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Graph Positional Autoencoders as Self-supervised Learners

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read GraphPAE claims that reconstructing node features together with relative node positions lets a graph autoencoder capture a broader range of frequency information and beat feature- and edge-masking baselines.

desk verdict A well-engineered dual-path graph autoencoder with strong results, but the paper's core claim that it learns diverse high-frequency information is not supported by the design and needs to be reined in. read the letter →

arxiv 2505.23345 v2 pith:DCJWSAVW submitted 2025-05-29 cs.LG

Yang Liu , Deyu Bo , Wenxuan Cao , Yuan Fang , Yawen Li , Chuan Shi This is my paper
classification cs.LG
keywords graphself-supervisedlearningautoencoderspositionalencodingLaplacianeigenvectorsfrequencydiversityheterophilicgraphsmolecularpropertypredictiondual-patharchitecture
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that standard graph autoencoders, which corrupt and reconstruct masked node features or edges, mostly recover low-frequency graph signals and leave higher-frequency structure unlearned. It proposes GraphPAE, a dual-path autoencoder that reconstructs both node features and relative node positions, where positions are pairwise distances between graph-Laplacian eigenvectors. The feature path injects positional encodings into message passing, and the position path refines those encodings with attention weights before reconstructing the distances. If the claim holds, GraphPAE is a generally stronger self-supervised graph pretraining method, with its largest gains on heterophilic graphs and molecular property prediction.

What carries the argument

The load-bearing object is the dual-path encoder with a relative-distance surrogate for eigenvectors. Raw node positions are the top-K eigenvectors of the normalized graph Laplacian; connected pairs are converted to Euclidean distances, lifted by Gaussian RBF kernels, and corrupted by adding uniform noise to some nodes' eigenvectors. In the feature path, position representations are added to attention weights during message passing to raise expressiveness; in the position path, the same attention weights refine position representations toward the true distances. A Huber loss on reconstructed pairwise distances, combined with a scaled cosine error on masked features, makes the encoder recover both modalities.

What would settle it

Train GraphPAE with and without the position-reconstruction loss, then measure the frequency distribution of the learned embeddings via the graph Laplacian; if the two embeddings have nearly identical spectral profiles while downstream accuracy still differs, the performance gain is not caused by broader frequency learning. A second check: replace the eigenvector-derived distances with random fixed positions and retrain; if the gains persist, the specific frequency content is not the driver.

Watch

Extended reading notes

Core claim

The central discovery is that corrupting eigenvector positions and forcing the encoder to reconstruct pairwise node distances exposes the model to a wider frequency band than feature or edge masking does. To make this work despite the sign and basis ambiguity of eigenvectors, GraphPAE replaces raw eigenvector reconstruction with reconstruction of relative Euclidean distances between connected nodes, and it separates feature and position learning into two paths so corrupted positions do not interfere with feature recovery. The paper reports that GraphPAE outperforms contrastive and autoencoder baselines on six heterophilic node-classification datasets, seven graph-property benchmarks, and a large-scale molecule transfer-learning setup.

Load-bearing premise

The load-bearing premise is that adding noise to Laplacian eigenvector positions and reconstructing pairwise distances forces the encoder to learn a broad range of graph frequencies; the paper supports this with a single illustrative spectral figure, not with spectral analysis of the learned embeddings.

Editorial extensions

If this is right

  • Heterophilic node classification improves on all six tested graphs, with the largest margins over feature-masking autoencoders.
  • Graph-level property prediction on seven OGB datasets improves or matches the best baselines on regression and classification.
  • Pre-training on ZINC15 and fine-tuning on QM9 yields consistently lower MAE across all twelve quantum properties.
  • Ablations show that position reconstruction and the dual-path design each contribute; removing either degrades results.
  • Because the position objective is a surrogate, the method avoids the sign- and basis-ambiguity that makes direct eigenvector reconstruction unstable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct test of the paper's frequency story would be to compute the spectral energy of the learned node embeddings with and without the position-reconstruction loss; the paper does not report such an analysis, so the frequency-diversity explanation remains an inference from downstream results.
  • If the mechanism transfers, the same dual-path idea could be applied to other positional encodings, such as random-walk or shortest-path distances, to see whether frequency diversity or positional expressiveness drives the gains.
  • The equal-weight combination of both paths suggests a natural extension: weighting the position path by a measure of task-relevant high-frequency content, which could sharpen gains on heterophilic graphs without hurting homophilic ones.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes GraphPAE, a graph autoencoder with a dual-path encoder that reconstructs both masked node features and pairwise distances of Laplacian eigenvectors (relative positions). The authors argue that existing feature/edge-masking GAEs mostly recover low-frequency information, and that reconstructing corrupted positions forces the encoder to learn diverse frequency content, which is claimed to explain large gains on heterophilic node classification, OGB graph property prediction, and molecular transfer learning. The manuscript includes the method, ablation studies, extensive benchmarks, and public code.

