# Leveraging Label Non-Uniformity for Node Classification in Graph Neural Networks

arXiv: https://arxiv.org/abs/2305.00139 · HTML: https://mlsanity.com/paper/2305.00139/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 29 Apr 2023.

## Builds on (most cited first, 29 of 29)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Learning to Drop: Robust Graph Neural Network via Topological Denoising](https://mlsanity.com/paper/2011.07057/) (2020)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks](https://mlsanity.com/paper/2110.12976/) (2021)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [Topology-Imbalance Learning for Semi-Supervised Node Classification](https://mlsanity.com/paper/2110.04099/) (2021)
- [Graph Geometry Interaction Learning](https://mlsanity.com/paper/2010.12135/) (2020)
- [Rethinking Graph Regularization for Graph Neural Networks](https://mlsanity.com/paper/2009.02027/) (2020)
- [On the Robustness of Graph Neural Diffusion to Topology Perturbations](https://mlsanity.com/paper/2209.07754/) (2022)
- [SGAT: Simplicial Graph Attention Network](https://mlsanity.com/paper/2207.11761/) (2022)
- [On distributional graph signals](https://mlsanity.com/paper/2302.11104/) (2023)
- [Distributional Signals for Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2304.03507/) (2023)

## Built on by (most cited first, 11 of 11)

- [Graph Neural Convection-Diffusion with Heterophily](https://mlsanity.com/paper/2305.16780/) (2023)
- [Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach](https://mlsanity.com/paper/2310.06396/) (2023)
- [Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND](https://mlsanity.com/paper/2404.17099/) (2024)
- [Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks](https://mlsanity.com/paper/2305.18965/) (2023)
- [Joint Graph Rewiring and Feature Denoising via Spectral Resonance](https://mlsanity.com/paper/2408.07191/) (2024)
- [Enhancing the Influence of Labels on Unlabeled Nodes in Graph Convolutional Networks](https://mlsanity.com/paper/2411.02279/) (2024)
- [FedSheafHN: Personalized Federated Learning on Graph-structured Data](https://mlsanity.com/paper/2405.16056/) (2024)
- [Krait: A Backdoor Attack Against Graph Prompt Tuning](https://mlsanity.com/paper/2407.13068/) (2024)
- [Graph Neural Networks with a Distribution of Parametrized Graphs](https://mlsanity.com/paper/2310.16401/) (2023)
- [Graph Distribution-valued Signals: A Wasserstein Space Perspective](https://mlsanity.com/paper/2509.25802/) (2025)
- [FSD-CAP: Fractional Subgraph Diffusion with Class-Aware Propagation for Graph Feature Imputation](https://mlsanity.com/paper/2601.18938/) (2026)

## Abstract (arXiv)

In node classification using graph neural networks (GNNs), a typical model generates logits for different class labels at each node. A softmax layer often outputs a label prediction based on the largest logit. We demonstrate that it is possible to infer hidden graph structural information from the dataset using these logits. We introduce the key notion of label non-uniformity, which is derived from the Wasserstein distance between the softmax distribution of the logits and the uniform distribution. We demonstrate that nodes with small label non-uniformity are harder to classify correctly. We theoretically analyze how the label non-uniformity varies across the graph, which provides insights into boosting the model performance: increasing training samples with high non-uniformity or dropping edges to reduce the maximal cut size of the node set of small non-uniformity. These mechanisms can be easily added to a base GNN model. Experimental results demonstrate that our approach improves the performance of many benchmark base models.