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Why Does Dropping Edges Usually Outperform Adding Edges in Graph Contrastive Learning?

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that the relative stability of edge dropping versus edge adding in graph contrastive learning is governed by the Error Passing Rate, with the change proportional to a degree-based coefficient and the threshold set by an…

desk verdict A genuinely good question and a working algorithm, but the central theoretical explanation rests on an unstated extra assumption, so the main claim is not established in the current form. read the letter →

arxiv 2412.08128 v4 pith:KTZONL7F submitted 2024-12-11 cs.LG

Yanchen Xu , Siqi Huang , Hongyuan Zhang , Xuelong Li This is my paper · ORCID
classification cs.LG
keywords graphcontrastivelearningedgedroppingaddingErrorPassingRateaugmentationneuralnetworkmessageself-supervised
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

Graph contrastive learning usually augments a graph by dropping edges; adding edges is empirically unstable, and the paper's question is why. It defines the Error Passing Rate (EPR), the fraction of message-passing traffic in a GCN that crosses class boundaries, and proves that the EPR change caused by adding or dropping one edge is proportional to a degree-based coefficient $\alpha_{ij}$. Under the paper's uniformity assumption, adding an edge between same-class nodes lowers EPR by $k\alpha/m'$, adding a cross-class edge raises it by $(1-k)\alpha/m'$, and dropping an edge has the mirror-image magnitudes. Since real graphs have $k<0.5$ and most candidate non-edges are cross-class, a random added edge injects the larger error term while a random dropped edge carries the smaller one, which is the paper's explanation for the empirical preference for dropping. The paper then turns this into an augmentation algorithm, EPAGCL, that weights edge additions and drops by EPR-derived coefficients and reports gains over existing contrastive baselines.

What carries the argument

The central object is the Error Passing Rate (EPR), $r_G=M_{\mathrm{wp}}/M$, the proportion of messages in GCN aggregation that travel along error edges, i.e. edges linking different classes. The load-bearing identity is $\delta_{G,G'}=m\,m'\,(r_G-r_{G'})=(k-\xi)\,\alpha_{ij}\,m$ under Assumption 3.4, where $\alpha_{ij}$ is the degree-normalized coefficient $2/\sqrt{(d_i+1)(d_j+1)}$ for an added edge and $2/\sqrt{d_i d_j}$ for a dropped edge. This identity reduces the effect of a single edge perturbation to a product of a universal error fraction, a class-concordance indicator, and a degree factor, which is what lets the paper compare the stability of adding and dropping without labels. It also supplies the algorithmic pre-screening criterion: candidate edges can be ranked by $\alpha$ and perturbed only when the EPR impact is small.

What would settle it

Use ground-truth labels on a benchmark graph to compute each node's error fraction $M_{\mathrm{wp},i}/M_i$ and check whether the values are nearly constant; if they vary widely, the uniform-$k$ assumption behind Theorem 3.5 does not hold. Alternatively, measure EPR after adding and dropping edges with known $\alpha$ values and test whether the change is proportional to $\alpha$ as predicted.

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Extended reading notes

Core claim

The paper's central claim is that the relative stability of edge dropping versus edge adding in graph contrastive learning is governed by an Error Passing Rate (EPR), defined as the ratio of GCN message-passing traffic that flows between different classes. For a graph $G$ and a graph $G'$ obtained by adding edge $(v_i,v_j)$, the paper proves the identity $\delta_{G,G'} = m\,m'\,(r_G - r_{G'}) = (k-\xi)\,\alpha_{ij}\,m$, where $k$ is the assumed uniform per-node error fraction, $\xi=1$ exactly when the endpoints have different classes, and $\alpha_{ij}=2/\sqrt{(d_i+1)(d_j+1)}$. For dropping the same edge the sign reverses, $\delta_{G',G}=(\xi-k)\alpha_{ij}m$, with $\alpha_{ij}=2/\sqrt{d_i d_j}$ in the original graph. The magnitudes are therefore $k\alpha/m'$ for a same-class addition, $(1-k)\alpha/m'$ for a cross-class addition, and the mirror image for drops. Because most real graphs have $k<0.5$ and because almost all non-edges are cross-class, this explains why dropping edges usually hurts less than adding edges; the paper goes on to construct an augmentation method that samples edges according to these $\alpha$ weights.

