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Yuan","paperDate":"2020-06-09","publishedOn":"2024-03-03","paperTitle":"On the Bottleneck of Graph Neural Networks and its Practical Implications","paperUrl":"https://arxiv.org/abs/2006.05205","bibliography":{"title":"On the Bottleneck of Graph Neural Networks and its Practical Implications","authors":["Uri Alon","Eran Yahav"],"url":"https://arxiv.org/abs/2006.05205","pdfUrl":"https://arxiv.org/pdf/2006.05205v4","codeUrl":"https://github.com/tech-srl/bottleneck","preprint":{"id":"2006.05205","submittedOn":"2020-06-09","url":"https://arxiv.org/abs/2006.05205"},"publication":{"venue":"ICLR","year":2021,"kind":"conference","url":"https://arxiv.org/abs/2006.05205"},"citation":"@misc{graphlearningoversquashing2020,\n  title = {{On the Bottleneck of Graph Neural Networks and its Practical Implications}},\n  author = {Uri Alon and Eran Yahav},\n  year = {2020},\n  eprint = {2006.05205},\n  archivePrefix = {arXiv},\n  url = {https://arxiv.org/abs/2006.05205}\n}\n","citationPath":"/content/papers/citations/graph-learning/over-squashing.af346c012204.bib"},"thumbnail":{"src":"/content/papers/assets/c3454ca38b6e53b6467ff66db7867788efed8d8a71eec3c6e7f754e586a99d4d.png","width":1078,"height":356},"locale":"en","path":"/content/papers/en/graph-learning/over-squashing.146d06e9e263.md","headings":[{"id":"defining-the-problem","text":"Defining the Problem","depth":2},{"id":"problem-radius","text":"Problem Radius","depth":3},{"id":"the-rnn-bottleneck","text":"The RNN Bottleneck","depth":3},{"id":"looking-only-at-propagation-shares","text":"Looking Only at Propagation Shares","depth":3},{"id":"a-deliberately-constructed-task","text":"A Deliberately Constructed Task","depth":3},{"id":"solving-the-problem","text":"Solving the Problem","depth":2},{"id":"a-fully-adjacent-final-layer","text":"A Fully Adjacent Final Layer","depth":3},{"id":"how-large-must-the-vector-be","text":"How Large Must the Vector Be?","depth":3},{"id":"discussion","text":"Discussion","depth":2},{"id":"tree-neighborsmatch","text":"Tree-NeighborsMatch","depth":3},{"id":"qm9","text":"QM9","depth":3},{"id":"biological-datasets","text":"Biological Datasets","depth":3},{"id":"conclusion","text":"Conclusion","depth":2}],"anchorAliases":{},"guide":null,"relatedReading":[{"id":"graph-learning/deeper-insights","relation":"referenced","topic":""},{"id":"graph-learning/graphgps","relation":"referenced","topic":""}]},{"id":"graph-learning/graphgps","category":"graph-learning","legacyPath":"","legacySlug":"","legacyPaths":[],"title":"GraphGPS","subtitle":"GPS for Graphs","author":"Z. Yuan","paperDate":"2022-05-25","publishedOn":"2025-09-09","world":"external/graphgps","paperTitle":"Recipe for a General, Powerful, Scalable Graph Transformer","paperUrl":"https://arxiv.org/abs/2205.12454","bibliography":{"title":"Recipe for a General, Powerful, Scalable Graph Transformer","authors":["Ladislav Rampášek","Mikhail Galkin","Vijay Prakash Dwivedi","Anh Tuan Luu","Guy Wolf","Dominique Beaini"],"url":"https://arxiv.org/abs/2205.12454","pdfUrl":"https://arxiv.org/pdf/2205.12454v4","codeUrl":"https://github.com/rampasek/GraphGPS","preprint":{"id":"2205.12454","submittedOn":"2022-05-25","url":"https://arxiv.org/abs/2205.12454"},"publication":{"venue":"NeurIPS","year":2022,"kind":"conference","url":"https://proceedings.neurips.cc/paper_files/paper/2022/hash/5d4834a159f1547b267a05a4e2b7cf5e-Abstract-Conference.html"},"citation":"@misc{graphlearninggraphgps2022,\n  title = {{Recipe for a General, Powerful, Scalable Graph Transformer}},\n  author = {Ladislav Rampášek and Mikhail Galkin and Vijay Prakash Dwivedi and Anh Tuan Luu and Guy Wolf and Dominique Beaini},\n  year = {2022},\n  eprint = {2205.12454},\n  archivePrefix = {arXiv},\n  url = {https://arxiv.org/abs/2205.12454}\n}\n","citationPath":"/content/papers/citations/graph-learning/graphgps.053e58fd5309.bib"},"thumbnail":{"src":"/content/papers/assets/e4177a894582643d7811bced6f6c6cf8bb51ff7738da4af5d98115883e1a4bb8.png","width":1116,"height":798},"locale":"en","path":"/content/papers/en/graph-learning/graphgps.88c624c18f31.md","headings":[{"id":"defining-the-problem","text":"Defining the Problem","depth":2},{"id":"position-and-structure","text":"Position and Structure","depth":3},{"id":"why-message-passing-needs-them","text":"Why Message Passing Needs Them","depth":3},{"id":"message-passing-before-attention-can-lose-information-first","text":"Message Passing before Attention Can Lose Information First","depth":3},{"id":"solving-the-problem","text":"Solving the Problem","depth":2},{"id":"three-ingredients","text":"Three