Significance. If the frequency-diversity mechanism were established, this would be a substantial contribution to graph self-supervised learning, because it would identify a principled reason why positional reconstruction helps beyond plain feature masking. The empirical work is broad: six heterophilic node datasets, seven OGB graph benchmarks, and a ZINC15-to-QM9 transfer study, with competitive results and an explicit ablation isolating the position loss. The authors also ship code and report tuned hyperparameters, which supports reproducibility. However, the paper's central explanatory claim is currently not supported by the evidence, and the headline claim of consistent large-margin gains is contradicted on two benchmark rows. The method may still be useful, but the paper needs either direct spectral evidence for the mechanism or a more modest framing of the contribution.

major comments (3)
  1. [Sec. 4.1-4.2, Eq. (3), Fig. 1(c)] The claimed frequency-diversity mechanism is not supported by the construction. The position target P in Eq. (3) is built only from U=[u_1,...,u_K] (top-K eigenvalues, ordered increasingly), and in the heterophilic node tasks K=50 while N≈2,300-7,600 (Tables 7 and 9), i.e., the bottom 1-2% of the spectrum. Both the corrupted eP and the target P therefore live entirely in the span of the K smallest-eigenvalue eigenvectors; eigenvectors u_{K+1}...u_N never enter the position reconstruction target. The statement in Sec. 4.2 that the relative distance contains frequencies 'from low-frequency u_1 to high-frequency u_K' is therefore misleading: unless K is close to N, u_K is not a high-frequency mode. Moreover, using the paper's own identity sum_{edges}(u_k(i)-u_k(j))^2 = lambda_k, low-λ modes contribute small edge differences, so the pairwise-distance signal is dominated by the lowest-frequency part of the selected subspace. Figure 1(c) shows the effect of perturbing U^T X with the full eigenbasis, which is not the actual position corruption used in training. To sustain the central claim, the authors should provide a spectral analysis of the learned embeddings (e.g., the projection of final node representations onto Laplacian eigenvectors) or otherwise directly demonstrate that high-frequency information is learned.
  2. [Table 3 and Table 11] The abstract's claim that GraphPAE 'consistently outperforms the baselines by a large margin' is contradicted by the paper's own tables. In Table 3, on molbbbp, Sp2GCL achieves 68.72±1.53 while GraphPAE achieves 68.56±0.71, so a baseline is numerically better. In Table 11, on ogbg-products, GraphMAE2 achieves 81.59±0.02 while GraphPAE achieves 79.10±0.02, a substantial gap in the baseline's favor. The authors should either soften the claim to reflect the actual pattern (strong gains on heterophilic node tasks, mixed results on some graph-level and homophilic tasks) or provide statistical significance tests showing that the differences on the reported rows are within noise.
  3. [Sec. 5.4, Table 6] The ablation in Table 6 shows that removing L_pos hurts performance even when PEs are retained, but it does not establish that the benefit comes from 'diverse frequency information.' The improvement could equally come from the position loss acting as an auxiliary denoising regularizer, from the position path refining PEs, or from improved optimization. The paper needs a control that isolates the frequency-content explanation, for example by training with a position target that is deliberately band-limited to high-frequency eigenvectors, or by reporting the spectral content of the reconstructed distances / learned embeddings. Without such evidence, the design rationale in Sec. 4.2 remains a hypothesis rather than a verified mechanism.
minor comments (5)
  1. [Table 3] The column header 'molcintox' is a typo; the dataset is molclintox elsewhere in the paper.
  2. [Sec. 5.3, Table 4] The text says the transfer-learning results are reported as mean MAE with standard deviation, but Table 4 shows only point estimates without standard deviations.
  3. [Eq. (7) and surrounding text] The symbol d is used both for the input feature dimension (Preliminaries) and for the hidden/attention dimension in Eq. (7); please clarify by using d_h throughout the encoder equations.
  4. [Sec. 4.3] In the sentence defining X'_i, 'X'_i is the is the reconstructed feature' contains a duplicated article.
  5. [Sec. 4.1, Eq. (2)] It would be helpful to state explicitly whether a fresh noise vector δ is sampled at each epoch for each node, since this affects the effective corruption distribution.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: GraphPAE is evaluated on external benchmarks, position reconstruction is a real training objective with ablations, and self-citations are background only.