Load-bearing premise

The entire quantitative comparison rests on the assumption that every node receives the same fraction $k$ of erroneous messages during aggregation, a condition real graphs will only approximate.

Editorial extensions

If this is right

  • Under $k<0.5$ in homophilic graphs, the expected EPR damage of a random edge addition ($(1-k)\alpha/m'$ for the typical cross-class non-edge) exceeds that of a random edge drop ($k\alpha/m$ for the typical same-class edge), which is the paper's quantitative explanation for the empirical rule.
  • Because non-edges vastly outnumber edges, blind edge adding is almost always a cross-class move and therefore raises EPR; limiting additions to non-edges with small $\alpha$ should make adding competitive with dropping.
  • Low-degree node pairs have larger $\alpha$, so their perturbation changes EPR more; augmentation policies that frequently drop low-degree edges are predicted to be higher-variance, a prediction the paper verifies against importance-based edge dropping.
  • A symmetric use of added edges is beneficial in only one of the two contrastive views; the paper's EPAGCL uses add-and-drop for one view and drop-only for the other, and reports lower standard deviation as well as higher accuracy.

Reading between the lines

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

  • If Assumption 3.4 is replaced by node-dependent error fractions $k_i$, the clean proportionality in the paper's Eq. (5) should become a weighted average; a per-node version of the theorem could predict which local neighborhoods benefit from drops versus adds.
  • The predicted reversal at $k=0.5$ is directly testable: on a heterophilic or dense graph with EPR above one half, the theory says edge adding should become the stable augmentation, turning EPR into a practical guide for augmentation choice.
  • The analysis treats one edge perturbation at a time; an extension to simultaneous perturbations or deeper GNNs would show whether the $\alpha$-based edge ranking survives interactions, which is the assumption the EPAGCL sampling procedure effectively makes.
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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

4 major / 4 minor

Summary. The paper asks why dropping edges is usually a more stable graph augmentation than adding edges in graph contrastive learning. It introduces a metric called Error Passing Rate (EPR), which measures the fraction of message-passing mass that flows along edges connecting different classes in a GCN. The authors derive formulas for the change in EPR when an edge is added or dropped, concluding that, under an assumption of uniform per-node error rates, the change is proportional to alpha_ij = 2/sqrt((d_i+1)(d_j+1)) or 2/sqrt(d_i d_j), and that for graphs with EPR below 0.5 dropping edges is more stable. Based on this analysis they propose EPAGCL, an augmentation method that adds and drops edges with probabilities derived from alpha_ij. Experiments on seven benchmark datasets report competitive or improved accuracy relative to several GCL baselines, together with ablation and efficiency studies.

Significance. The question addressed is relevant and the proposed EPR viewpoint is interpretable: it gives a concrete, label-free-in-principle measure of how well a graph structure matches a GNN's message-passing scheme. If the theoretical derivation were sound, the paper would provide a useful explanation for a widely observed empirical phenomenon and a principled basis for designing augmentations. The paper also ships code and includes a reasonably broad experimental comparison, ablations, efficiency measurements, and appendices with EPR values for real datasets. The main weakness is that the central theorem supporting the paper's explanation contains a derivation gap that is not fixed by the stated assumptions, and the key uniformity assumption is neither justified nor empirically checked. Until these points are repaired, the paper's contribution is primarily an empirical augmentation method rather than an established theoretical explanation.

