InfoNCE is a Free Lunch for Semantically guided Graph Contrastive Learning

Bingbing Xu; Huawei Shen; Xueqi Cheng; Yige Yuan; Zixu Wang

REVIEW 3 major objections 6 minor 53 references

InfoNCE is a Free Lunch for Semantically guided Graph Contrastive Learning

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read InfoNCE's learned similarity preserves the ordering of the positive-class posterior, so the contrastive score itself can act as a free semantic classifier inside graph contrastive learning.

desk verdict A useful GCL debiasing recipe whose theoretical 'free lunch' bridge is broken; worth a serious referee, but not acceptance as-is. read the letter →

arxiv 2505.06282 v1 pith:KPZJBARM submitted 2025-05-07 cs.LG

Zixu Wang , Bingbing Xu , Yige Yuan , Huawei Shen , Xueqi Cheng This is my paper · ORCID

classification cs.LG

keywords graphcontrastivelearningInfoNCEpositive-unlabeledsemanticsimilaritysamplingbiaspre-trainingout-of-distributiongeneralizationLLM-enhancedgraphs

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

This paper claims that standard graph contrastive learning contains a hidden semantic signal: the InfoNCE similarity between two node representations preserves the ordering of the probability that the pair is semantically positive, even though training only labels augmented views as positive. On that basis, the paper argues GCL should be seen as a Positive-Unlabeled learning problem, where augmented pairs are labeled positives and non-augmented pairs are unlabeled rather than negatives. Using InfoNCE as a free density-ratio estimator, the method extracts semantically similar non-augmented pairs and redefines the maximum-likelihood objective into a corrected loss. If correct, this removes the need for extra supervision or a separate density-ratio estimator and directly mitigates the sampling bias that hurts GCL, with reported gains of up to 9.05% on one OOD benchmark and consistent improvements in LLM-enhanced graph settings.

What carries the argument

The load-bearing identity is the density-ratio interpretation of InfoNCE: the learned similarity $s_\theta(n,n')$ is proportional to $r(\mathbf{x}) = p(\mathbf{x}|y=+1,o=+1)/p(\mathbf{x})$, and by the Invariance of Order assumption this density ratio is ordered exactly like the true positive probability $p(y=+1|\mathbf{x})$. This identity converts a contrastive score into a semantic classifier, allowing the method to mine $D_U^+$ by thresholding and then to reweight the InfoNCE objective so that discovered positives are promoted proportionally to their similarity.

What would settle it

Train a GCL model on a graph with known class labels, then check whether the InfoNCE similarity $s_\theta(n,n')$ consistently ranks same-class non-augmented pairs above different-class pairs after warm-up; if the ordering is violated, the free-lunch theorem fails. A more direct test: construct synthetic augmentations where only low-semantic pairs are labeled positive, and see whether thresholding $s_\theta$ recovers the withheld high-semantic positive pairs.

Watch

Extended reading notes

Core claim

The central claim is the order-invariance identity of Eq. (19): for any contrastive samples $\mathbf{x}=(n,n')$ and $\hat{\mathbf{x}}=(\hat{n},\hat{n}')$, $p(y=+1|\mathbf{x}) \le p(y=+1|\hat{\mathbf{x}})$ if and only if $s_\theta(n,n') \le s_\theta(\hat{n},\hat{n}')$, where $s_\theta$ is the exponential cosine similarity used in InfoNCE. The paper proves this by connecting InfoNCE's score to the density ratio $r(\mathbf{x}) = p(\mathbf{x}|y=+1,o=+1)/p(\mathbf{x})$, which under the Invariance of Order assumption has the same ordering as the positive-class posterior. Therefore, thresholding $s_\theta$ recovers unlabeled positive pairs $D_U^+$, which the paper then inserts into a corrected maximum-likelihood loss, Eq. (27), with confidence weights. The authors frame this as a free lunch: the contrastive score already carries semantic ordering, so no additional model or label is needed to correct sampling bias.

Load-bearing premise

The load-bearing premise is the Invariance of Order assumption: the chance that a contrastive sample gets labeled positive by data augmentation is ordered exactly like its true semantic positivity, so a higher labeling probability always means a higher true positive probability.

