# Why Propagate Alone? Parallel Use of Labels and Features on Graphs

arXiv: https://arxiv.org/abs/2110.07190 · HTML: https://mlsanity.com/paper/2110.07190/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 14 Oct 2021.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Learning to Propagate Labels: Transductive Propagation Network for Few-shot Learning](https://mlsanity.com/paper/1805.10002/) (2018)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [Training Graph Neural Networks with 1000 Layers](https://mlsanity.com/paper/2106.07476/) (2021)
- [Unifying Graph Convolutional Neural Networks and Label Propagation](https://mlsanity.com/paper/2002.06755/) (2020)
- [LanczosNet: Multi-Scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1901.01484/) (2019)
- [Graph Neural Networks Inspired by Classical Iterative Algorithms](https://mlsanity.com/paper/2103.06064/) (2021)
- [Boost then Convolve: Gradient Boosting Meets Graph Neural Networks](https://mlsanity.com/paper/2101.08543/) (2021)
- [Bag of Tricks for Node Classification with Graph Neural Networks](https://mlsanity.com/paper/2103.13355/) (2021)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)

## Built on by (most cited first, 9 of 9)

- [Automated Data Curation for Robust Language Model Fine-Tuning](https://mlsanity.com/paper/2403.12776/) (2024)
- [Label Information Enhanced Fraud Detection against Low Homophily in Graphs](https://mlsanity.com/paper/2302.10407/) (2023)
- [4DBInfer: A 4D Benchmarking Toolbox for Graph-Centric Predictive Modeling on Relational DBs](https://mlsanity.com/paper/2404.18209/) (2024)
- [Training-free Graph Neural Networks and the Power of Labels as Features](https://mlsanity.com/paper/2404.19288/) (2024)
- [Unifying Label-inputted Graph Neural Networks with Deep Equilibrium Models](https://mlsanity.com/paper/2211.10629/) (2022)
- [BloomGML: Graph Machine Learning through the Lens of Bilevel Optimization](https://mlsanity.com/paper/2403.04763/) (2024)
- [Nonlinear Correct and Smooth for Semi-Supervised Learning](https://mlsanity.com/paper/2310.05757/) (2023)
- [ReDiSC: A Reparameterized Masked Diffusion Model for Scalable Node Classification with Structured Predictions](https://mlsanity.com/paper/2507.14484/) (2025)
- [InvWeaver: Deductive Feedback for Invariant Synthesis in Interacting-Loop Programs](https://mlsanity.com/paper/2607.05478/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) and label propagation represent two interrelated modeling strategies designed to exploit graph structure in tasks such as node property prediction. The former is typically based on stacked message-passing layers that share neighborhood information to transform node features into predictive embeddings. In contrast, the latter involves spreading label information to unlabeled nodes via a parameter-free diffusion process, but operates independently of the node features. Given then that the material difference is merely whether features or labels are smoothed across the graph, it is natural to consider combinations of the two for improving performance. In this regard, it has recently been proposed to use a randomly-selected portion of the training labels as GNN inputs, concatenated with the original node features for making predictions on the remaining labels. This so-called label trick accommodates the parallel use of features and labels, and is foundational to many of the top-ranking submissions on the Open Graph Benchmark (OGB) leaderboard. And yet despite its wide-spread adoption, thus far there has been little attempt to carefully unpack exactly what statistical properties the label trick introduces into the training pipeline, intended or otherwise. To this end, we prove that under certain simplifying assumptions, the stochastic label trick can be reduced to an interpretable, deterministic training objective composed of two factors. The first is a data-fitting term that naturally resolves potential label leakage issues, while the second serves as a regularization factor conditioned on graph structure that adapts to graph size and connectivity. Later, we leverage this perspective to motivate a broader range of label trick use cases, and provide experiments to verify the efficacy of these extensions.