Ingredients","depth":3},{"id":"one-gps-layer","text":"One GPS Layer","depth":3},{"id":"linear-complexity","text":"Linear Complexity","depth":3},{"id":"discussion","text":"Discussion","depth":2},{"id":"ablation-each-paths-contribution","text":"Ablation: Each Path's Contribution","depth":3},{"id":"comparison-with-other-models","text":"Comparison with Other Models","depth":3},{"id":"reassessment-a-year-later","text":"Reassessment a Year Later","depth":3},{"id":"conclusion","text":"Conclusion","depth":2}],"anchorAliases":{},"guide":null,"relatedReading":[{"id":"graph-learning/graph-transformer","relation":"referenced","topic":""},{"id":"graph-learning/san","relation":"referenced","topic":""},{"id":"graph-learning/graphormer","relation":"referenced","topic":""}]}],"text":"In 2022, Graph Transformer papers arrive one after another with similar selling points: message passing GNNs see only one-hop neighbors per layer and struggle with distant information, while Transformers connect every node to all others and establish long-range relationships at once.\n\nThe usual benchmarks make this hard to prove. Molecular datasets such as ZINC and ogbg-mol* average only twenty-odd nodes per graph. Message passing GNNs with positional encodings often match or beat Transformers there, and local models still dominate many top leaderboard positions.\n\nVijay Prakash Dwivedi, Ladislav Rampášek, Mikhail Galkin and colleagues at Mila, Nanyang Technological University and Valence Discovery think the questions are the problem. Testing long-range interaction requires an exam that genuinely needs distant information to answer.\n\nTheir exam is LRGB, the Long Range Graph Benchmark.\n\n## Defining the Problem\n\nWhat makes a dataset require long-range information? The authors propose three characteristics.\n\n**Graph size.** A message passing GNN needs at least $r$ layers for distance-$r$ interactions. Its receptive field grows exponentially with depth, causing over-squashing. But with only twenty-odd nodes, $r$ is naturally small, bottlenecks are less obvious and local GNNs can learn well. Graphs must be large enough to expose differences.\n\n**Task properties.** Size alone is insufficient: the task must depend on distant information. The authors give two examples. ZINC depends on counts of local substructures, with research finding that length-7 substructures suffice and longer ones add nothing. MalNet-Tiny can have thousands of nodes per graph, yet fully connected modules bring little improvement.\n\n**Contribution of global structure.** If global positional encodings help, or the target itself concerns distances—such as molecular 2D or 3D structural properties—global information is needed.\n\n## Solving the Problem\n\n### Five Datasets\n\nUsing these characteristics, the authors create five datasets from computer vision and chemistry.\n\n**PascalVOC-SP** and **COCO-SP** come from image semantic segmentation. SLIC divides images into superpixels, each becoming a node; adjacent superpixels connect in a rag-boundary graph. The task predicts each node's semantic class.\n\n[![Figure 2 of the paper: four panels from left to right. The original image shows toy animals; the second shows SLIC superpixels with green boundaries; the third overlays the rag-boundary graph; the fourth shows only the graph, with nodes colored by class.](/content/papers/assets/1c4286bdcce2817b9755835b80dd77ae2c30adc996a6665ccf8f7be2ba7c964f.png)](/content/papers/assets/1c4286bdcce2817b9755835b80dd77ae2c30adc996a6665ccf8f7be2ba7c964f.png)\n\n*Figure 2 from Dwivedi et al., taken from [**PDF page 5**](https://arxiv.org/pdf/2206.08164v4#page=5), CC BY 4.0. Fewer than 50 superpixels are used for illustration; the original caption is omitted.*\n\nEarlier superpixel datasets, MNIST and CIFAR10, have at most 75 and 150 nodes per graph. Here the limit is 500, with mean shortest-path length 10.74 and diameter 27.62, compared with MNIST's 3.03 and 6.03 and CIFAR10's 3.97 and 8.46.\n\n**PCQM-Contact** is molecular link prediction: predict atom pairs more than 5 graph hops apart but less than 3.5 Å apart in 3D. The 5-hop threshold excludes already-nearby graph pairs, requiring the model to learn properties related to 3D structure.\n\n**Peptides-func** and **Peptides-struct** share 15,535 peptide molecules. Peptides are short amino-acid chains, shorter than proteins but much larger than typical drug-like small molecules. Nodes are heavy atoms, edges chemical bonds. Peptides-func is multilabel classification into 10 functions, such as antibacterial and antiviral activity. Peptides-struct is multilabel regression of properties computed from 3D structure, including inertia, length and sphericity. Inputs contain no 2D or 3D coordinates.