full rationale

GraphPAE's derivation chain is self-contained. The position target P is constructed as pairwise Laplacian-eigenvector distances (Eq. 3), corrupted with noise (Eq. 2), and reconstructed through L_pos (Eqs. 14-16); the encoder is then tested on held-out splits of external benchmarks (Tables 2, 3, 4, and 11). No parameter is fitted to a subset and then reported as a prediction of the same quantity. The ablation in Table 6 isolates the contribution of L_pos and PEs, and the dual-path study in Table 5 further separates the design choices. The authors' self-citations (Refs. 1-4, 60) are used as background on spectral GNNs and high-frequency information; they do not supply the correctness of GraphPAE, and no uniqueness theorem or ansatz is imported from the authors' prior work. The paper's claim that reconstructing P forces the encoder to learn diverse frequency information is not directly verified by a spectral analysis of the learned embeddings, but that is an evidential gap, not circularity: the reported 'predictions' are evaluated against independent downstream labels and strong external baselines. Thus there is no circular step by the definitions used here.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical or formal entities. All free parameters are hyperparameters of the training objective; the most consequential are the number of eigenvectors K and the position loss weight alpha, both tuned per dataset.

free parameters (6)
  • K (number of Laplacian eigenvectors for positions) = 6, 8, 15, 30, 50, 100, 200 (dataset-dependent)
    Controls the frequency range of positions; tuned per dataset in Tables 9/10, not derived.
  • alpha (position loss weight) = 0.001, 0.01, 0.1 (dataset-dependent)
    Weight of L_pos in Eq. 17; tuned per dataset; Figure 3 shows optimum varies.
  • r (masking ratio) = 0.25, 0.5, 0.75, 0.35 (dataset-dependent)
    Corruption ratio for features and positions; tuned per dataset.
  • mu_p (position offset noise scale) = 0.001 or 0.01
    Section 4.1 says it is set differently for datasets but tables do not report the per-dataset value.
  • Gaussian RBF centers and sigma (Eq. 5) = not reported
    Position lifting from scalar distances depends on RBF basis parameters; no values are given in main text or appendix.
  • SCE exponent gamma (Eq. 13) = not reported
    Feature reconstruction loss follows GraphMAE, but gamma is not restated, so reproduction depends on the code.
assumptions (5)
  • standard math Normalized graph Laplacian eigendecomposition L = U Lambda U^T and Rayleigh quotient identify eigenvalues with frequency magnitudes.
    Used in Section 3 and Appendix A to define low/high-frequency bands.
  • domain assumption Eigenvectors of the graph Laplacian are meaningful node positions and their pairwise Euclidean distances encode structural information.
    Section 4.1, Eq. 3; inherited from the PE literature [9,10,58].
  • domain assumption Injecting position representations into message passing increases GNN expressiveness beyond 1-WL.
    Section 4.2, Eq. 7; relies on prior results [11,22,57].
  • ad hoc to paper Reconstructing noisy pairwise distances forces the encoder to learn diverse frequency information.
    Section 4.2 and Section 5.1; central mechanism, supported only by downstream ablations, not by direct spectral measurement of learned features.
  • domain assumption Top-K eigenvectors provide a good trade-off between frequency coverage and computational cost.
    Section 3 and Appendix C; choice of K is a practical compromise.

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Cite this review

Pith. "Pith review of Graph Positional Autoencoders as Self-supervised Learners." pith.science (2026). https://pith.science/paper/DCJWSAVW

@misc{pith2026250523345,
  author       = {Pith},
  title        = {Pith review of: Graph Positional Autoencoders as Self-supervised Learners},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DCJWSAVW}},
  note         = {Machine review of arXiv:2505.23345}
}
read the original abstract

Graph self-supervised learning seeks to learn effective graph representations without relying on labeled data. Among various approaches, graph autoencoders (GAEs) have gained significant attention for their efficiency and scalability. Typically, GAEs take incomplete graphs as input and predict missing elements, such as masked nodes or edges. While effective, our experimental investigation reveals that traditional node or edge masking paradigms primarily capture low-frequency signals in the graph and fail to learn the expressive structural information. To address these issues, we propose Graph Positional Autoencoders (GraphPAE), which employs a dual-path architecture to reconstruct both node features and positions. Specifically, the feature path uses positional encoding to enhance the message-passing processing, improving GAE's ability to predict the corrupted information. The position path, on the other hand, leverages node representations to refine positions and approximate eigenvectors, thereby enabling the encoder to learn diverse frequency information. We conduct extensive experiments to verify the effectiveness of GraphPAE, including heterophilic node classification, graph property prediction, and transfer learning. The results demonstrate that GraphPAE achieves state-of-the-art performance and consistently outperforms baselines by a large margin.

