Node Identifiers: Compact, Discrete Representations for Efficient Graph Learning
Abstract
We present a novel end-to-end framework that generates highly compact (typically 6-15 dimensions), discrete (int4 type), and interpretable node representations, termed node identifiers (node IDs), to tackle inference challenges on large-scale graphs. By employing vector quantization, we compress continuous node embeddings from multiple layers of a Graph Neural Network (GNN) into discrete codes, applicable under both self-supervised and supervised learning paradigms. These node IDs capture high-level abstractions of graph data and offer interpretability that traditional GNN embeddings lack. Extensive experiments on 34 datasets, encompassing node classification, graph classification, link prediction, and attributed graph clustering tasks, demonstrate that the generated node IDs significantly enhance speed and memory efficiency while achieving competitive performance compared to current state-of-the-art methods.
Benchmark Results
Tested on 12 datasets 10 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: 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) best today: Adaptive Tokenization: On the Hop-Overpriority Problem in Tokenized Graph Learning Models (2025) Difference within reported uncertainty; not counted as underperformance. |
| 107 | NID_GCN | 0.8788
±0.0069 | This paper |
| 128 | NID_GAT | 0.8735
±0.0057 | This paper |
| 143 | Graph-MLP | 0.8706
±0.0138 | |
| 184 | VQGraph | 0.8611
±0.0126 | prev best: VQGraph: Rethinking Graph Representation Space for Bridging GNNs and MLPs (ICLR 2023) |
| 620 | NID_MAE | 0.8080
±0.0070 | This paper |
| 724 | MLP | 0.7768 best reported | best at pub: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | CNA | 0.9575
±0.0058 | |
| 2 | IS-GIB | 0.9390
±0.0187 | |
| 3 | EERM | 0.9112
±0.0145 | |
| 35 | GAT | 0.8080
±0.0026 best reported | best at pub: Feature Expansion for Graph Neural Networks (ICML 2023) |
| 44 | GCN | 0.8033
±0.0088 best reported | best at pub: Gophormer: Ego-Graph Transformer for Node Classification (2021) |
| 61 | GraphSAGE | 0.7923
±0.0053 | |
| 69 | Graph-MLP | 0.7886
±0.0008 best reported | |
| 116 | NID_GCN | 0.7689
±0.0109 | This paper |
| 130 | NID_GAT | 0.7613
±0.0135 | This paper |
| 152 | VQGraph | 0.7564
±0.0092 | This paper |
| 224 | NID_MAE | 0.7420
±0.0060 | This paper |
| 350 | MLP | 0.7289
±0.0010 best reported | best at pub: On the Equivalence of Graph Convolution and Mixup (TMLR 2023) best today: Gumbel-MPNN: Graph Rewiring with Gumbel-Softmax (2025) |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | LGTL | 0.9518
±0.0011 | |
| 2 | MixHop (LO) | 0.9513
±0.0038 | |
| 3 | GraphSAGE (LO) | 0.9511
±0.0036 | |
| 18 | GCN | 0.9004
±0.0025 | |
| 20 | GAT | 0.9233
±0.0018 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 90 | NID_GCN | 0.8942
±0.0044 | This paper |
| 106 | VQGraph | 0.8905
±0.0032 best reported | best today: VecFormer: Towards Efficient and Generalizable Graph Transformer with Graph Token Attention (WWW 2026) |
| 111 | NID_GAT | 0.8897
±0.0036 | This paper |
| 113 | Graph-MLP | 0.8893
±0.0063 | |
| 116 | SAGE | 0.8881
±0.0015 | |
| 210 | MLP | 0.8690
±0.0074 best reported | best at pub: On the Equivalence of Graph Convolution and Mixup (TMLR 2023) |
| 759 | NID_MAE | 0.7640
±0.0080 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GCN | 0.9302
±0.0011 | |
| 2 | RSE + RGCN (70b) | 0.8852
±0.0019 | |
| 3 | LEMP+T | 0.8825 | |
| 9 | SAGE | 0.8771 | |
| 111 | NID_GAT | 0.7956
±0.0043 | This paper |
| 157 | NID_GCN | 0.7855
±0.0015 | This paper |
| 178 | VQGraph | 0.7792
±0.0061 | This paper |
| 229 | Graph-MLP | 0.7535
±0.0055 | This paper |
| 237 | MLP | 0.7469
±0.0085 |
OGB
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | Jacobi | 0.8968 | |
| 2 | GPR | 0.8953 | |
| 3 | LEMP4HG | 0.8939 | |
| 4 | SAGE | 0.8327
±0.0035 | prev best: Learning on Large-scale Text-attributed Graphs via Variational Inference (ICLR 2022) |
| 6 | GCN | 0.8868 | |
| 79 | Polynormer | 0.8297
±0.0028 | This paper |
| 104 | NID_SAGE | 0.8183
±0.0026 | This paper |
| 293 | SGFormer | 0.7416
±0.0031 | This paper |
| 323 | LINKX | 0.7159
±0.0071 | This paper |