Editorial extensions

If this is right

A GCL model can be warmed up with standard InfoNCE, then use its own similarity scores to resample semantically positive non-augmented pairs and train with the corrected loss, yielding accuracy gains up to 9.05% on GOODCBAS and consistent positive deltas over the GRACE and GCA baselines in both IID and OOD scenarios.
The same correction works when node features come from LLM encoders, and the reported improvement tends to grow with LLM scale, suggesting the method becomes more effective as semantic modeling improves.
The corrected objective imposes a stronger constraint on the discovered positives than a linear combination of likelihoods, because it multiplies the likelihoods with exponential confidence weights, which the paper argues leads to more thorough bias correction.
Because the method treats semantically similar cross-distribution pairs as positives, it reports larger improvements on OOD benchmarks than on IID ones, indicating a transferable-knowledge effect.
The theoretical result is not limited to a specific graph model: it applies to any InfoNCE-trained encoder with the same augmentation semantics, opening a generic upgrade path for existing contrastive pre-training pipelines.

Reading between the lines

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

(Editorial inference) If the order-invariance theorem holds, any InfoNCE-trained representation already encodes an implicit semantic-pair classifier, which could be reused for tasks like unsupervised node retrieval, pairwise link scoring, or outlier detection without additional training; the paper does not explore these applications.
(Editorial inference) The free lunch is not fully free in practice because the method depends on a warm-up phase and a similarity threshold $t_s$; the reported hyperparameter sensitivity indicates that a too-low threshold can inject false positives and worsen bias, so the gains hinge on selecting these well.
(Editorial inference) The Invariance of Order assumption could be tested directly per dataset by comparing the ranking of augmentation-label probabilities against the ranking of true semantic positivity for held-out pairs; the paper's own OOD results suggest this ordering may be more reliable in some graphs than others, which would predict where the method helps most.
(Editorial inference) A natural extension, not studied in the paper, is to apply the same density-ratio interpretation to other self-supervised objectives that minimize alignment and uniformity; the proof specifically targets InfoNCE, so transferring it would require a new argument.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. The empirical package is real: IFL-GCL gives consistent gains over GRACE/GCA across nine datasets, including OOD and LLM-feature setups, and code is public. The theoretical claim that InfoNCE is a free lunch for semantic positivity does not hold as stated; the proof hinges on IOD, which is vacuous for exactly the pairs the method needs to rank.

What is new: the PU framing is not novel—PU contrastive learning appears in refs [1,18,38]—but the dynamic resampling plus product-weighted corrected loss is a legitimate extension. Experiments are broad; IID gains are small but consistent, OOD gains on GOODTwitch/GOODCBAS are larger but noisy. The analysis of same-class ratio and supervised similarity of D_U^+ is a nice check.

Where it falls apart: Eq. 19 is load-bearing. IOD (Eq. 10) requires ordering of p(y=+1|x) to match ordering of p(o=+1|x). In augmentation-based GCL, p(o=+1|x)=0 for every distinct-node pair, so the assumption cannot rank semantic positives among D_U. The density ratio InfoNCE estimates is relative to augmentation-defined positives, not semantic positives. Once Eq. 27 replaces the InfoNCE objective, the earlier optimality no longer applies. So the free-lunch theorem is not established; the method is a self-training heuristic. That can work, and the evidence suggests it does, but the title overclaims.

Minor: threshold t_s is dataset-dependent and selected per dataset; the paper does not say whether selection uses validation only. With a 1:1:8 split, leakage is a real worry. Many tunable knobs mean small IID gains could be tuning artifacts. Citations look fair.

Bottom line: I would send this to a serious referee rather than desk-reject. The empirical contribution and public code deserve scrutiny. But I would not accept the theory as is; either repair the bridge between InfoNCE similarity and semantic positivity or reframe the method as empirical debiasing. For GCL practitioners the recipe is easy to try; for theory readers it is a cautionary example.

Referee Report

3 major / 6 minor

Summary. The paper proposes IFL-GCL, a graph contrastive learning method that reframes GCL as a positive-unlabeled (PU) learning problem. The central idea is that InfoNCE's learned similarity s_theta(n,n') is a 'free lunch' estimate of the density ratio r(x)=p(x|y=+1,o=+1)/p(x), and that under an Invariance of Order (IOD) assumption this similarity preserves the ordering of the true positive-class posterior p(y=+1|x). The method uses this ordering to threshold s_theta and identify semantically similar non-augmented pairs D_U^+, then redefines the InfoNCE objective (Eq. 27) so that these pairs are treated as positive with confidence-weighted losses. Experiments on nine graph datasets, in both IID and OOD settings and with LLM-based features, report consistent improvements over GRACE and GCA, with gains up to 9.05%.