Figures

Figures reproduced from arXiv: 2505.23345 by the authors.

Figure 1
Figure 1. Frequency magnitudes of the original and corrupted graphs in the Squirrel dataset. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. (a): GraphPAE integrates a positional corruption-reconstruction mechanism to encourage the GAE to capture diverse [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Influence of the loss weight 𝛼 and the number of eigenvectors 𝐾. from the position corruption-reconstruction mechanism, and how much from the positional information itself. Therefore, we conduct ablation studies on both L𝑝𝑜𝑠 and positional encodings. Specifically, we remove L𝑝𝑜𝑠 from Equation 17 while keeping PEs, to evaluate the effect of position reconstruction. Then, we remove both L𝑝𝑜𝑠 and PEs to isolate the imp… view at source ↗

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Evaluating Loss Functions for Graph Neural Networks: Towards Pretraining and Generalization

    cs.LG 2025-06 reject novelty 4.0 of 10

    A benchmark of 7 GNNs and 30 losses on 3 graphs claims hybrid losses and GIN rank best on average, but a central summary table contradicts the paper's full results.

Reference graph

Works this paper leans on

83 extracted references · 40 canonical work pages · cited by 1 Pith paper

  1. [1]

    Deyu Bo, Yuan Fang, Yang Liu, and Chuan Shi. 2024. Graph contrastive learning with stable and scalable spectral encoding.Advances in Neural Information Processing Systems36 (2024)

    2024

  2. [2]

    Deyu Bo, Chuan Shi, Lele Wang, and Renjie Liao. 2023. Specformer: Spectral graph neural networks meet transformers.arXiv preprint arXiv:2303.01028(2023)

    arXiv 2023

  3. [3]

    Deyu Bo, Xiao Wang, Yang Liu, Yuan Fang, Yawen Li, and Chuan Shi. 2023. A survey on spectral graph neural networks.arXiv preprint arXiv:2302.05631(2023)

    arXiv 2023

  4. [4]

    Deyu Bo, Xiao Wang, Chuan Shi, and Huawei Shen. 2021. Beyond low-frequency information in graph convolutional networks. InProceedings of the AAAI confer- ence on artificial intelligence, Vol. 35. 3950–3957

    2021

  5. [5]

    Pietro Bongini, Monica Bianchini, and Franco Scarselli. 2021. Molecular gen- erative graph neural networks for drug discovery.Neurocomputing450 (2021), 242–252

    2021

  6. [6]

    Semih Cantürk, Renming Liu, Olivier Lapointe-Gagné, Vincent Létourneau, Guy Wolf, Dominique Beaini, and Ladislav Rampášek. [n. d.]. Graph Positional and Structural Encoder. InForty-first International Conference on Machine Learning

    work page

  7. [7]

    2005.Models and methods in social network analysis

    Peter J Carrington, John Scott, and Stanley Wasserman. 2005.Models and methods in social network analysis. Vol. 28. Cambridge university press

    work page 2005

  8. [8]

    Jiashun Cheng, Man Li, Jia Li, and Fugee Tsung. 2023. Wiener graph deconvo- lutional network improves graph self-supervised learning. InProceedings of the AAAI conference on artificial intelligence, Vol. 37. 7131–7139

    work page 2023

Show all 83 references
  1. [9]

    Vijay Prakash Dwivedi and Xavier Bresson. 2020. A generalization of transformer networks to graphs.arXiv preprint arXiv:2012.09699(2020)

    2020 arXiv

  2. [10]

    Vijay Prakash Dwivedi, Chaitanya K Joshi, Anh Tuan Luu, Thomas Laurent, Yoshua Bengio, and Xavier Bresson. 2023. Benchmarking graph neural networks. Journal of Machine Learning Research24, 43 (2023), 1–48

    2023

  3. [11]

    Vijay Prakash Dwivedi, Anh Tuan Luu, Thomas Laurent, Yoshua Bengio, and Xavier Bresson. 2021. Graph neural networks with learnable structural and positional representations.arXiv preprint arXiv:2110.07875(2021)

    2021 arXiv

  4. [12]

    Vijay Prakash Dwivedi, Ladislav Rampášek, Michael Galkin, Ali Parviz, Guy Wolf, Anh Tuan Luu, and Dominique Beaini. 2022. Long range graph benchmark. Advances in Neural Information Processing Systems35 (2022), 22326–22340

    2022

  5. [13]

    Chen Gao, Yu Zheng, Nian Li, Yinfeng Li, Yingrong Qin, Jinghua Piao, Yuhan Quan, Jianxin Chang, Depeng Jin, Xiangnan He, et al. 2023. A survey of graph KDD ’25, August 3–7, 2025, Toronto, ON, Canada Yang Liu et al. neural networks for recommender systems: Challenges, methods, ...