major comments (4)
  1. [Appendix B / Eq. (5)] The derivation of Eq. (5) from Assumption 3.4 is incomplete. Assumption 3.4 states Mwp,i/Mi = k for every node, which gives e2 = k m2 and e3 = k m3 for the edge sets incident to vi and vj, but for the set E1 (edges with neither endpoint equal to vi or vj) it gives only the aggregate constraint 2e1 + C_err = k(2m1 + C_tot), where C_err and C_tot are the error and total message masses on the cut between {vi,vj} and the remaining nodes. The equality e1 = k m1 used in Appendix B therefore requires the additional, unstated condition C_err = k C_tot. Since Eq. (5) and hence Theorem 3.5 are derived entirely from this step, the paper's central explanation for why dropping edges is more stable than adding edges is not established even under Assumption 3.4.
  2. [Section 3.3 / Appendix F] Assumption 3.4 is load-bearing for Theorem 3.5 but is never justified or tested. Table 6 reports only the global EPR rG for benchmark graphs; a global value below 0.5 is compatible with arbitrarily large per-node variation in Mwp,i/Mi, so it does not support the uniformity assumption or the inference that 'k < 0.5 for most graphs' in the sense required by Theorem 3.5. The authors should report the empirical distribution of per-node error fractions on the datasets used in Section 4, or replace Assumption 3.4 with a condition that can actually be checked on real graphs.
  3. [Theorem 3.3 / Appendix A] Theorem 3.3.2 as stated is false without an additional assumption. The proof introduces Assumption A.2 (at least one same-class edge) only in the appendix and uses it to rule out the equality case t1 = t2 = t3 = 1. If every edge of G connects different classes, then adding a different-class edge leaves rG unchanged, so delta_G,G' = 0 rather than < 0. The theorem statement in Section 3.3 must include this condition or a replacement, and the main text should state it explicitly rather than burying it in the proof.
  4. [Section 4 / Theorem 3.3] The benchmark datasets used in the experiments do not satisfy the degree condition dmax <= 4 dmin - 1 assumed by Theorem 3.3. For example, Cora has a maximum degree far above 4 dmin - 1, so the experiments in Section 4 cannot be said to validate Theorem 3.3 on these graphs. If the intended validation target is instead Theorem 3.5, this should be stated explicitly, since Theorem 3.5 does not inherit the degree condition from Theorem 3.3.
minor comments (4)
  1. [Proposition 3.2 / Eq. (2)] In Eq. (2) the numerator and denominator are written with the same symbol E, which is confusing: the numerator should be the sum over the error edge set (edges connecting different classes), while the denominator is the sum over all edges. Please use distinct notation, e.g. an overline or a calligraphic symbol for the error edge set, throughout the paper.
  2. [Appendix E / Table 5] The Wilcoxon signed-rank test is applied after repeating each of the 5 runs five times to obtain 25 observations. This pseudo-replication violates the independence assumption of the test and inflates the reported significance levels. The test should be run on the original 5 paired observations, or a different procedure should be used.
  3. [Section 3.3 / Appendix B] The symbol for the class-indicator term is xi in Eq. (5) in the main text but becomes s in Appendix B; please standardize the notation.
  4. [Throughout] There are several typographical errors, including 'recursivly' in Section 3.2, 'summarzied' before Theorem 3.3, and 'Memroy' in Table 3; a careful proofread is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the EPR derivation is self-contained and the self-citations are inspirational rather than load-bearing.

full rationale

The central derivation (Eq. 5 and Theorem 3.5) starts from Definition 3.1 and Assumption 3.4, neither of which is fitted to the claims. Under Assumption 3.4, e2 = k m2 and e3 = k m3 are exactly the per-node constraints at vi and vj, and subtracting these from the summed per-node constraints over all nodes yields e1 = k m1; hence Appendix B's reduction delta = (k - xi) alpha m follows from the stated assumptions rather than from a hidden fit. EPR is introduced as a definition, not as a renamed known result, and Theorems 3.3 and 3.5 are derived inequalities with stated degree conditions. The alpha weights used in the algorithm are computed from graph degrees, not fitted to performance. Citations to Li (2022) and Zhang et al. (2024), which share authors with this paper, are used only as inspiration and related-work context; the EPR analysis does not depend on them. The empirical EPR values in Appendix F validate the k < 0.5 assumption on benchmarks but are not used as fitted inputs to the derivation. Therefore no equation in the paper reduces by construction to its own inputs. The main scientific weaknesses, namely the uniform per-node k assumption and the degree condition d_max <= 4 d_min - 1 being violated by benchmark graphs, are concerns about assumption validity, not circularity, and are outside this pass.