Significance. If the theoretical link were valid, the contribution would be significant: it would turn InfoNCE's density-ratio estimation into a principled semantic signal for debiasing GCL, and the proposed corrected loss would be a natural maximum-likelihood consequence. The paper has concrete strengths: the code is publicly available, the experimental protocol is standard, the improvements over directly related baselines are consistent across many datasets, and Section 4.4.1 provides an interesting analysis of the quality of the discovered D_U^+ pairs. However, the central theoretical claim is not sound. The IOD assumption is violated in exactly the GCL setting the paper studies, the density-ratio derivation conflates the data-generating process of augmentation-based contrastive pairs with independent node sampling, and the corrected loss changes the training objective so that the proof of Eq. (19) no longer covers the model actually used for resampling. The empirical results may still indicate a useful heuristic, but they do not establish the paper's advertised 'free lunch' claim.

major comments (3)

[Section 3.2.1, Eq. (10), (11), (19)] The IOD assumption is violated by the GCL labeling process. In this paper, o=+1 is assigned deterministically to augmented same-node pairs, while every distinct-node non-augmented pair has p(o=+1|x)=0 (Eq. 1). For any two distinct-node pairs x and x' in D_U, the right-hand side of Eq. (10) holds in both directions because 0 <= 0, so Eq. (10) would force p(y=+1|x)=p(y=+1|x'). This is directly contradicted by the paper's own Section 2.2 and Fig. 2, which show that non-augmented pairs vary widely in semantic similarity, with some exceeding augmented pairs. Consequently, Eq. (11) and the central claim Eq. (19) do not follow, and the classifier in Eq. (20) has no theoretical basis for identifying D_U^+.
[Section 3.2.2, Eq. (27) and Algorithm 1] The proof of Eq. (19) applies to a model trained with the original InfoNCE loss Eq. (3). After the warm-up stage, Algorithm 1 switches to the corrected loss Eq. (27), which is a different objective. The density-ratio interpretation of s_theta is not established for the model trained under this corrected loss, so using s_theta from subsequent iterations to select D_U^+ is not justified by the theorem. Moreover, the procedure is a self-training loop: samples selected by the model's own similarity scores are then upweighted to increase those scores. The paper does not discuss confirmation bias or provide any control for it, and the 'free lunch' claim depends precisely on the model being trained under the original InfoNCE objective.
[Section 3.2.1, Eq. (17)-(18)] The identification p(x)=q(n)q(n') used in Eq. (17) does not reflect the actual sampling process in GCL. Contrastive samples are not obtained by independently sampling two nodes from their marginal distributions; they are constructed by generating two augmented views of the same graph and pairing nodes across views, so the marginal distribution of pairs is determined by the augmentation process and the graph structure. Therefore the density-ratio equality s_theta(n,n') ∝ q(n,n')/(q(n)q(n')) = r(x) in Eq. (18) is not established. The step from Eq. (16) to Eq. (18) requires a model of how x is sampled that the manuscript does not provide.

minor comments (6)

[Section 2.2, caption of Fig. 2] The phrase 'decently sorted' should be 'descendingly sorted' or 'sorted in descending order'.
[Section 3.2.1] There are several typos: 'proof' should be 'prove' in 'We will now proof this', and 'Invariance of OrDer' should be 'Invariance of Order'.
[Eq. (1) and Eq. (2)] The negative set D_aug^- in Eq. (1) contains only cross-view pairs (u_i,v_j) and (v_i,u_j) for i≠j, but the denominator of Eq. (2) also includes intra-view pairs s_theta(u_i,u_j) for j≠i. Please clarify whether intra-view pairs are part of the negative set and how they relate to D_aug^-.
[Section 4.2, discussion of Table 1] The text says 'Our methods occupy the best performances across all datasets apart from Computers' but then says 'our models rank second-best on all but PubMed and Photo'. These statements are inconsistent with the table: IFL-GC is best on PubMed, Photo, GOODTwitch, and GOODCora, while IFL-GR is best on Cora and GOODCBAS. Please rephrase to match the reported numbers.
[Section 3.2.2, Eq. (25)-(27) and Algorithm 1] The hyperparameter beta appears in Eq. (25) but is not listed in the inputs of Algorithm 1, and its role as a weighting exponent for all D_U^+ terms is not fully specified. Please define beta explicitly and include it in the algorithm's input list.
[Abstract] The phrase 'show significantly improvements of IFL-GCL' should be 'show significant improvements of IFL-GCL' for grammatical correctness.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Eq.19 is a conditional consequence of the external IOD assumption plus the standard InfoNCE density-ratio property; the self-training resampling loop is a correctness concern, not a circular derivation.