    2023

  6. [14]

    Zhangyang Gao, Daize Dong, Cheng Tan, Jun Xia, Bozhen Hu, and Stan Z Li. [n. d.]. A Graph is Worth𝐾 Words: Euclideanizing Graph using Pure Transformer. InForty-first International Conference on Machine Learning

  7. [15]

    Kaveh Hassani and Amir Hosein Khasahmadi. 2020. Contrastive multi-view representation learning on graphs. InInternational conference on machine learning. PMLR, 4116–4126

    2020

  8. [16]

    Girshick

    Kaiming He, Xinlei Chen, Saining Xie, Yanghao Li, Piotr Dollár, and Ross B. Girshick. 2022. Masked Autoencoders Are Scalable Vision Learners. InCVPR. IEEE, 15979–15988

    2022

  9. [17]

    Zhenyu Hou, Yufei He, Yukuo Cen, Xiao Liu, Yuxiao Dong, Evgeny Kharlamov, and Jie Tang. 2023. Graphmae2: A decoding-enhanced masked self-supervised graph learner. InProceedings of the ACM web conference 2023. 737–746

    2023

  10. [18]

    Zhenyu Hou, Xiao Liu, Yukuo Cen, Yuxiao Dong, Hongxia Yang, Chunjie Wang, and Jie Tang. 2022. Graphmae: Self-supervised masked graph autoencoders. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 594–604

    2022

  11. [19]

    Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec. 2020. Open graph benchmark: Datasets for machine learning on graphs.Advances in neural information processing systems 33 (2020), 22118–22133

    2020

  12. [20]

    Weihua Hu, Bowen Liu, Joseph Gomes, Marinka Zitnik, Percy Liang, Vijay Pande, and Jure Leskovec. [n. d.]. STRATEGIES FOR PRE-TRAINING GRAPH NEURAL NETWORKS. ([n. d.])

  13. [21]

    Ziniu Hu, Yuxiao Dong, Kuansan Wang, Kai-Wei Chang, and Yizhou Sun. 2020. Gpt-gnn: Generative pre-training of graph neural networks. InProceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining. 1857–1867

    2020

  14. [22]

    Yinan Huang, William Lu, Joshua Robinson, Yu Yang, Muhan Zhang, Stefanie Jegelka, and Pan Li. 2023. On the stability of expressive positional encodings for graph neural networks.arXiv preprint arXiv:2310.02579(2023)

    2023 arXiv

  15. [23]

    Peter J Huber. [n. d.]. Robust estimation of a location parameter. InBreakthroughs in statistics: Methodology and distribution. Springer, 492–518

  16. [24]

    Dejun Jiang, Zhenxing Wu, Chang-Yu Hsieh, Guangyong Chen, Ben Liao, Zhe Wang, Chao Shen, Dongsheng Cao, Jian Wu, and Tingjun Hou. 2021. Could graph neural networks learn better molecular representation for drug discovery? A comparison study of descriptor-based and graph-based ...

    2021

  17. [25]

    Wei Ju, Yifan Wang, Yifang Qin, Zhengyang Mao, Zhiping Xiao, Junyu Luo, Jun- wei Yang, Yiyang Gu, Dongjie Wang, Qingqing Long, et al. 2024. Towards Graph Contrastive Learning: A Survey and Beyond.arXiv preprint arXiv:2405.11868 (2024)

    2024 arXiv

  18. [26]

    Thomas N Kipf and Max Welling. 2016. Variational graph auto-encoders.arXiv preprint arXiv:1611.07308(2016)

    2016 arXiv

  19. [27]

    Devin Kreuzer, Dominique Beaini, Will Hamilton, Vincent Létourneau, and Pru- dencio Tossou. 2021. Rethinking graph transformers with spectral attention. Advances in Neural Information Processing Systems34 (2021), 21618–21629

    2021

  20. [28]

    Jintang Li, Ruofan Wu, Wangbin Sun, Liang Chen, Sheng Tian, Liang Zhu, Changhua Meng, Zibin Zheng, and Weiqiang Wang. 2023. What’s Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders. InPro- ceedings of the 29th ACM SIGKDD Conference on Knowledge Discov...

