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Reassessing the Long-Range Graph Benchmark}},\n  author = {Jan Tönshoff and Martin Ritzert and Eran Rosenbluth and Martin Grohe},\n  year = {2023},\n  eprint = {2309.00367},\n  archivePrefix = {arXiv},\n  url = {https://arxiv.org/abs/2309.00367}\n}\n","citationPath":"/content/papers/citations/graph-learning/where-did-the-gap-go.288771073197.bib"},"thumbnail":{"src":"/content/papers/assets/2381a94a5409a041eaab5b06f8dd33ebdd448087d689d89d780486cf3b900353.png","width":1118,"height":416},"locale":"zh-hant","path":"/content/papers/zh-hant/graph-learning/where-did-the-gap-go.ea95f280ee9a.md","headings":[{"id":"定義問題","text":"定義問題","depth":2},{"id":"解決問題","text":"解決問題","depth":2},{"id":"基本的超參數搜尋","text":"基本的超參數搜尋","depth":3},{"id":"逐通道正規化","text":"逐通道正規化","depth":3},{"id":"filtered-mrr","text":"filtered MRR","depth":3},{"id":"討論","text":"討論","depth":2},{"id":"胜肽資料集","text":"胜肽資料集","depth":3},{"id":"一個預測頭","text":"一個預測頭","depth":3},{"id":"超像素資料集","text":"超像素資料集","depth":3},{"id":"pcqm-contact","text":"PCQM-Contact","depth":3},{"id":"結論","text":"結論","depth":2}],"anchorAliases":{},"guide":null,"relatedReading":[{"id":"graph-learning/lrgb","relation":"referenced","topic":""},{"id":"graph-learning/gnn-plus","relation":"referenced","topic":""}]}],"text":"GraphGPS 之後，圖分類、圖回歸這類圖層級任務的排行榜，幾乎被 Graph Transformer 佔滿。論文裡的說法也大致一致，訊息傳遞的 GNN 有表達力上限，疊深會 over-smoothing，傳遠會 over-squashing，全域注意力正好補上這些缺口。\n\n北京航空航天大學與香港理工大學的 Yuankai Luo、Lei Shi、Xiao-Ming Wu 不太相信。前一年，他們在節點分類上做過一次，把 GCN、GAT、GraphSAGE 放進和新模型一樣大的超參數搜尋空間，結果在 18 個資料集裡的 17 個打平甚至超過當時最好的模型。\n\n\n> [!TIP]\n> \n> 節點分類上的那次重新比較，可以參考我們的筆記：\n> \n> - **[[24.06] Classic GNNs：調好再比](/blog/papers/graph-learning/classic-gnns)**\n\n\n這篇換到圖層級的任務，問同一個問題。經典的 GNN 只要配上現在常用的訓練技巧，能不能和 Graph Transformer 一較高下？\n\n## 定義問題\n\n### 兩種任務\n\n作者先把節點層級和圖層級的任務分清楚。節點分類通常是一張大圖，例如社群網路或引用網路，訓練、驗證、測試是同一張圖上不同的節點。圖層級的任務則以整張圖為單位，資料集是一大堆小圖，例如分子或蛋白質，切分的也是圖。\n\n兩者的資料組成、切分方式、訓練策略都不同，在節點分類上成立的結論，不能直接搬到圖層級。\n\n### 比較公不公平\n\n文獻裡，Graph Transformer 勝過 GNN 的證據，大多來自圖層級的任務，尤其是小分子的分類與回歸。但這些比較裡的 GNN 基準，常常是好幾年前的設定，沒有用上後來新模型習以為常的技巧。\n\n作者想知道的是，差距有多少來自架構本身，又有多少來自基準沒有調好。\n\n## 解決問題\n\n### 三個經典模型\n\n作者挑了三個訊息傳遞模型當骨架：\n\n- **GCN**：鄰居和自己依度數做對稱正規化後加總，再乘權重。\n- **GIN**：自己乘上 $1+\\epsilon$，加上鄰居總和，再過一個 MLP。\n- **GatedGCN**：在聚合時，每條邊有一個由兩端節點與邊特徵算出的閘門，決定這個鄰居的訊息能通過多少。\n\n### 六個技巧\n\n再把六個常見的技巧加上去，稱為 GNN+：\n\n1. **邊特徵**：把邊的特徵 $e_{uv}$ 乘上一個可學的矩陣，加進訊息傳遞裡。分子圖的化學鍵、超像素圖的空間關係，都在邊上。\n2. **正規化**：每一層聚合之後、啟動函數之前，加上 BatchNorm，穩定各層的分布。