Assumptions & free parameters 5 free parameters · 4 assumptions · 1 invented entities

The theory introduces one new metric (EPR) that depends on ground-truth class labels, and the central derivation leans on two assumptions: a uniform per-node error rate (Assumption 3.4) and a bounded degree ratio (dmax <= 4 dmin - 1). Neither is validated on the benchmark graphs, and the EPR values in Appendix F are computed with labels, which are unavailable in the self-supervised setting. The algorithm itself adds a handful of tunable hyperparameters.

free parameters (5)
  • padd = grid-searched, not tied to theory
    Controls overall probability of adding edges in Eq (9); tuned per dataset in Appendix D.
  • pdrop (edge dropping rates pe1, pe2) = grid-searched over {0.1..0.6}
    Controls edge removal probability; chosen per dataset to maximize accuracy.
  • feature mask rates pf1, pf2 = grid-searched over {0.1,0.3,0.5}
    Feature masking augments views; tuned per dataset.
  • temperature tau = grid-searched over {0.3,0.4,0.5}
    InfoNCE temperature; tuned per dataset.
  • candidate node threshold = top sqrt(2|E|) highest-degree nodes
    Algorithm 1 line 5 restricts the add-edge candidate set; choice is heuristic, not derived.
assumptions (4)
  • ad hoc to paper Assumption 3.4: Mwp,i/Mi = k for all nodes i
    Uniform per-node error fraction; used to derive Eq (5) and Theorem 3.5. Not empirically tested.
  • domain assumption Degree regularity: dmax <= 4 dmin - 1
    Required for Theorem 3.3; violated by the datasets in Table 1.
  • domain assumption Assumption A.2: at least one same-class edge exists
    Used in proof of Theorem 3.3.2; reasonable for most graphs but not universal.
  • domain assumption Ground-truth class labels exist for defining the error edge set E
    EPR is defined relative to underlying classes, which are unknown in self-supervised learning; the paper uses labels only for analysis.
invented entities (1)
  • Error Passing Rate (EPR) independent evidence
    purpose: Quantify the fraction of messages passed between different-class nodes in a GNN; used to motivate degree-based augmentation probabilities.
    Defined in Definition 3.1 and measured on benchmark datasets (Appendix F), so it is operationally computable when labels are available.

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Pith. "Pith review of Why Does Dropping Edges Usually Outperform Adding Edges in Graph Contrastive Learning?." pith.science (2026). https://pith.science/paper/KTZONL7F

@misc{pith2026241208128,
  author       = {Pith},
  title        = {Pith review of: Why Does Dropping Edges Usually Outperform Adding Edges in Graph Contrastive Learning?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KTZONL7F}},
  note         = {Machine review of arXiv:2412.08128}
}
read the original abstract

Graph contrastive learning (GCL) has been widely used as an effective self-supervised learning method for graph representation learning. However, how to apply adequate and stable graph augmentation to generating proper views for contrastive learning remains an essential problem. Dropping edges is a primary augmentation in GCL while adding edges is not a common method due to its unstable performance. To our best knowledge, there is no theoretical analysis to study why dropping edges usually outperforms adding edges. To answer this question, we introduce a new metric, namely Error Passing Rate (EPR), to quantify how a graph fits the network. Inspired by the theoretical conclusions and the idea of positive-incentive noise, we propose a novel GCL algorithm, Error-PAssing-based Graph Contrastive Learning (EPAGCL), which uses both edge adding and edge dropping as its augmentations. To be specific, we generate views by adding and dropping edges based on the weights derived from EPR. Extensive experiments on various real-world datasets are conducted to validate the correctness of our theoretical analysis and the effectiveness of our proposed algorithm. Our code is available at: https://github.com/hyzhang98/EPAGCL.