    2023

  21. [29]

    Pan Li, Yanbang Wang, Hongwei Wang, and Jure Leskovec. 2020. Distance encod- ing: Design provably more powerful neural networks for graph representation learning.Advances in Neural Information Processing Systems33 (2020), 4465–4478

    2020

  22. [30]

    Xiang Li, Tiandi Ye, Caihua Shan, Dongsheng Li, and Ming Gao. 2023. Seegera: Self-supervised semi-implicit graph variational auto-encoders with masking. In Proceedings of the ACM web conference 2023. 143–153

    2023

  23. [31]

    Derek Lim, Joshua Robinson, Lingxiao Zhao, Tess Smidt, Suvrit Sra, Haggai Maron, and Stefanie Jegelka. 2022. Sign and basis invariant networks for spectral graph representation learning.arXiv preprint arXiv:2202.13013(2022)

    2022 arXiv

  24. [32]

    Chuang Liu, Yuyao Wang, Yibing Zhan, Xueqi Ma, Dapeng Tao, Jia Wu, and Wenbin Hu. 2024. Where to mask: structure-guided masking for graph masked autoencoders. InProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence(Jeju, Korea)(IJCAI ’24). A...

    2024 doi

  25. [33]

    Yixin Liu, Ming Jin, Shirui Pan, Chuan Zhou, Yu Zheng, Feng Xia, and S Yu Philip

  26. [34]

    Zhiyuan Liu, Yaorui Shi, An Zhang, Enzhi Zhang, Kenji Kawaguchi, Xiang Wang, and Tat-Seng Chua. 2024. Rethinking tokenizer and decoder in masked graph modeling for molecules.Advances in Neural Information Processing Systems36 (2024)

    2024

  27. [35]

    Zaiqiao Meng, Shangsong Liang, Hongyan Bao, and Xiangliang Zhang. 2019. Co- embedding attributed networks. InProceedings of the twelfth ACM international conference on web search and data mining. 393–401

    2019

  28. [36]

    Péter Mernyei and Cătălina Cangea. 2020. Wiki-cs: A wikipedia-based benchmark for graph neural networks.arXiv preprint arXiv:2007.02901(2020)

    2020 arXiv

  29. [37]

    Grégoire Mialon, Dexiong Chen, Margot Selosse, and Julien Mairal. 2021. Graphit: Encoding graph structure in transformers.arXiv preprint arXiv:2106.05667(2021)

    2021 arXiv

  30. [38]

    Shirui Pan, Ruiqi Hu, Guodong Long, Jing Jiang, Lina Yao, and Chengqi Zhang

  31. [39]

    Jiwoong Park, Minsik Lee, Hyung Jin Chang, Kyuewang Lee, and Jin Young Choi. 2019. Symmetric graph convolutional autoencoder for unsupervised graph representation learning. InProceedings of the IEEE/CVF international conference on computer vision. 6519–6528

    2019

  32. [40]

    Hongbin Pei, Bingzhe Wei, Kevin Chen-Chuan Chang, Yu Lei, and Bo Yang

  33. [41]

    Ladislav Rampášek, Michael Galkin, Vijay Prakash Dwivedi, Anh Tuan Luu, Guy Wolf, and Dominique Beaini. 2022. Recipe for a general, powerful, scalable graph transformer.Advances in Neural Information Processing Systems35 (2022), 14501–14515

    2022

  34. [42]

    Benedek Rozemberczki, Carl Allen, and Rik Sarkar. 2021. Multi-scale attributed node embedding.Journal of Complex Networks9, 2 (2021), cnab014

    2021

  35. [43]

    Amin Salehi and Hasan Davulcu. 2019. Graph attention auto-encoders.arXiv preprint arXiv:1905.10715(2019)

    2019 arXiv

  36. [44]

    Kartik Sharma, Yeon-Chang Lee, Sivagami Nambi, Aditya Salian, Shlok Shah, Sang-Wook Kim, and Srijan Kumar. 2024. A survey of graph neural networks for social recommender systems.Comput. Surveys56, 10 (2024), 1–34

    2024

  37. [45]

    Yucheng Shi, Yushun Dong, Qiaoyu Tan, Jundong Li, and Ninghao Liu. 2023. Gigamae: Generalizable graph masked autoencoder via collaborative latent space reconstruction. InProceedings of the 32nd ACM International Conference on Infor- mation and Knowledge Management. 2259–2269

    2023

  38. [46]

    Vighnesh Shiv and Chris Quirk. 2019. Novel positional encodings to enable tree-based transformers.Advances in neural information processing systems32 (2019)

    2019

  39. [47]

    Shashank Sheshar Singh, Samya Muhuri, Shivansh Mishra, Divya Srivastava, Harish Kumar Shakya, and Neeraj Kumar. 2024. Social Network Analysis: A Survey on Process, Tools, and Application.Comput. Surveys56, 8 (2024), 1–39

    2024

  40. [48]

    Teague Sterling and John J Irwin. 2015. ZINC 15–ligand discovery for everyone. Journal of chemical information and modeling55, 11 (2015), 2324–2337