full rationale

The paper's central theoretical claim, Eq.19, is derived as a syllogism from two external ingredients: (i) the InfoNCE density-ratio estimation property, attributed to Oord et al. [25] and stated in Eqs.14 and 18, and (ii) the Invariance of Order (IOD) assumption, attributed to Kato et al. [17] and stated in Eq.10. Neither ingredient is defined in terms of the paper's own output, and neither is fitted to the reported datasets; the proof is conditional: if IOD holds, then the ordering of s_theta matches the ordering of p(y=+1|x). The paper's own Section 2.2 evidence that "some node pairs in D_aug- exhibit semantic similarity either higher than (the red ones) or close to (the blue ones) that of the samples in D_aug+" appears to contradict IOD in the augmentation-GCL setting, because those non-augmented pairs have labeling probability p(o=+1|x)=0 by construction. That is a serious correctness risk for Eq.19, but a false or violated assumption is not the same as a circular reduction. The resampling method does form a self-training loop: Eq.21 defines D_U^+ by thresholding s_theta, and Eq.27 then trains the encoder to increase s_theta on exactly those pairs. This is a legitimate methodological concern about confirmation bias, but the paper does not present D_U^+ as an independently predicted quantity; it validates the mined samples with supervised metrics (SameClassRatio and SupSim) in Section 4.4.1 and evaluates downstream accuracy against external baselines. The only self-citations ([2], [32], [42]) are background or comparative; reference [42] is cited as a heuristic alternative and does not supply the IOD or InfoNCE results. Thus, while the main theorem may be unsound for its intended setting, the derivation chain does not reduce by construction to its own inputs, and no enumerated circularity pattern is exhibited.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the IOD assumption and on the optimality of InfoNCE as a density-ratio estimator. Both are assumptions that the paper does not independently validate in the GCL setting. The threshold t_s and weight beta are free parameters fitted to downstream performance.

free parameters (5)

threshold t_s = per dataset in {0.8,0.85,0.90,0.95,0.99}; optimal varies (e.g., 0.90 for Cora, 0.95 for GOODTwitch)
Controls which non-augmented pairs are classified as D_U^+; the paper reports high sensitivity to this value (Fig. 5).
exponential weight beta = not reported
Eq. 27 introduces beta as a weight on D_U^+ likelihoods; no ablation or chosen value is given in the text.
warm-up epochs M = varies by dataset (Fig. 4)
Number of epochs with the original InfoNCE loss before dynamic resampling starts.
update interval K = varies by dataset (Fig. 4)
Epochs between resampling refreshes.
max updating times T = not specified
Algorithm 1 iterates T times; the value is not reported.

assumptions (4)

domain assumption IOD (Invariance of Order) assumption: p(y=+1|x) ordering equals p(o=+1|x) ordering for all contrastive samples x (Eq. 10).
Borrowed from PU learning literature [17]; the paper asserts it holds in GCL because labeling should align with semantics, but this is not proven and is questionable since augmentation defines labeling.
domain assumption The InfoNCE-trained similarity s_theta(n,n') is proportional to the density ratio q(n,n')/(q(n)q(n')) (optimal critic property, Eq. 15-18).
Assumes the encoder is expressive enough and training converges to the InfoNCE optimum; the paper treats the proportionality as an equality once the loss is modified.
standard math Non-augmented pairs are independent samples: p(x=(n,n'))=q(n)q(n') (Eq. 17).
Standard contrastive learning assumption that negatives are independent draws.
domain assumption All labeled positives are true positives: p(y=+1|o=+1)=1.
Implicit in treating augmented pairs as D_L^+; reasonable but unstated.

