ROD: Reception-aware Online Distillation for Sparse Graphs
Abstract
Graph neural networks (GNNs) have been widely used in many graph-based tasks such as node classification, link prediction, and node clustering. However, GNNs gain their performance benefits mainly from performing the feature propagation and smoothing across the edges of the graph, thus requiring sufficient connectivity and label information for effective propagation. Unfortunately, many real-world networks are sparse in terms of both edges and labels, leading to sub-optimal performance of GNNs. Recent interest in this sparse problem has focused on the self-training approach, which expands supervised signals with pseudo labels. Nevertheless, the self-training approach inherently cannot realize the full potential of refining the learning performance on sparse graphs due to the unsatisfactory quality and quantity of pseudo labels. In this paper, we propose ROD, a novel reception-aware online knowledge distillation approach for sparse graph learning. We design three supervision signals for ROD: multi-scale reception-aware graph knowledge, task-based supervision, and rich distilled knowledge, allowing online knowledge transfer in a peer-teaching manner. To extract knowledge concealed in the multi-scale reception fields, ROD explicitly requires individual student models to preserve different levels of locality information. For a given task, each student would predict based on its reception-scale knowledge, while simultaneously a strong teacher is established on-the-fly by combining multi-scale knowledge. Our approach has been extensively evaluated on 9 datasets and a variety of graph-based tasks, including node classification, link prediction, and node clustering. The result demonstrates that ROD achieves state-of-art performance and is more robust for the graph sparsity.
Benchmark Results
Tested on 6 datasets 17 baseline values reported too low Non-standard metric on 1 dataset
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 | |
| 161 | SIGN | 0.8672
±0.0137 best reported | |
| 195 | JK-Net | 0.8579
±0.0001 best reported | |
| 223 | SGC | 0.8509
±0.0648 best reported | best at pub: Learning Conjoint Attentions for Graph Neural Nets (NeurIPS 2021) |
| 239 | ROD | 0.8470
±0.0060 | This paper |
| 382 | AP-GCN | 0.8340
±0.0030 | prev best: Adversarial Graph Disentanglement with Component-specific Aggregation (2021) |
| 724 | MLP | 0.7768 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphTARIF | 0.9703
±0.0019 | |
| 2 | GAT | 0.9669
±0.0014 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 3 | GAT+T | 0.9660
±0.0007 | |
| 7 | SAGE | 0.9643
±0.0027 | |
| 8 | GCN | 0.9632
±0.0008 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 21 | APPNP | 0.9573
±0.0012 best reported | |
| 50 | SGC | 0.9160
±0.0070 | |
| 195 | ROD | 0.9320
±0.0070 | This paper |
| 332 | AP-GCN | 0.9210
±0.0030 | This paper |
| 349 | JK-Net | 0.9190
±0.0070 | Improvement within reported uncertainty; not highlighted. |
| 363 | SIGN | 0.9170
±0.0070 | This paper |
| 390 | MLP | 0.9128
±0.0063 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphTARIF | 0.9461
±0.0017 | |
| 2 | GCN | 0.9412
±0.0008 best reported | best at pub: Learning on Attribute-Missing Graphs (2020) |
| 3 | GAT | 0.9398
±0.0022 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 8 | SAGE | 0.9351
±0.0006 | |
| 58 | APPNP | 0.9093
±0.0018 best reported | best at pub: A Unified View on Graph Neural Networks as Graph Signal Denoising (2020) |
| 82 | SGC | 0.9022
±0.0021 best reported | |
| 305 | ROD | 0.8530
±0.0080 | This paper |
| 308 | AP-GCN | 0.8518
±0.0023 best reported | best at pub: Adaptive Propagation Graph Convolutional Network (2020) |
| 320 | MLP | 0.8463 | |
| 378 | SIGN | 0.8310
±0.0080 | This paper |
| 404 | JK-Net | 0.8200
±0.0060 |
Sorted by Accuracy. Highlighted rows are from other papers.