    2015

  41. [49]

    Fan-Yun Sun, Jordan Hoffmann, Vikas Verma, and Jian Tang. 2019. Infograph: Un- supervised and semi-supervised graph-level representation learning via mutual information maximization.arXiv preprint arXiv:1908.01000(2019)

    2019 arXiv

  42. [50]

    Qiaoyu Tan, Ninghao Liu, Xiao Huang, Soo-Hyun Choi, Li Li, Rui Chen, and Xia Hu. 2023. S2gae: Self-supervised graph autoencoders are generalizable learners with graph masking. InProceedings of the sixteenth ACM international conference on web search and data mining. 787–795

    2023

  43. [51]

    Shantanu Thakoor, Corentin Tallec, Mohammad Gheshlaghi Azar, Rémi Munos, Petar Veličković, and Michal Valko. 2021. Bootstrapped representation learning on graphs. InICLR 2021 Workshop on Geometrical and Topological Representation Learning

    2021

  44. [52]

    Amanda L Traud, Peter J Mucha, and Mason A Porter. 2012. Social structure of facebook networks.Physica A: Statistical Mechanics and its Applications391, 16 (2012), 4165–4180

    2012

  45. [53]

    A Vaswani. 2017. Attention is all you need.Advances in Neural Information Processing Systems(2017)

    2017

  46. [54]

    Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. 2018. Graph Attention Networks. InInternational Con- ference on Learning Representations

    2018

  47. [55]

    Petar Veličković, William Fedus, William L Hamilton, Pietro Liò, Yoshua Bengio, and R Devon Hjelm. 2018. Deep graph infomax.arXiv preprint arXiv:1809.10341 (2018)

    2018 arXiv

  48. [56]

    Lilapati Waikhom and Ripon Patgiri. 2023. A survey of graph neural networks in various learning paradigms: methods, applications, and challenges.Artificial Intelligence Review56, 7 (2023), 6295–6364

    2023

  49. [57]

    Haorui Wang, Haoteng Yin, Muhan Zhang, and Pan Li. [n. d.]. Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks. In International Conference on Learning Representations

  50. [58]

    Haorui Wang, Haoteng Yin, Muhan Zhang, and Pan Li. 2022. Equivariant and stable positional encoding for more powerful graph neural networks.arXiv preprint arXiv:2203.00199(2022)

    2022 arXiv

  51. [59]

    Liang Wang, Xiang Tao, Qiang Liu, and Shu Wu. 2024. Rethinking Graph Masked Autoencoders through Alignment and Uniformity. InProceedings of the AAAI Conference on Artificial Intelligence, Vol. 38. 15528–15536

    2024

  52. [60]

    Xiao Wang, Meiqi Zhu, Deyu Bo, Peng Cui, Chuan Shi, and Jian Pei. 2020. Am- gcn: Adaptive multi-channel graph convolutional networks. InProceedings of the 26th ACM SIGKDD International conference on knowledge discovery & data mining. 1243–1253

    2020

  53. [61]

    Asiri Wijesinghe, Hao Zhu, and Piotr Koniusz. [n. d.]. Graph Self-Supervised Learning with Learnable Structural and Positional Encodings. InTHE WEB CON- FERENCE 2025. Graph Positional Autoencoders as Self-supervised Learners KDD ’25, August 3–7, 2025, Toronto, ON, Canada

    2025

  54. [62]

    Lirong Wu, Haitao Lin, Cheng Tan, Zhangyang Gao, and Stan Z Li. 2021. Self- supervised learning on graphs: Contrastive, generative, or predictive.IEEE Transactions on Knowledge and Data Engineering35, 4 (2021), 4216–4235

    2021

  55. [63]

    Zhanghao Wu, Paras Jain, Matthew Wright, Azalia Mirhoseini, Joseph E Gonzalez, and Ion Stoica. 2021. Representing long-range context for graph neural networks with global attention.Advances in Neural Information Processing Systems34 (2021), 13266–13279

    2021

  56. [64]

    Zhenqin Wu, Bharath Ramsundar, Evan N Feinberg, Joseph Gomes, Caleb Ge- niesse, Aneesh S Pappu, Karl Leswing, and Vijay Pande. 2018. MoleculeNet: a benchmark for molecular machine learning.Chemical science9, 2 (2018), 513–530

    2018

  57. [65]

    Jun Xia, Chengshuai Zhao, Bozhen Hu, Zhangyang Gao, Cheng Tan, Yue Liu, Siyuan Li, and Stan Z Li. 2023. Mole-bert: Rethinking pre-training graph neural networks for molecules. (2023)

    2023

  58. [66]

    Yaochen Xie, Zhao Xu, Jingtun Zhang, Zhengyang Wang, and Shuiwang Ji. 2022. Self-supervised learning of graph neural networks: A unified review.IEEE trans- actions on pattern analysis and machine intelligence45, 2 (2022), 2412–2429

    2022

  59. [67]

    Zhaoping Xiong, Dingyan Wang, Xiaohong Liu, Feisheng Zhong, Xiaozhe Wan, Xutong Li, Zhaojun Li, Xiaomin Luo, Kaixian Chen, Hualiang Jiang, et al. 2019. Pushing the boundaries of molecular representation for drug discovery with the graph attention mechanism.Journal of medicinal...