how reviews work

0 comments

Cite this review

Pith. "Pith review of InfoNCE is a Free Lunch for Semantically guided Graph Contrastive Learning." pith.science (2026). https://pith.science/paper/KPZJBARM

@misc{pith2026250506282,
  author       = {Pith},
  title        = {Pith review of: InfoNCE is a Free Lunch for Semantically guided Graph Contrastive Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KPZJBARM}},
  note         = {Machine review of arXiv:2505.06282}
}

read the original abstract

As an important graph pre-training method, Graph Contrastive Learning (GCL) continues to play a crucial role in the ongoing surge of research on graph foundation models or LLM as enhancer for graphs. Traditional GCL optimizes InfoNCE by using augmentations to define self-supervised tasks, treating augmented pairs as positive samples and others as negative. However, this leads to semantically similar pairs being classified as negative, causing significant sampling bias and limiting performance. In this paper, we argue that GCL is essentially a Positive-Unlabeled (PU) learning problem, where the definition of self-supervised tasks should be semantically guided, i.e., augmented samples with similar semantics are considered positive, while others, with unknown semantics, are treated as unlabeled. From this perspective, the key lies in how to extract semantic information. To achieve this, we propose IFL-GCL, using InfoNCE as a "free lunch" to extract semantic information. Specifically, We first prove that under InfoNCE, the representation similarity of node pairs aligns with the probability that the corresponding contrastive sample is positive. Then we redefine the maximum likelihood objective based on the corrected samples, leading to a new InfoNCE loss function. Extensive experiments on both the graph pretraining framework and LLM as an enhancer show significantly improvements of IFL-GCL in both IID and OOD scenarios, achieving up to a 9.05% improvement, validating the effectiveness of semantically guided. Code for IFL-GCL is publicly available at: https://github.com/Camel-Prince/IFL-GCL.

Figures

Figures reproduced from arXiv: 2505.06282 by the authors.

**Figure 1.** (a) illustrates the sampling bias via a case example; (b) validates sampling bias by comparing the nodes’ representation [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Semantics similarity matrix of G𝑎𝑢𝑔1 and G𝑎𝑢𝑔2 after supervised-learning which is rearranged with the 𝐷 𝑎𝑢𝑔+ at the first column and decently sorted 𝐷 𝑎𝑢𝑔− as follows. Specifically, we train a graph encoder 𝑓𝜃 (·) using a supervised learning paradigm to capture the semantic information to the best extent: 𝜃 ∗ = arg min 𝜃 𝐿𝑠𝑢𝑝 (𝑓𝜃 (G), 𝑌) (5) where 𝑓𝜃 (·) is the graph neural network encoder: GAT[35], 𝐿𝑠𝑢𝑝 is the supe… view at source ↗

**Figure 3.** Analysis of semantic similarity of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 5.** Figure 5: Analysis of Hyper-parameter: threshold 𝑡𝑠 5 Conclusion This paper addresses the sampling bias issue in traditional graph contrastive learning by treating it as a Positive-Unlabeled learning problem where the definition of self-supervised tasks and contrastive samples …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

53 extracted references · 29 canonical work pages

[1]

Anish Acharya, Sujay Sanghavi, Li Jing, Bhargav Bhushanam, Dhruv Choud- hary, Michael Rabbat, and Inderjit Dhillon. 2022. Positive unlabeled contrastive learning. arXiv preprint arXiv:2206.01206 (2022)

work page Pith review arXiv 2022
[2]

Peng Bao, Hua-Wei Shen, Wei Chen, and Xue-Qi Cheng. 2013. Cumulative effect in information diffusion: empirical study on a microblogging network. PloS one 8, 10 (2013), e76027

work page 2013
[3]

Piotr Bielak, Tomasz Kajdanowicz, and Nitesh V Chawla. 2022. Graph bar- low twins: A self-supervised representation learning framework for graphs. Knowledge-Based Systems 256 (2022), 109631

work page 2022
[4]

Xingping Dong and Jianbing Shen. 2018. Triplet loss in siamese network for object tracking. In Proceedings of the European conference on computer vision (ECCV). 459–474

2018
[5]