\n\n| Dataset | Graphs | Mean nodes | Mean shortest path | Mean diameter | Task |\n| --- | ---: | ---: | ---: | ---: | --- |\n| PascalVOC-SP | 11,355 | 479.40 | 10.74 | 27.62 | Node classification |\n| COCO-SP | 123,286 | 476.88 | 10.66 | 27.39 | Node classification |\n| PCQM-Contact | 529,434 | 30.14 | 4.63 | 9.86 | Link prediction |\n| Peptides-func | 15,535 | 150.94 | 20.89 | 56.99 | Graph classification |\n| Peptides-struct | 15,535 | 150.94 | 20.89 | 56.99 | Graph regression |\n\nPeptide diameter averages nearly 57, around six times PCQM-Contact's, while average degree is only about 2: long chains along which information must travel step by step.\n\n### Baseline Models\n\nThe authors choose two families: message passing GCN, GCNII, GINE and GatedGCN, and fully connected Transformers—a Transformer with Laplacian encodings and an improved SAN. All have roughly 500,000 parameters and use 4 seeds per experiment. On peptides, message passing models have 5 layers and Transformers 4.\n\n\n> [!TIP]\n> \n> For SAN's learned positional encodings and two attention mechanisms, see our note:\n> \n> - **[[21.06] SAN: Hearing the Shape of a Graph](/blog/papers/graph-learning/san)**\n\n\n## Discussion\n\n### Peptide Datasets\n\n| Model | Peptides-func AP ↑ | Peptides-struct MAE ↓ |\n| --- | ---: | ---: |\n| GCN | 0.5930 | 0.3496 |\n| GCNII | 0.5543 | 0.3471 |\n| GINE | 0.5498 | 0.3547 |\n| GatedGCN | 0.5864 | 0.3420 |\n| GatedGCN + RWSE | 0.6069 | 0.3357 |\n| Transformer + LapPE | 0.6326 | **0.2529** |\n| SAN + LapPE | 0.6384 | 0.2683 |\n| SAN + RWSE | **0.6439** | 0.2545 |\n\nTransformer models lead clearly on both peptide datasets, especially Peptides-struct, reducing MAE from around 0.34 to around 0.25.\n\n### Superpixel Datasets\n\nOn PascalVOC-SP, 8-layer message passing models score F1 0.1268 for GCN, 0.1265 for GINE and 0.2873 for GatedGCN. Transformer + LapPE reaches 0.2694 and SAN + LapPE 0.3230. On COCO-SP, Transformer and GatedGCN are close; SAN fails to converge within the 60-hour A100 limit.\n\n### The Authors' Observations\n\nThe authors draw four observations:\n\n1. **Simple local GNNs perform poorly.** GCN and GINE struggle everywhere except Peptides-func, consistent with the over-squashing paper's finding that GCN and GIN suffer more from bottlenecks than attention-based GNNs.\n2. **Very shallow GNNs cannot learn enough.** Two message passing layers clearly underfit, unlike classic Cora and Citeseer benchmarks where shallow GCNs outperform deep ones.\n3. **Fully connected Transformers perform best**, especially on peptides. The authors attribute this to long-range tasks, nonlocal information and graph size.\n4. **Scale is a Transformer weakness.** SAN's failure to finish on COCO-SP exposes scalability problems on larger graphs.\n\nThe same group's GraphGPS paper uses this long-range benchmark and wins on four of the five datasets.\n\n\n> [!TIP]\n> \n> For GraphGPS and the over-squashing problem it addresses, see our notes:\n> \n> - **[[20.06] Over-squashing: No Room Left](/blog/papers/graph-learning/over-squashing)**\n> - **[[22.05] GraphGPS: GPS for Graphs](/blog/papers/graph-learning/graphgps)**\n\n\n### Reexamining the Benchmark Itself\n\nA year later, Tönshoff et al. at RWTH Aachen rerun the benchmark. Without changing the models, basic GNN hyperparameter searches and visual-feature normalization greatly reduce the gap, erasing it on peptides. They also find that PCQM-Contact evaluation code differs from the paper's definition.\n\nLRGB's November 2023 revision adds a passage directing readers to this reassessment.\n\n\n> [!TIP]\n> \n> For details of the reassessment, see our note:\n> \n> - **[[23.09] Where Did the Gap Go?: Where Did the Gap Go?](/blog/papers/graph-learning/where-did-the-gap-go)**\n\n\n## Conclusion\n\nLRGB asks what makes a long-range dataset, using graph size, task properties and global structure's contribution to build five datasets from superpixel images and peptide molecules. In the authors' baseline experiments, local message passing GNNs trail fully connected Transformers, most clearly on peptides.\n\nThis exam becomes a standard testing ground for Graph Transformers. Read its tables alongside Tönshoff et al.'s reassessment: the same GCN's Peptides-func scores differ by nearly 0.09 across the two.\n","imageSizes":{"/content/papers/assets/1c4286bdcce2817b9755835b80dd77ae2c30adc996a6665ccf8f7be2ba7c964f.png":{"width":1098,"height":214}}}