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GAP-EDP | 0.9870
±0.0003 | |
| 2 | NE-ASGCN | 0.9758
±0.0027 | |
| 3 | HSGT | 0.9730
±0.0024 | |
| 15 | ROD | 0.9670
±0.0010 | This paper |
| 18 | GraphSAINT | 0.9660
±0.0010 | |
| 21 | GraphSAGE | 0.9653
±0.0011 best reported | best at pub: DropEdge: Towards Deep Graph Convolutional Networks on Node Classification (ICLR 2019) best today: Hierarchical Transformer for Scalable Graph Learning (IJCAI 2023) |
| 23 | SAGE | 0.9650
±0.0003 | |
| 47 | ClusterGCN | 0.9570 | This paper |
| 86 | FastGCN | 0.9370 | This paper |
| 147 | MLP | 0.8240
±0.0010 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GrokFormer | 0.9831
±0.0018 | |
| 2 | PolyFormer | 0.9808
±0.0027 | |
| 3 | SGFormer | 0.9796
±0.0081 | |
| 6 | GAT | 0.9782
±0.0028 best reported | best at pub: SelfGNN: Self-supervised Graph Neural Networks without explicit negative sampling (WWW 2021) best today: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 9 | GCN | 0.9774
±0.0035 best reported | best at pub: SelfGNN: Self-supervised Graph Neural Networks without explicit negative sampling (WWW 2021) best today: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 17 | SAGE | 0.9739
±0.0018 | |
| 42 | APPNP | 0.9654
±0.0007 best reported | best at pub: Elastic Graph Neural Networks (ICML 2021) best today: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) |
| 58 | MLP | 0.9597
±0.0007 | |
| 70 | SGC | 0.9580
±0.0010 best reported | best at pub: Elastic Graph Neural Networks (ICML 2021) best today: Unifying Graph Contrastive Learning with Flexible Contextual Scopes (2022) |
| 196 | ROD | 0.9410
±0.0070 | This paper |
| 236 | AP-GCN | 0.9310
±0.0090 | This paper |
| 240 | SIGN | 0.9303
±0.0115 best reported | best today: Alternately Optimized Graph Neural Networks (ICML 2022) Difference within reported uncertainty; not counted as underperformance. |
| 254 | JK-Net | 0.9250
±0.0040 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DoG | 0.9690
±0.0030 | |
| 2 | GWN-fa | 0.9667
±0.0026 | |
| 3 | GWN-sym | 0.9666
±0.0026 | |
| 6 | GraphSAGE | 0.9593
±0.0025 | |
| 12 | GCN | 0.9514
±0.0025 best reported | best at pub: Unifying Graph Convolutional Neural Networks and Label Propagation (2020) best today: Graph Wave Networks (WWW 2025) |
| 21 | GAT | 0.9437
±0.0028 best reported | best at pub: Unifying Graph Convolutional Neural Networks and Label Propagation (2020) best today: Graph Wave Networks (WWW 2025) |
| 25 | APPNP | 0.9400
±0.0030 best reported | best at pub: A Unified View on Graph Neural Networks as Graph Signal Denoising (2020) best today: Diffusion on Graph: Augmentation of Graph Structure for Node Classification (TMLR 2025) |
| 47 | ROD | 0.9340
±0.0050 | This paper |
| 88 | MLP | 0.9280
±0.0020 | |
| 96 | SGC | 0.9030
±0.0050 | prev best: Towards Deeper Graph Neural Networks with Differentiable Group Normalization (NeurIPS 2020) best today: Towards Graph Self-Supervised Learning with Contrastive Adjusted Zooming (2021) |
| 106 | JK-Net | 0.9240
±0.0040 best reported | best at pub: Unifying Graph Convolutional Neural Networks and Label Propagation (2020) |
| 128 | SIGN | 0.9190
±0.0030 | This paper |
| 136 | AP-GCN | 0.9160
±0.0070 | This paper |