    2019

  60. [68]

    Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. 2018. How powerful are graph neural networks?arXiv preprint arXiv:1810.00826(2018)

    2018 arXiv

  61. [69]

    Chengxuan Ying, Tianle Cai, Shengjie Luo, Shuxin Zheng, Guolin Ke, Di He, Yanming Shen, and Tie-Yan Liu. 2021. Do transformers really perform badly for graph representation?Advances in neural information processing systems34 (2021), 28877–28888

    2021

  62. [70]

    Yuning You, Tianlong Chen, Yang Shen, and Zhangyang Wang. 2021. Graph contrastive learning automated. InInternational Conference on Machine Learning. PMLR, 12121–12132

    2021

  63. [71]

    Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, and Yang Shen. 2020. Graph contrastive learning with augmentations.Advances in neural information processing systems33 (2020), 5812–5823

    2020

  64. [72]

    Xingtong Yu, Zhou Chang, Kuai Zhongwei, Zhang Xinming, and Fang Yuan

  65. [73]

    Xingtong Yu, Yuan Fang, Zemin Liu, Yuxia Wu, Zhihao Wen, Jianyuan Bo, Xin- ming Zhang, and Steven CH Hoi. 2024. Few-Shot Learning on Graphs: from Meta-learning to Pre-training and Prompting.arXiv preprint arXiv:2402.01440 (2024)

    2024 arXiv

  66. [74]

    Xingtong Yu, Zhenghao Liu, Yuan Fang, Zemin Liu, Sihong Chen, and Xinming Zhang. 2024. Generalized graph prompt: Toward a unification of pre-training and downstream tasks on graphs.IEEE TKDE(2024)

    2024

  67. [75]

    Hengrui Zhang, Qitian Wu, Junchi Yan, David Wipf, and Philip S Yu. 2021. From canonical correlation analysis to self-supervised graph neural networks.Advances in Neural Information Processing Systems34 (2021), 76–89

    2021

  68. [76]

    Zaixi Zhang, Qi Liu, Hao Wang, Chengqiang Lu, and Chee-Kong Lee. 2021. Motif- based graph self-supervised learning for molecular property prediction.Advances in Neural Information Processing Systems34 (2021), 15870–15882

    2021

  69. [77]

    Ziwen Zhao, Yuhua Li, Yixiong Zou, Jiliang Tang, and Ruixuan Li. 2024. Masked Graph Autoencoder with Non-discrete Bandwidths. InProceedings of the ACM on Web Conference 2024. 377–388

    2024

  70. [78]

    Gengmo Zhou, Zhifeng Gao, Qiankun Ding, Hang Zheng, Hongteng Xu, Zhewei Wei, Linfeng Zhang, and Guolin Ke. 2023. Uni-Mol: A Universal 3D Molecular Representation Learning Framework. InICLR. OpenReview.net

    2023

  71. [79]

    Yun Zhu, Haizhou Shi, Xiaotang Wang, Yongchao Liu, Yaoke Wang, Boci Peng, Chuntao Hong, and Siliang Tang. 2025. Graphclip: Enhancing transferability in graph foundation models for text-attributed graphs. InProceedings of the ACM on Web Conference 2025. 2183–2197. Appendices A ...

    2025

  72. [2018]

    Adversarially regularized graph autoencoder for graph embedding.arXiv preprint arXiv:1802.04407(2018)

    2018 arXiv

  73. [2020]

    Geom-gcn: Geometric graph convolutional networks.arXiv preprint arXiv:2002.05287(2020)

    2020 arXiv

  74. [2022]

    Graph self-supervised learning: A survey.IEEE transactions on knowledge and data engineering35, 6 (2022), 5879–5900

    2022

  75. [2025]

    Inthe ACM SIGKDD Conference on Knowledge Discovery and Data Mining (SIGKDD)

    GCoT: Chain-of-Thought Prompt Learning for Graphs. Inthe ACM SIGKDD Conference on Knowledge Discovery and Data Mining (SIGKDD)

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.