# Lying Graph Convolution: Learning to Lie for Node Classification Tasks

arXiv: https://arxiv.org/abs/2405.01247 · HTML: https://mlsanity.com/paper/2405.01247/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 43 references that are in the map.
- First posted on arXiv 2 May 2024.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [GNN-FiLM: Graph Neural Networks with Feature-wise Linear Modulation](https://mlsanity.com/paper/1906.12192/) (2019)
- [Anti-Symmetric DGN: a stable architecture for Deep Graph Networks](https://mlsanity.com/paper/2210.09789/) (2022)
- [Dissecting the Diffusion Process in Linear Graph Convolutional Networks](https://mlsanity.com/paper/2102.10739/) (2021)
- [Simplifying approach to Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2111.06748/) (2021)
- [High-Order Pooling for Graph Neural Networks with Tensor Decomposition](https://mlsanity.com/paper/2205.11691/) (2022)
- [Beyond Real-world Benchmark Datasets: An Empirical Study of Node Classification with GNNs](https://mlsanity.com/paper/2206.09144/) (2022)
- [2-hop Neighbor Class Similarity (2NCS): A graph structural metric indicative of graph neural network performance](https://mlsanity.com/paper/2212.13202/) (2022)
- [Investigating the Interplay between Features and Structures in Graph Learning](https://mlsanity.com/paper/2308.09570/) (2023)
- [Learning from Non-Binary Constituency Trees via Tensor Decomposition](https://mlsanity.com/paper/2011.00860/) (2020)

## Abstract (arXiv)

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.