Yi Fang, Dongzhe Fan, Daochen Zha, and Qiaoyu Tan. 2024. Gaugllm: Improving graph contrastive learning for text-attributed graphs with large language models. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 747–758

2024
[6]

C Lee Giles, Kurt D Bollacker, and Steve Lawrence. 1998. CiteSeer: An automatic citation indexing system. InProceedings of the third ACM conference on Digital libraries. 89–98

1998
[7]

Shurui Gui, Xiner Li, Limei Wang, and Shuiwang Ji. 2022. Good: A graph out-of- distribution benchmark. Advances in Neural Information Processing Systems 35 (2022), 2059–2073

work page 2022
[8]

Zayd Hammoudeh and Daniel Lowd. 2020. Learning from positive and unlabeled data with arbitrary positive shift. Advances in Neural Information Processing Systems 33 (2020), 13088–13099

work page 2020

Show all 53 references

[9]

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

2020
[10]

Shohei Hido, Yuta Tsuboi, Hisashi Kashima, Masashi Sugiyama, and Takafumi Kanamori. 2011. Statistical outlier detection using direct density ratio estimation. Knowledge and information systems 26 (2011), 309–336

2011
[11]

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

2020
[12]

Kristen Jaskie and Andreas Spanias. 2019. Positive and unlabeled learning al- gorithms and applications: A survey. In 2019 10th International Conference on Information, Intelligence, Systems and Applications (IISA). IEEE, 1–8

2019
[13]

Wei Jin, Tyler Derr, Haochen Liu, Yiqi Wang, Suhang Wang, Zitao Liu, and Jiliang Tang. 2020. Self-supervised learning on graphs: Deep insights and new direction. arXiv preprint arXiv:2006.10141 (2020)

2020 arXiv
[14]

Baoyu Jing, Chanyoung Park, and Hanghang Tong. 2021. Hdmi: High-order deep multiplex infomax. In Proceedings of the Web Conference 2021. 2414–2424

2021
[15]

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
[16]

Takafumi Kanamori, Shohei Hido, and Masashi Sugiyama. 2009. A least-squares approach to direct importance estimation. The Journal of Machine Learning Research 10 (2009), 1391–1445

2009
[17]

Masahiro Kato, Takeshi Teshima, and Junya Honda. 2019. Learning from positive and unlabeled data with a selection bias. In International conference on learning representations

2019
[18]

Zhiqiang Li, Jie Wang, and Jiye Liang. 2024. Debiased graph contrastive learning based on positive and unlabeled learning. International Journal of Machine Learning and Cybernetics 15, 6 (2024), 2527–2538

2024
[19]

Gang Liu, Tong Zhao, Jiaxin Xu, Tengfei Luo, and Meng Jiang. 2022. Graph ratio- nalization with environment-based augmentations. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 1069– 1078

2022
[20]

Mengyue Liu, Yun Lin, Jun Liu, Bohao Liu, Qinghua Zheng, and Jin Song Dong
[21]

Yixin Liu, Ming Jin, Shirui Pan, Chuan Zhou, Yu Zheng, Feng Xia, and S Yu Philip
[22]

Yujia Liu, Kang Zeng, Haiyang Wang, Xin Song, and Bin Zhou. 2021. Content matters: A GNN-based model combined with text semantics for social network cascade prediction. In Pacific-Asia Conference on Knowledge Discovery and Data Mining. Springer, 728–740

2021
[23]

Andrew Kachites McCallum, Kamal Nigam, Jason Rennie, and Kristie Seymore
[24]

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

2020 arXiv
[25]

Aaron van den Oord, Yazhe Li, and Oriol Vinyals. 2018. Representation learning with contrastive predictive coding. arXiv preprint arXiv:1807.03748 (2018)

2018 arXiv
[26]

Zhen Peng, Yixiang Dong, Minnan Luo, Xiao-Ming Wu, and Qinghua Zheng
[27]

Jiezhong Qiu, Qibin Chen, Yuxiao Dong, Jing Zhang, Hongxia Yang, Ming Ding, Kuansan Wang, and Jie Tang. 2020. Gcc: Graph contrastive coding for graph neu- ral network pre-training. InProceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mini...

