# GRAND+: Scalable Graph Random Neural Networks

arXiv: https://arxiv.org/abs/2203.06389 · HTML: https://mlsanity.com/paper/2203.06389/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 32 references that are in the map.
- First posted on arXiv 12 Mar 2022.

## Builds on (most cited first, 26 of 26)

- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [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)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Layer-Dependent Importance Sampling for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1911.07323/) (2019)
- [Scaling Graph Neural Networks with Approximate PageRank](https://mlsanity.com/paper/2007.01570/) (2020)
- [Scalable Graph Neural Networks via Bidirectional Propagation](https://mlsanity.com/paper/2010.15421/) (2020)
- [Optimizing Generalized PageRank Methods for Seed-Expansion Community Detection](https://mlsanity.com/paper/1905.10881/) (2019)
- [Semi-supervised Learning on Graphs with Generative Adversarial Nets](https://mlsanity.com/paper/1809.00130/) (2018)
- [Fast Bidirectional Probability Estimation in Markov Models](https://mlsanity.com/paper/1507.05998/) (2015)

## Built on by (most cited first, 25 of 25)

- [NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs](https://mlsanity.com/paper/2206.04910/) (2022)
- [FedGTA: Topology-aware Averaging for Federated Graph Learning](https://mlsanity.com/paper/2401.11755/) (2024)
- [VCR-Graphormer: A Mini-batch Graph Transformer via Virtual Connections](https://mlsanity.com/paper/2403.16030/) (2024)
- [Unifying Generation and Prediction on Graphs with Latent Graph Diffusion](https://mlsanity.com/paper/2402.02518/) (2024)
- [Learning Graph Quantized Tokenizers](https://mlsanity.com/paper/2410.13798/) (2024)
- [Rethinking Node-wise Propagation for Large-scale Graph Learning](https://mlsanity.com/paper/2402.06128/) (2024)
- [RSC: Accelerating Graph Neural Networks Training via Randomized Sparse Computations](https://mlsanity.com/paper/2210.10737/) (2022)
- [MA-GCL: Model Augmentation Tricks for Graph Contrastive Learning](https://mlsanity.com/paper/2212.07035/) (2022)
- [A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectiveness](https://mlsanity.com/paper/2406.09675/) (2024)
- [Tokenized Graph Transformer with Neighborhood Augmentation for Node Classification in Large Graphs](https://mlsanity.com/paper/2305.12677/) (2023)
- [Diffusion on Graph: Augmentation of Graph Structure for Node Classification](https://mlsanity.com/paper/2503.12563/) (2025)
- [Label Efficient Regularization and Propagation for Graph Node Classification](https://mlsanity.com/paper/2204.08646/) (2022)
- [Neural Machine Translation with Dynamic Graph Convolutional Decoder](https://mlsanity.com/paper/2305.17698/) (2023)
- [Tokenphormer: Structure-aware Multi-token Graph Transformer for Node Classification](https://mlsanity.com/paper/2412.15302/) (2024)
- [Unifying Graph Contrastive Learning via Graph Message Augmentation](https://mlsanity.com/paper/2401.03638/) (2024)
- [Infinite-Horizon Graph Filters: Leveraging Power Series to Enhance Sparse Information Aggregation](https://mlsanity.com/paper/2401.09943/) (2024)
- [Toward Scalable Graph Unlearning: A Node Influence Maximization based Approach](https://mlsanity.com/paper/2501.11823/) (2025)
- [ScaDyG:A New Paradigm for Large-scale Dynamic Graph Learning](https://mlsanity.com/paper/2501.16002/) (2025)
- [ScaleGNN: Towards Scalable Graph Neural Networks via Adaptive High-order Neighboring Feature Fusion](https://mlsanity.com/paper/2504.15920/) (2025)
- [Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification](https://mlsanity.com/paper/2402.09600/) (2024)
- [Trading off Quality for Efficiency of Community Detection: An Inductive Method across Graphs](https://mlsanity.com/paper/2209.14825/) (2022)
- [Learning a Mini-batch Graph Transformer via Two-stage Interaction Augmentation](https://mlsanity.com/paper/2407.09904/) (2024)
- [DAM-GT: Dual Positional Encoding-Based Attention Masking Graph Transformer for Node Classification](https://mlsanity.com/paper/2505.17660/) (2025)
- [CoATA: Effective Co-Augmentation of Topology and Attribute for Graph Neural Networks](https://mlsanity.com/paper/2506.22299/) (2025)
- [Graph Cascades: Contagion-Based Mesoscopic Rewiring for Structure-Aware Graph Machine Learning](https://mlsanity.com/paper/2606.05046/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have been widely adopted for semi-supervised learning on graphs. A recent study shows that the graph random neural network (GRAND) model can generate state-of-the-art performance for this problem. However, it is difficult for GRAND to handle large-scale graphs since its effectiveness relies on computationally expensive data augmentation procedures. In this work, we present a scalable and high-performance GNN framework GRAND+ for semi-supervised graph learning. To address the above issue, we develop a generalized forward push (GFPush) algorithm in GRAND+ to pre-compute a general propagation matrix and employ it to perform graph data augmentation in a mini-batch manner. We show that both the low time and space complexities of GFPush enable GRAND+ to efficiently scale to large graphs. Furthermore, we introduce a confidence-aware consistency loss into the model optimization of GRAND+, facilitating GRAND+'s generalization superiority. We conduct extensive experiments on seven public datasets of different sizes. The results demonstrate that GRAND+ 1) is able to scale to large graphs and costs less running time than existing scalable GNNs, and 2) can offer consistent accuracy improvements over both full-batch and scalable GNNs across all datasets.