node classification tasks when the graph structure is homophilic (\ie adjacent nodes are similar). In this paper, we introduce Lying-GCN, a new DGN inspired by opinion dynamics that can adaptively work in both the heterophilic and the homophilic setting. At each layer, each agent (node) shares its own opinions (node embeddings) with its neighbours. Instead of sharing its opinion directly as in GCN, we introduce a mechanism which allows agents to lie. Such a mechanism is adaptive, thus the agents learn how and when to lie according to the task that should be solved. We provide a characterisation of our proposal in terms of dynamical systems, by studying the spectral property of the coefficient matrix of the system. While the steady state of the system collapses to zero, we believe the lying mechanism is still usable to solve node classification tasks. We empirically prove our belief on both synthetic and real-world datasets, by showing that the lying mechanism allows to increase the performances in the heterophilic setting without harming the results in the homophilic one.

Lying Graph Convolution: Learning to Lie for Node Classification Tasks

TL;DR

This work addresses node classification across graphs with varying homophily by introducing Lying-GCN, an adaptive propagation scheme inspired by opinion dynamics where nodes may lie about their private embeddings when sharing messages. The method defines per-edge, per-channel lying weights that modulate messages, resulting in an asymmetric diffusion process whose dynamics are analyzed via a spectral view of the operator E = \tilde{L}^{sym} ⊙ (Z+I) and the resulting complex eigenvalues that induce early oscillations. Empirically, Lying-GCN improves performance on heterophilic graphs and remains competitive on homophilic graphs, with Lying-GCNII delivering robust results in deeper architectures and often matching or surpassing state-of-the-art baselines. The work highlights that adaptively modulated diffusion per channel can address heterophily without sacrificing homophily performance, offering a complementary tool alongside existing techniques like GCNII and attention-based methods.

Abstract

In the context of machine learning for graphs, many researchers have empirically observed that Deep Graph Networks (DGNs) perform favourably on node classification tasks when the graph structure is homophilic (\ie adjacent nodes are similar). In this paper, we introduce Lying-GCN, a new DGN inspired by opinion dynamics that can adaptively work in both the heterophilic and the homophilic setting. At each layer, each agent (node) shares its own opinions (node embeddings) with its neighbours. Instead of sharing its opinion directly as in GCN, we introduce a mechanism which allows agents to lie. Such a mechanism is adaptive, thus the agents learn how and when to lie according to the task that should be solved. We provide a characterisation of our proposal in terms of dynamical systems, by studying the spectral property of the coefficient matrix of the system. While the steady state of the system collapses to zero, we believe the lying mechanism is still usable to solve node classification tasks. We empirically prove our belief on both synthetic and real-world datasets, by showing that the lying mechanism allows to increase the performances in the heterophilic setting without harming the results in the homophilic one.
Paper Structure (12 sections, 1 theorem, 10 equations, 3 figures, 2 tables)

This paper contains 12 sections, 1 theorem, 10 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Opinion Dynamics on Graphs
  4. Diffusion & Deep Graph Networks
  5. Lying Graph Convolutional Network
  6. Computational Complexity
  7. The Lying Diffusion Process
  8. Other Related Works
  9. Experiments & Results
  10. Synthetic Experiments
  11. Real-world Experiments
  12. Conclusion

Key Result

Proposition 1

The real part of each non-zero eigenvalue of $E$ is strictly positive.

Figures (3)

  • Figure 1: From left to right, the evolution of the heat, sheaf and lying diffusion process on a chain graph with three nodes. In each plot, we show how the value attached to each node evolves over time.
  • Figure 2: t-SNE plot of node information on the tripartite graph: (a) the input features, (b) the node embeddings of the best GCNII configuration, and (c) the node embeddings of the best Lying-GCNII configuration.
  • Figure 3: Validation accuracy w.r.t. the number of layers for all models on synthetic datasets.

Theorems & Definitions (1)

  • Proposition 1