Figures

Figures reproduced from arXiv: 2412.08128 by the authors.

Figure 1
Figure 1. Performance on WikiCS and CiteSeer. All the [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Framework of EPAGCL: Before training, the weight of all existing edges and candidate edge for adding is computed [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. t-SNE embeddings of the raw features and learned embeddings obtained through EPAGCL on Cora and CiteSeer. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Performance improvement of five augmentation [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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Reference graph

Works this paper leans on

44 extracted references · 19 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

  3. [3]

    Chen, D.; Lin, Y.; Li, W.; Li, P.; Zhou, J.; and Sun, X. 2020 a . Measuring and relieving the over-smoothing problem for graph neural networks from the topological view. In Proceedings of the AAAI conference on artificial intelligence, volume 34, 3438--3445

    work page 2020

  4. [4]

    Chen, T.; Kornblith, S.; Norouzi, M.; and Hinton, G. 2020 b . A simple framework for contrastive learning of visual representations. In International conference on machine learning, 1597--1607. PMLR

    work page 2020

  5. [5]

    Gao, T.; Yao, X.; and Chen, D. 2021. SimCSE : Simple Contrastive Learning of Sentence Embeddings. In Empirical Methods in Natural Language Processing (EMNLP)

    work page 2021

  6. [6]

    S.; Ribeiro, A.; and Sadler, B

    Gao, Z.; Bhattacharya, S.; Zhang, L.; Blum, R. S.; Ribeiro, A.; and Sadler, B. M. 2021. Training robust graph neural networks with topology adaptive edge dropping

    work page 2021

  7. [7]

    Hassani, K.; and Khasahmadi, A. H. 2020. Contrastive multi-view representation learning on graphs. In International conference on machine learning, 4116--4126. PMLR

    2020

  8. [8]

    He, K.; Fan, H.; Wu, Y.; Xie, S.; and Girshick, R. 2020. Momentum contrast for unsupervised visual representation learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 9729--9738

    2020

Show all 44 references
  1. [9]

    Hu, W.; Fey, M.; Zitnik, M.; Dong, Y.; Ren, H.; Liu, B.; Catasta, M.; and Leskovec, J. 2020. Open graph benchmark: Datasets for machine learning on graphs. Advances in neural information processing systems, 33: 22118--22133

    2020

  2. [10]

    Kingma, D.; and Ba, J. 2015. Adam: A Method for Stochastic Optimization. In International Conference on Learning Representations (ICLR). San Diega, CA, USA

    2015

  3. [11]

    N.; and Welling, M

    Kipf, T. N.; and Welling, M. 2017. Semi-Supervised Classification with Graph Convolutional Networks. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings

    2017

  4. [12]

    Li, X. 2022. Positive-incentive noise. IEEE Transactions on Neural Networks and Learning Systems

    2022

  5. [13]

    C.; and Pan, S

    Liu, Y.; Zheng, Y.; Zhang, D.; Lee, V. C.; and Pan, S. 2023. Beyond smoothing: Unsupervised graph representation learning with edge heterophily discriminating. In Proceedings of the AAAI conference on artificial intelligence, volume 37, 4516--4524

    2023

  6. [14]

    Mernyei, P.; and Cangea, C. 2020. Wiki-cs: A wikipedia-based benchmark for graph neural networks. arXiv preprint arXiv:2007.02901

    2020 arXiv

  7. [15]

    Peng, Z.; Huang, W.; Luo, M.; Zheng, Q.; Rong, Y.; Xu, T.; and Huang, J. 2020. Graph representation learning via graphical mutual information maximization. In Proceedings of The Web Conference 2020, 259--270

    2020

  8. [16]