\n3. **Dropout**：加在啟動函數之後，減少神經元之間的共同適應。\n4. **殘差連接**：把這一層的輸入直接加到輸出上。\n5. **前饋網路（FFN）**：每層再接一個兩層的 FFN，和 Transformer 裡的那一塊一樣，也帶殘差與正規化。\n6. **位置編碼**：把隨機遊走結構編碼（RWSE），也就是從節點出發走 $m$ 步回到自己的機率，接在輸入特徵後面，再過一個線性層。\n\n以 GCN 為例，加上全部技巧之後，一層 GCN+ 寫成：\n\n$$\nh_v^l=\\mathrm{FFN}\\left(\\mathrm{Dropout}\\left(\\sigma\\left(\\mathrm{BN}\\left(\\sum_{u\\in\\mathcal N(v)\\cup\\{v\\}}\\frac{1}{\\sqrt{\\hat d_u\\hat d_v}}h_u^{l-1}W^l+e_{uv}W_e^l\\right)\\right)\\right)+h_v^{l-1}\\right)\n$$\n\n$$\n\\mathrm{FFN}(h)=\\mathrm{BN}\\left(\\sigma\\left(hW_{\\mathrm{FFN}_1}^l\\right)W_{\\mathrm{FFN}_2}^l+h\\right)\n$$\n\n從內到外讀，鄰居訊息加上邊特徵，接 BatchNorm、ReLU、dropout，再加上一層的輸入當殘差，最後過 FFN。\n\n[![原論文 Figure 2：GNN+ 的架構。節點特徵先接上位置編碼，連同邊特徵送進重複 L 次的區塊；每個區塊是 GNN 層接 FFN，最後做 readout。右側展開 GNN 層的內部，由下往上依序是訊息傳遞、正規化、啟動與 dropout、殘差連接；FFN 內部則是 MLP 接 Add & Norm。](/content/papers/assets/0be1b8a606332519d042698f1c6afd3ef8857eb95682b95df1cdeb9e3bfe7648.png)](/content/papers/assets/0be1b8a606332519d042698f1c6afd3ef8857eb95682b95df1cdeb9e3bfe7648.png)\n\n*原論文 Figure 2（Luo 等人），取自 [**PDF 第 3 頁**](https://arxiv.org/pdf/2502.09263v3#page=3)。圖說未收錄。*\n\n這六樣東西沒有一樣是新的。殘差、正規化、dropout 來自 CNN；FFN 和位置編碼來自 Transformer，RWSE 則是 GraphGPS 等 Graph Transformer 常用的結構編碼。作者的貢獻是把它們系統地組合起來，再做一次公平的比較。\n\n### 怎麼比\n\n14 個圖層級資料集，分成三組：\n\n- **Benchmarking GNNs**：ZINC（分子回歸）、MNIST 與 CIFAR10（影像轉成超像素圖後分類）、PATTERN 與 CLUSTER（合成圖上的節點分類）。\n- **LRGB**：Peptides-func、Peptides-struct（胜肽分子）、PascalVOC-SP、COCO-SP（超像素圖上的語意分割），加上 MalNet-Tiny（惡意程式的呼叫圖）。\n- **OGB**：ogbg-molhiv、ogbg-molpcba、ogbg-ppa、ogbg-code2。\n\n超參數的搜尋空間比照 GraphGPS，參數預算也照各基準的規定，例如 ZINC 約 50 萬個參數。作者也用同樣的搜尋空間和訓練環境，重新訓練了作為基準的 Graph Transformer；其餘基準取各自論文或排行榜上的數字，這些多半已經是調過的結果。每組實驗跑 5 個亂數種子。\n\n## 討論\n\n### 整體結果\n\n在 14 個資料集上，加強後的經典 GNN 每一個都排進前三，其中 8 個拿第一。挑幾組數字看：\n\n| 資料集（指標） | 原版 GCN | GCN+ | GatedGCN+ | GraphGPS | 表中其他模型最佳 |\n| --- | ---: | ---: | ---: | ---: | ---: |\n| ZINC（MAE ↓） | 0.367 | 0.076 | 0.077 | 0.070 | 0.057（TIGT） |\n| CIFAR10（準確率 ↑） | 55.71% | 69.82% | **77.22%** | 72.30% | 76.85%（GRED） |\n| Peptides-func（AP ↑） | 0.6860 | **0.7261** | 0.7006 | 0.6535 | 0.7150（DRew） |\n| Peptides-struct（MAE ↓） | 0.2460 | **0.2421** | 0.2431 | 0.2500 | 0.2449（Graph ViT） |\n| PascalVOC-SP（F1 ↑） | 0.2078 | 0.3357 | 0.4263 | 0.4440 | 0.4561（GSSC） |\n\n幾件事可以看：\n\n1. **原版和加強版差很多**。ZINC 上，GCN 的 MAE 從 0.367 降到 0.076，GIN 從 0.526 降到 0.065，同一個骨架，只是補上了六個技巧。\n2. **小分子上，差距幾乎消失**。ZINC 上 GIN+ 的 0.065 已經優於 GraphGPS；最好的 Graph Transformer 仍然略勝一籌，但差距從原本的數倍縮到零點零幾。