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Generalizing CNNs to graphs with learnable neighborhood quantization
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Proposes Quantized Graph Convolution Networks (QGCNs), which decompose graph convolution into non-overlapping sub-kernels with a learnable QuantNet assigning neighbors to sub-kernels, reducing to a 2D CNN on grid graphs and matching or beating GNN baselines on graph benchmarks.
Problem
Existing spatial GNNs do not truly generalize the CNN convolution layer: they lack fixed neighborhood sizes and node orderings, so they fail to reduce to a CNN on array data and lose CNN's local inductive bias.
Approach
Quantize local neighborhoods into a fixed set of non-overlapping sub-kernels via masks; a satisficing angular mapping reproduces 3x3 CNN convolution exactly on 2D grid graphs, and a learnable QuantNet (MLP + Gumbel-softmax) generalizes the assignment to arbitrary graphs; wrapped in a residual block (QGRL/QGRN).
Key results
- QGCN matches CNN on MNIST (98.98 vs 98.92) and FashionMNIST (92.39 vs 92.56), and is slightly lower on CIFAR-10 (79.59 vs 80.21).
- QGRN reaches 99.50% on AIDS and 94.10% on Letters (high), above all listed GNN baselines in the reported tables.
- On the EEG supervised autoencoder, QGRN improves test AUC to 0.59 versus 0.56 for SGCN.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace CNN convolution layers with QGCL layers | CNN architecture · MNIST, Fashion-MNIST, and CIFAR-10 | test accuracy: 98.92 ± 0.10 -> 98.98 ± 0.04; 92.56 ± 0.18 -> 92.39 ± 0.13; 80.21 ± 0.29 -> 79.59 ± 0.35 | No clear effect |
| use QGRN instead of the strongest listed GNN baseline | graph classification models · AIDS, Frankenstein, Mutag, Synthie, Letters (high), Enzymes, COIL-DEL, Mutagenicity, Proteins-Full, Letters (low), and Letters (med) | test accuracy: 99.17 ± 0.14 -> 99.50 ± 0.10; 66.74 ± 00.42 -> 75.58 ± 0.40; 98.37 ± 01.41 -> 99.99 ± 00.26; 92.68 ± 0.11 -> 99.99 ± 0.2 | Helped |
| use QGRN instead of the strongest listed GNN baseline | node classification models · Computers, Cora, PubMed, Chameleon, and Squirrel | test accuracy: 91.66 ± 0.05 -> 90.02 ± 0.02; 88.34 ± 0.30 -> 89.02 ± 0.14; 88.97 ± 0.09 -> 89.11 ± 0.15; 78.11 ± 0.29 -> 74.15 ± 0.37; | Mixed |
| increase QGRN depth from 3 to 18 layers (ablation) | QGRN · AIDS | mean test accuracy: 99.50 -> 99.00 | Hurt |
| increase QGRN depth from 3 to 18 layers (ablation) | QGRN · Letters (high) | mean test accuracy: 94.10 -> 90.86 | Hurt |
Surprising findings
- QGRN inference latency on TPU is substantially higher than baseline GNNs (e.g., 12.38 ms vs 1.25-3.8 ms on AIDS), which the authors attribute to an unoptimized implementation.
- On the Chameleon and Squirrel heterophilic datasets, QGRN is outperformed by GeneralConv and GraphConv on Squirrel, and deeper QGRNs lose accuracy with depth.
Limitations
- Current QGCL implementation is computationally inefficient in wall-clock runtime.
- Cannot represent convolutions with odd-sized kernels or stride greater than one.
- Performance degrades with deeper networks, especially on complex datasets like Letters (high).
Experimental setup
Datasets: MNIST FashionMNIST CIFAR-10 AIDS Letters Enzymes Coil-Del Frankenstein Mutag Mutagenicity Proteins Synthie
Benchmarks: MNIST FashionMNIST CIFAR-10 AIDS Letters Enzymes Coil-Del Frankenstein Mutag Mutagenicity Proteins Synthie
Metrics: test accuracy parameter count FLOPs inference latency MSE cross-entropy AUC
Baselines: GCNConv ChebConv GraphConv SGConv GENConv GeneralConv GATv2Conv TransformerConv SGCN EGConv
Builds on: GCN SGCN DeeperGCNs (GENConv) ResNet Gumbel-softmax
Closest papers by meaning
- VQ-GNN: A Universal Framework to Scale up Graph Neural Networks using Vector Quantization (NeurIPS 2021 · similarity 0.93)
- Beyond Graph Convolutional Network: An Interpretable Regularizer-Centered Optimization Framework (AAAI 2023 · similarity 0.91)
- Simplifying Graph Convolutional Networks (ICML 2019 · similarity 0.90)
- Efficient Learning of Linear Graph Neural Networks via Node Subsampling (NeurIPS 2023 · similarity 0.90)
- A Manifold Perspective on the Statistical Generalization of Graph Neural Networks (ICML 2025 · similarity 0.90)
- Can Classic GNNs Be Strong Baselines for Graph-level Tasks? Simple Architectures Meet Excellence (ICML 2025 · similarity 0.89)
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