    Qu, Y.; Shen, D.; Shen, Y.; Sajeev, S.; Chen, W.; and Han, J. 2021. Co \ DA \ : Contrast-enhanced and Diversity-promoting Data Augmentation for Natural Language Understanding. In International Conference on Learning Representations

    2021

  9. [17]

    W.; Hallacy, C.; Ramesh, A.; Goh, G.; Agarwal, S.; Sastry, G.; Askell, A.; Mishkin, P.; Clark, J.; Krueger, G.; and Sutskever, I

    Radford, A.; Kim, J. W.; Hallacy, C.; Ramesh, A.; Goh, G.; Agarwal, S.; Sastry, G.; Askell, A.; Mishkin, P.; Clark, J.; Krueger, G.; and Sutskever, I. 2021. Learning Transferable Visual Models From Natural Language Supervision. In Proceedings of the 38th International Conferen...

    2021

  10. [18]

    Rong, Y.; Huang, W.; Xu, T.; and Huang, J. 2020. DropEdge: Towards Deep Graph Convolutional Networks on Node Classification. In International Conference on Learning Representations

    2020

  11. [19]

    Sen, P.; Namata, G.; Bilgic, M.; Getoor, L.; Galligher, B.; and Eliassi-Rad, T. 2008. Collective Classification in Network Data. AI Magazine, 29(3): 93

    2008

  12. [20]

    Shchur, O.; Mumme, M.; Bojchevski, A.; and G \"u nnemann, S. 2018. Pitfalls of graph neural network evaluation. arXiv preprint arXiv:1811.05868

    2018 arXiv

  13. [21]

    Shen, X.; Sun, D.; Pan, S.; Zhou, X.; and Yang, L. T. 2023. Neighbor contrastive learning on learnable graph augmentation. In Proceedings of the AAAI conference on artificial intelligence, volume 37, 9782--9791

    2023

  14. [22]

    Srivastava, N.; Hinton, G.; Krizhevsky, A.; Sutskever, I.; and Salakhutdinov, R. 2014. Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research, 15(1): 1929--1958

    2014

  15. [23]

    Suresh, S.; Li, P.; Hao, C.; and Neville, J. 2021. Adversarial Graph Augmentation to Improve Graph Contrastive Learning. In Ranzato, M.; Beygelzimer, A.; Dauphin, Y.; Liang, P.; and Vaughan, J. W., eds., Advances in Neural Information Processing Systems, volume 34, 15920--1593...

    2021

  16. [24]

    G.; Azabou, M.; Dyer, E

    Thakoor, S.; Tallec, C.; Azar, M. G.; Azabou, M.; Dyer, E. L.; Munos, R.; Veli c kovi \'c , P.; and Valko, M. 2022. Large-Scale Representation Learning on Graphs via Bootstrapping. In International Conference on Learning Representations

    2022

  17. [25]

    Tian, Y.; Sun, C.; Poole, B.; Krishnan, D.; Schmid, C.; and Isola, P. 2020. What makes for good views for contrastive learning? Advances in neural information processing systems, 33: 6827--6839

    2020

  18. [26]

    K.; Gelly, S.; and Lucic, M

    Tschannen, M.; Djolonga, J.; Rubenstein, P. K.; Gelly, S.; and Lucic, M. 2020. On Mutual Information Maximization for Representation Learning. In International Conference on Learning Representations

    2020

  19. [27]

    van den Oord, A.; Li, Y.; and Vinyals, O. 2018. Representation Learning with Contrastive Predictive Coding. CoRR, abs/1807.03748

    2018 arXiv

  20. [28]

    Van der Maaten, L.; and Hinton, G. 2008. Visualizing data using t-SNE. Journal of machine learning research, 9(11)

    2008

  21. [29]

    Veličković, P.; Cucurull, G.; Casanova, A.; Romero, A.; Liò, P.; and Bengio, Y. 2018. Graph Attention Networks. In International Conference on Learning Representations