\n3. **長距離的資料集上，經典 GNN 反而領先**。Peptides-func 上 GCN+ 是 0.7261，高於所有列出的 Graph Transformer 和 Graph Mamba。注意表中「原版 GCN」在 LRGB 上用的，已經是 Tönshoff 等人 2023 年調過參數的數字；LRGB 原論文裡的 GCN 只有 0.5930。\n4. **不是每一項都贏**。PascalVOC-SP 上，GatedGCN+ 仍落後 GraphGPS 的 2023 年版本與 GSSC。\n\nOGB 上，GatedGCN+ 在四個資料集都排進前三，其中三個拿第一。ogbg-ppa 上提升約 9%，在 OGB 排行榜上排第一；ogbg-molhiv 和 ogbg-molpcba 上，它和先在其他資料集預訓練過的 Graphormer、EGT 表現相當。\n\n### 也比較快\n\n經典 GNN 沒有全域注意力，計算量小得多。以每個 epoch 的訓練時間來看，ZINC 上 GraphGPS 要 21 秒，GCN+ 要 7 秒；MalNet-Tiny 的圖平均有 1,410 個節點，GraphGPS 要 46 秒，GCN+ 只要 6 秒。\n\n### 每個技巧各管什麼\n\n作者對每個模型逐一拿掉六個技巧，整理出六點觀察：\n\n1. **邊特徵在分子與超像素圖上特別重要**。分子的邊是化學鍵，超像素的邊是空間關係；程式碼的呼叫圖上，邊特徵和任務比較無關，拿掉影響不大。\n2. **正規化在大資料集上影響比較大**。ogbg-ppa 有 15 萬張圖，拿掉正規化，三個模型的準確率都掉了約 15%。\n3. **Dropout 幾乎都有幫助，但只要一點點**。最佳的 dropout 率有 97% 不超過 0.2，64% 不超過 0.1。作者指出這和他們在節點分類上的觀察相反，那邊通常需要比較高的 dropout。\n4. **殘差連接大多不可或缺**，只有在小圖上的淺層網路例外。胜肽資料集只用 3 到 5 層，拿掉殘差影響不大；其他資料集用了 10 層以上，拿掉殘差常常大幅退步。\n5. **FFN 對 GCN+ 和 GIN+ 很關鍵**。MNIST 上，GIN+ 拿掉 FFN，準確率從 98.29% 掉到 11.35%，相對下降 88%。GatedGCN+ 本身有閘門，對 FFN 的依賴就小得多。\n6. **位置編碼在小資料集上有效，大資料集上作用不大**。ZINC、PATTERN、CLUSTER、Peptides-func、ogbg-molhiv 只有一到四萬張圖，拿掉 RWSE 明顯退步；超過十萬張圖的資料集，影響就不明顯了。作者推測，資料夠多時，模型比較不需要靠編碼來理解圖的結構。\n\n消融表裡最誇張的是 CLUSTER。這是一個 6 類的節點分類任務，亂猜大約是 16.7%；三個模型只要拿掉殘差連接，準確率都掉到 16.5% 到 16.8% 之間，GCN+ 拿掉正規化也一樣。在這種 10 層以上的深網路裡，少了殘差或正規化，模型等於沒學到東西。\n\n\n> [!TIP]\n> \n> 被拿來比較的 GraphGPS、表中 LRGB 基準所依據的重新評估，以及這篇用到的 GCN、GIN，可以參考我們的筆記：\n> \n> - **[[22.05] GraphGPS：圖上的 GPS](/blog/papers/graph-learning/graphgps)**\n> - **[[23.09] Where Did the Gap Go?：差距去哪了？](/blog/papers/graph-learning/where-did-the-gap-go)**\n> - **[[16.09] GCN：一個參數夠嗎？](/blog/papers/graph-learning/gcn)**\n> - **[[18.10] GIN：加總才算數](/blog/papers/graph-learning/gin)**\n\n\n### 作者自己說的限制\n\n作者承認，這些結論完全來自實驗，沒有理論解釋經典 GNN 為什麼能追上來；六個技巧之間如何互相影響、能不能真的緩解 over-smoothing 和 over-squashing，也還需要理論上的分析。\n\n他們也引用了 Bechler-Speicher 等人 2025 年的討論，指出現有的圖資料集，未必能反映真實世界圖問題的複雜與多樣。等更有挑戰性、更貼近應用的基準出現，經典 GNN 和 Graph Transformer 的相對位置，可能又會改變。\n\n## 結論\n\n這篇把 GCN、GIN、GatedGCN 補上六個常見的技巧，在 14 個圖層級資料集上和 Graph Transformer 正面比較。結果全部排進前三，8 個第一，訓練還快上好幾倍。\n\n讀這篇最好連同它的前作與 Tönshoff 等人的重新評估一起看。三篇都在說，一個新架構的優勢，得在基準也調到同樣好之後才算數。\n\n注意力也沒有因此退場。GNN+ 裡的 FFN 和 RWSE，本來就是 Graph Transformer 那一系常用的元件；兩條路線的工具箱，已經混在一起了。\n\n要在圖層級的任務上試新模型，先把 GatedGCN+ 跑起來當基準吧。作者把[程式碼](https://github.com/LUOyk1999/GNNPlus)和每個資料集的超參數都公開了，花不了多少時間。\n","imageSizes":{"/content/papers/assets/0be1b8a606332519d042698f1c6afd3ef8857eb95682b95df1cdeb9e3bfe7648.png":{"width":604,"height":510}}}