| 351 | MLP | 0.6605
±0.0020 |
| # | Model | Hits@50 ↑ | Paper |
|---|---|---|---|
| 1 | PROXI | 0.7650
±0.0027 | |
| 2 | OGB Leader | 0.7129
±0.0018 | |
| 3 | GIDN | 0.7096
±0.0055 | |
| 9 | GCN | 0.6405
±0.0063 | prev best: GNNBenchmark (JMLR 2023) best today: On the Impact of Feature Heterophily on Link Prediction with Graph Neural Networks (NeurIPS 2024) |
| 10 | Neo-GNN | 0.6613
±0.0061 best reported | best at pub: Neo-GNNs: Neighborhood Overlap-aware Graph Neural Networks for Link Prediction (NeurIPS 2022) best today: PROXI: Challenging the GNNs for Link Prediction (TMLR 2024) |
| 14 | BUDDY | 0.6594
±0.0058 | This paper |
| 19 | NCN | 0.6476
±0.0087 | This paper |
| 20 | SEAL | 0.6474
±0.0043 | This paper |
| 24 | NID_GCN | 0.6431
±0.0048 | This paper |
| 28 | SAGE | 0.5944
±0.0137 | |
| 94 | MLP | 0.4438
±0.0347 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GIANT-XRT | 0.7612
±0.0016 | |
| 2 | GEGCN | 0.7576
±0.0064 | |
| 3 | AGDN | 0.7522
±0.0007 | |
| 23 | GCN | 0.7300
±0.0017 | |
| 26 | SAGE | 0.7267
±0.0031 | This paper |
| 28 | SGFormer | 0.7263
±0.0013 | This paper |
| 51 | Polynormer | 0.7182
±0.0023 | This paper |
| 55 | GPRGNN | 0.7168
±0.0044 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) Difference within reported uncertainty; not counted as underperformance. |
| 75 | GraphGPS | 0.7097
±0.0041 | This paper |
| 80 | NID_SAGE | 0.7052
±0.0014 | This paper |
| 99 | LINKX | 0.6618
±0.0033 | This paper |
| 107 | MLP | 0.5765
±0.0012 |
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | LD | 0.8942
±0.0007 | |
| 2 | X_WO/LD | 0.8915
±0.0012 | |
| 3 | X_PNE | 0.8894
±0.0014 | |
| 16 | GraphSAGE | 0.8430 | |
| 27 | SGFormer | 0.7984
±0.0061 best reported | best today: Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitions (2026) Difference within reported uncertainty; not counted as underperformance. |
| 29 | SAGE | 0.7943
±0.0075 | This paper |
| 30 | Polynormer | 0.7941
±0.0056 best reported | |
| 46 | GraphGPS | 0.7725
±0.0042 best reported | best today: Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitions (2026) Difference within reported uncertainty; not counted as underperformance. |
| 50 | NID_SAGE | 0.7678
±0.0059 | This paper |
| 54 | GPRGNN | 0.7568
±0.0049 | This paper |
| 65 | LINKX | 0.7137
±0.0058 | This paper |
Heterophilic Graphs
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | Hetero-S (GAT 8-layer) | 0.8693 | |
| 2 | Dir-GNN+CNA | 0.8586
±0.0180 | |
| 3 | GAT | 0.8560 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) best today: The Heterophilic Snowflake Hypothesis: Training and Empowering GNNs for Heterophilic Graphs (KDD 2024) |
| 52 | GCN | 0.7033 best reported | best at pub: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 108 | SAGE | 0.6340
±0.0300 | |
| 169 | MLP | 0.5429 | |
| 217 | NID_GCN | 0.4629
±0.0292 | This paper |
| 240 | NID_GAT | 0.4283
±0.0342 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | IBG-NN | 0.7763
±0.0179 | |
| 2 | Dir-GNN+CNA | 0.7747
±0.0128 | |
| 3 | DHGNN | 0.7684
±0.0161 | |
| 46 | GCN | 0.6067 | |
| 118 | NID_GCN | 0.4509
±0.0172 | This paper |
| 172 | MLP | 0.3930
±0.0079 | |
| 191 | NID_GAT | 0.3768
±0.0204 | This paper |
Heterophily Benchmark
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | NID_GAT | 0.9703
±0.0002 | This paper |
| 2 | NID_GCN | 0.9685
±0.0010 | This paper |
| 3 | UniGAP | 0.8421
±0.0080 | |
| 16 | GCN | 0.7740
±0.0107 | prev best: Evolving Computation Graphs (ICML 2023) best today: UniGAP: A Universal and Adaptive Graph Upsampling Approach to Mitigate Over-Smoothing in Node Classification Tasks (2024) Improvement within reported uncertainty; not highlighted. |
| 26 | GAT | 0.7835
±0.0116 | prev best: Bundle Neural Networks for message diffusion on graphs (2024) Improvement within reported uncertainty; not highlighted. |
| 46 | GraphSAGE | 0.7721
±0.0130 | |
| 96 | MLP | 0.7082
±0.0010 |
LINKX Benchmarks
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | SAGE | 0.8597
±0.0021 | This paper |
| 2 | Polynormer | 0.8595
±0.0007 | This paper |
| 3 | NID_SAGE | 0.8563
±0.0031 | This paper |
| 23 | GCN | 0.7601
±0.0049 | |
| 25 | SGFormer | 0.7376
±0.0024 | This paper |
| 31 | MLP | 0.7048
±0.0077 |