    2018

  22. [30]

    L.; Liò, P.; Bengio, Y.; and Hjelm, R

    Veličković, P.; Fedus, W.; Hamilton, W. L.; Liò, P.; Bengio, Y.; and Hjelm, R. D. 2019. Deep Graph Infomax. In International Conference on Learning Representations

    2019

  23. [31]

    Wei, C.; Wang, Y.; Bai, B.; Ni, K.; Brady, D.; and Fang, L. 2023. Boosting graph contrastive learning via graph contrastive saliency. In International conference on machine learning, 36839--36855. PMLR

    2023

  24. [32]

    A.; et al

    Wilcoxon, F.; Katti, S.; Wilcox, R. A.; et al. 1970. Critical values and probability levels for the Wilcoxon rank sum test and the Wilcoxon signed rank test. Selected tables in mathematical statistics, 1: 171--259

    1970

  25. [33]

    Wu, M.; Zhuang, C.; Mosse, M.; Yamins, D.; and Goodman, N. 2020. On mutual information in contrastive learning for visual representations. arXiv preprint arXiv:2005.13149

    2020 arXiv

  26. [34]

    Xu, D.; Cheng, W.; Luo, D.; Chen, H.; and Zhang, X. 2021. Infogcl: Information-aware graph contrastive learning. Advances in Neural Information Processing Systems, 34: 30414--30425

    2021

  27. [35]

    You, Y.; Chen, T.; Shen, Y.; and Wang, Z. 2021. Graph contrastive learning automated. In International Conference on Machine Learning, 12121--12132. PMLR

    2021

  28. [36]

    You, Y.; Chen, T.; Sui, Y.; Chen, T.; Wang, Z.; and Shen, Y. 2020. Graph contrastive learning with augmentations. Advances in neural information processing systems, 33: 5812--5823

    2020

  29. [37]

    Yu, J.; Yin, H.; Xia, X.; Chen, T.; Cui, L.; and Nguyen, Q. V. H. 2022. Are graph augmentations necessary? simple graph contrastive learning for recommendation. In Proceedings of the 45th international ACM SIGIR conference on research and development in information retrieval, ...

    2022

  30. [38]

    Zhang, H.; Shi, J.; Zhang, R.; and Li, X. 2022. Non-Graph Data Clustering via O (n) Bipartite Graph Convolution. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(7): 8729--8742

    2022

  31. [39]

    Zhang, H.; Wu, Q.; Yan, J.; Wipf, D.; and Philip, S. Y. 2021. From canonical correlation analysis to self-supervised graph neural networks. In Thirty-Fifth Conference on Neural Information Processing Systems

    2021

  32. [40]

    Zhang, H.; Xu, Y.; Huang, S.; and Li, X. 2024. Data Augmentation of Contrastive Learning is Estimating Positive-incentive Noise. arXiv preprint arXiv:2408.09929

    2024 arXiv

  33. [41]

    Zhang, H.; Zhu, Y.; and Li, X. 2024. Decouple Graph Neural Networks: Train Multiple Simple GNNs Simultaneously Instead of One. IEEE Transactions on Pattern Analysis and Machine Intelligence

    2024

  34. [42]

    Zhao, T.; Liu, Y.; Neves, L.; Woodford, O.; Jiang, M.; and Shah, N. 2021. Data augmentation for graph neural networks. In Proceedings of the aaai conference on artificial intelligence, volume 35, 11015--11023

    2021

  35. [43]

    Zhu, Y.; Xu, Y.; Yu, F.; Liu, Q.; Wu, S.; and Wang, L. 2020. Deep Graph Contrastive Representation Learning . In ICML Workshop on Graph Representation Learning and Beyond

    2020

  36. [44]

    Zhu, Y.; Xu, Y.; Yu, F.; Liu, Q.; Wu, S.; and Wang, L. 2021. Graph contrastive learning with adaptive augmentation. In Proceedings of the web conference 2021, 2069--2080

    2021

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