# Node Dependent Local Smoothing for Scalable Graph Learning

arXiv: https://arxiv.org/abs/2110.14377 · HTML: https://mlsanity.com/paper/2110.14377/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 27 of 27)

- [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)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [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)
- [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)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)
- [Scaling Graph Neural Networks with Approximate PageRank](https://mlsanity.com/paper/2007.01570/) (2020)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Attributed Graph Clustering via Adaptive Graph Convolution](https://mlsanity.com/paper/1906.01210/) (2019)
- [Adaptive Graph Encoder for Attributed Graph Embedding](https://mlsanity.com/paper/2007.01594/) (2020)
- [Scalable Graph Neural Networks via Bidirectional Propagation](https://mlsanity.com/paper/2010.15421/) (2020)
- [Policy-GNN: Aggregation Optimization for Graph Neural Networks](https://mlsanity.com/paper/2006.15097/) (2020)
- [OpenBox: A Generalized Black-box Optimization Service](https://mlsanity.com/paper/2106.00421/) (2021)
- [Adaptive Propagation Graph Convolutional Network](https://mlsanity.com/paper/2002.10306/) (2020)
- [Evaluating Deep Graph Neural Networks](https://mlsanity.com/paper/2108.00955/) (2021)
- [ROD: Reception-aware Online Distillation for Sparse Graphs](https://mlsanity.com/paper/2107.11789/) (2021)

## Built on by (most cited first, 30 of 45)

- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Graph Attention Multi-Layer Perceptron](https://mlsanity.com/paper/2206.04355/) (2022)
- [PaSca: a Graph Neural Architecture Search System under the Scalable Paradigm](https://mlsanity.com/paper/2203.00638/) (2022)
- [Graph Neural Networks with Learnable and Optimal Polynomial Bases](https://mlsanity.com/paper/2302.12432/) (2023)
- [PC-Conv: Unifying Homophily and Heterophily with Two-fold Filtering](https://mlsanity.com/paper/2312.14438/) (2023)
- [Model Degradation Hinders Deep Graph Neural Networks](https://mlsanity.com/paper/2206.04361/) (2022)
- [Rethinking and Accelerating Graph Condensation: A Training-Free Approach with Class Partition](https://mlsanity.com/paper/2405.13707/) (2024)
- [Partitioning Message Passing for Graph Fraud Detection](https://mlsanity.com/paper/2412.00020/) (2024)
- [Rethinking Node-wise Propagation for Large-scale Graph Learning](https://mlsanity.com/paper/2402.06128/) (2024)
- [Graph Neural Networks for Tabular Data Learning: A Survey with Taxonomy and Directions](https://mlsanity.com/paper/2401.02143/) (2024)
- [NAFS: A Simple yet Tough-to-beat Baseline for Graph Representation Learning](https://mlsanity.com/paper/2206.08583/) (2022)
- [SmoothGNN: Smoothing-aware GNN for Unsupervised Node Anomaly Detection](https://mlsanity.com/paper/2405.17525/) (2024)
- [Are GATs Out of Balance?](https://mlsanity.com/paper/2310.07235/) (2023)
- [Efficient Graph Neural Network Inference at Large Scale](https://mlsanity.com/paper/2211.00495/) (2022)
- [Accelerating Scalable Graph Neural Network Inference with Node-Adaptive Propagation](https://mlsanity.com/paper/2310.10998/) (2023)
- [Mixture of Weak & Strong Experts on Graphs](https://mlsanity.com/paper/2311.05185/) (2023)
- [From Cluster Assumption to Graph Convolution: Graph-based Semi-Supervised Learning Revisited](https://mlsanity.com/paper/2309.13599/) (2023)
- [GATE: How to Keep Out Intrusive Neighbors](https://mlsanity.com/paper/2406.00418/) (2024)
- [Mamba-Based Graph Convolutional Networks: Tackling Over-smoothing with Selective State Space](https://mlsanity.com/paper/2501.15461/) (2025)
- [View Space: Learning Representation across Arbitrary Graphs](https://mlsanity.com/paper/2512.11561/) (2025)
- [ZOOMER: Boosting Retrieval on Web-scale Graphs by Regions of Interest](https://mlsanity.com/paper/2203.12596/) (2022)
- [Steering Graph Neural Networks with Pinning Control](https://mlsanity.com/paper/2303.01265/) (2023)
- [Simplified PCNet with Robustness](https://mlsanity.com/paper/2403.03676/) (2024)
- [Unifews: You Need Fewer Operations for Efficient Graph Neural Networks](https://mlsanity.com/paper/2403.13268/) (2024)
- [TSC: A Simple Two-Sided Constraint against Over-Smoothing](https://mlsanity.com/paper/2408.03152/) (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)
- [CAMPA: Efficient and Aligned Multimodal Graph Learning via Decoupled Propagation and Aggregation](https://mlsanity.com/paper/2605.11468/) (2026)
- [LION: A Clifford Neural Paradigm for Multimodal-Attributed Graph Learning](https://mlsanity.com/paper/2608.24795/) (2026)
- [DFG-NAS: Deep and Flexible Graph Neural Architecture Search](https://mlsanity.com/paper/2206.08582/) (2022)

## Abstract (arXiv)

Recent works reveal that feature or label smoothing lies at the core of Graph Neural Networks (GNNs). Concretely, they show feature smoothing combined with simple linear regression achieves comparable performance with the carefully designed GNNs, and a simple MLP model with label smoothing of its prediction can outperform the vanilla GCN. Though an interesting finding, smoothing has not been well understood, especially regarding how to control the extent of smoothness. Intuitively, too small or too large smoothing iterations may cause under-smoothing or over-smoothing and can lead to sub-optimal performance. Moreover, the extent of smoothness is node-specific, depending on its degree and local structure. To this end, we propose a novel algorithm called node-dependent local smoothing (NDLS), which aims to control the smoothness of every node by setting a node-specific smoothing iteration. Specifically, NDLS computes influence scores based on the adjacency matrix and selects the iteration number by setting a threshold on the scores. Once selected, the iteration number can be applied to both feature smoothing and label smoothing. Experimental results demonstrate that NDLS enjoys high accuracy -- state-of-the-art performance on node classifications tasks, flexibility -- can be incorporated with any models, scalability and efficiency -- can support large scale graphs with fast training.