Node Dependent Local Smoothing for Scalable Graph Learning
Abstract
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.
Benchmark Results
Tested on 2 datasets 5 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphSAGE+CNA | 0.9418
±0.0033 | |
| 2 | GCN+CNA | 0.9366
±0.0048 | |
| 3 | TransformerConv | 0.9350
±0.0058 | |
| 21 | GCN | 0.9004 best reported | best at pub: SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels (2017) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 39 | SAGE | 0.8911
±0.0012 | |
| 44 | GAT | 0.8897
±0.0014 best reported | best at pub: Learned Low Precision Graph Neural Networks (2020) |
| 108 | APPNP | 0.8787 best reported | best at pub: Orthogonal Graph Neural Networks (AAAI 2021) best today: Feature Transportation Improves Graph Neural Networks (AAAI 2023) |
| 161 | SIGN | 0.8672
±0.0137 best reported | best at pub: ROD: Reception-aware Online Distillation for Sparse Graphs (KDD 2021) |
| 195 | JK-Net | 0.8579
±0.0001 best reported | best at pub: ROD: Reception-aware Online Distillation for Sparse Graphs (KDD 2021) |
| 223 | SGC | 0.8509
±0.0648 best reported | best at pub: Learning Conjoint Attentions for Graph Neural Nets (NeurIPS 2021) |
| 246 | NDLS | 0.8460
±0.0050 | This paper |
| 259 | DAGNN (Gate) | 0.8440
±0.0050 | This paper |
| 279 | SGC+NDLS-L | 0.8420
±0.0020 | This paper |
| 290 | NDLS-F+MLP | 0.8410
±0.0060 | This paper |
| 308 | GBP | 0.8390
±0.0070 | This paper |
| 366 | S^2GC | 0.8350
±0.0020 best reported | best today: Diffusion on Graph: Augmentation of Graph Structure for Node Classification (TMLR 2025) |
| 382 | AP-GCN | 0.8340
±0.0030 | This paper |
| 473 | PPRGo | 0.8240
±0.0020 | This paper |
| 724 | MLP | 0.7768 best reported | best at pub: Adversarial Graph Disentanglement with Component-specific Aggregation (2021) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
OGB
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | SGC | 0.7910 best reported | best at pub: Graph Attention MLP with Reliable Label Utilization (2021) best today: Unifews: You Need Fewer Operations for Efficient Graph Neural Networks (ICML 2024) |
| 2 | GAMLP | 0.7036
±0.0002 | |
| 3 | GLEM-GNN | 0.7036
±0.0002 | |
| 35 | SAGE | 0.6644
±0.0017 | |
| 38 | SIGN | 0.6636
±0.0005 best reported | best at pub: Scalable and Adaptive Graph Neural Networks with Self-Label-Enhanced Training (2021) best today: Graph Learning at Scale: Characterizing and Optimizing Pre-Propagation GNNs (2025) |
| 55 | NDLS | 0.6561
±0.0029 best reported | best today: Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited (NeurIPS 2022) Difference within reported uncertainty; not counted as underperformance. |
| 58 | NDLS-F+MLP | 0.6530
±0.0050 | This paper |
| 59 | GBP | 0.6524
±0.0013 best reported | best at pub: Evaluating Deep Graph Neural Networks (2021) best today: Model Degradation Hinders Deep Graph Neural Networks (KDD 2022) Difference within reported uncertainty; not counted as underperformance. |
| 63 | SGC+NDLS-L | 0.6490
±0.0030 | This paper |
| 64 | S^2GC | 0.6473
±0.0021 best reported | best at pub: Evaluating Deep Graph Neural Networks (2021) best today: Model Degradation Hinders Deep Graph Neural Networks (KDD 2022) Difference within reported uncertainty; not counted as underperformance. |
| 66 | MLP+NDLS-L | 0.6460
±0.0040 | This paper |
| 70 | MLP+C&S | 0.6390 | This paper |
| 95 | MLP | 0.4960
±0.0030 best reported | best at pub: SIGN: Scalable Inception Graph Neural Networks (2020) |