2020
[28]

Saeed Rahmani, Asiye Baghbani, Nizar Bouguila, and Zachary Patterson. 2023. Graph neural networks for intelligent transportation systems: A survey. IEEE Transactions on Intelligent Transportation Systems 24, 8 (2023), 8846–8885

2023
[29]

Yu Rong, Yatao Bian, Tingyang Xu, Weiyang Xie, Ying Wei, Wenbing Huang, and Junzhou Huang. 2020. Self-supervised graph transformer on large-scale molecular data. Advances in neural information processing systems 33 (2020), 12559–12571

2020
[30]

Yu Rong, Wenbing Huang, Tingyang Xu, and Junzhou Huang. 2019. Drope- dge: Towards deep graph convolutional networks on node classification. arXiv preprint arXiv:1907.10903 (2019)

2019 arXiv
[31]

Prithviraj Sen, Galileo Namata, Mustafa Bilgic, Lise Getoor, Brian Galligher, and Tina Eliassi-Rad. 2008. Collective classification in network data. AI magazine 29, 3 (2008), 93–93

2008
[32]

Hua-Wei Shen, Xue-Qi Cheng, and Jia-Feng Guo. 2011. Exploring the structural regularities in networks. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 84, 5 (2011), 056111

2011
[33]

Kihyuk Sohn. 2016. Improved deep metric learning with multi-class n-pair loss objective. Advances in neural information processing systems 29 (2016)

2016
[34]

Shantanu Thakoor, Corentin Tallec, Mohammad Gheshlaghi Azar, Mehdi Azabou, Eva L Dyer, Remi Munos, Petar Veličković, and Michal Valko. 2021. Large- scale representation learning on graphs via bootstrapping. arXiv preprint arXiv:2102.06514 (2021)

2021 arXiv
[35]

Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. 2017. Graph attention networks. arXiv preprint arXiv:1710.10903 (2017)

2017 arXiv
[36]

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
[37]

Duo Wang, Yuan Zuo, Fengzhi Li, and Junjie Wu. 2024. LLMs as Zero-shot Graph Learners: Alignment of GNN Representations with LLM Token Embeddings. arXiv preprint arXiv:2408.14512 (2024)

2024 arXiv
[38]

Lu Wang, Chao Du, Pu Zhao, Chuan Luo, Zhangchi Zhu, Bo Qiao, Wei Zhang, Qingwei Lin, Saravan Rajmohan, Dongmei Zhang, et al. 2024. Contrastive Learn- ing with Negative Sampling Correction. arXiv preprint arXiv:2401.08690 (2024)

2024 arXiv
[39]

Tongzhou Wang and Phillip Isola. 2020. Understanding contrastive representation learning through alignment and uniformity on the hypersphere. In International conference on machine learning. PMLR, 9929–9939

2020
[40]

Xiao Wang, Nian Liu, Hui Han, and Chuan Shi. 2021. Self-supervised hetero- geneous graph neural network with co-contrastive learning. In Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining. 1726–1736

2021
[41]

Yuyang Wang, Zijie Li, and Amir Barati Farimani. 2023. Graph neural networks for molecules. In Machine learning in molecular sciences. Springer, 21–66

2023
[42]

Zixu Wang, Bingbing Xu, Yige Yuan, Huawei Shen, and Xueqi Cheng. 2024. Negative as Positive: Enhancing Out-of-distribution Generalization for Graph Contrastive Learning. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Re...

2024
[43]

Yaochen Xie, Zhao Xu, Jingtun Zhang, Zhengyang Wang, and Shuiwang Ji. 2022. Self-supervised learning of graph neural networks: A unified review. IEEE transactions on pattern analysis and machine intelligence 45, 2 (2022), 2412– 2429

2022
[44]

Makoto Yamada, Taiji Suzuki, Takafumi Kanamori, Hirotaka Hachiya, and Masashi Sugiyama. 2013. Relative density-ratio estimation for robust distri- bution comparison. Neural computation 25, 5 (2013), 1324–1370

2013
[45]

Yuning You, Tianlong Chen, Yang Shen, and Zhangyang Wang. 2021. Graph con- trastive learning automated. In International Conference on Machine Learning. PMLR, 12121–12132

2021
[46]

Yifei Zhang, Hao Zhu, Zixing Song, Piotr Koniusz, and Irwin King. 2022. COSTA: covariance-preserving feature augmentation for graph contrastive learning. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2524–2534

2022
[47]

Han Zhao, Xu Yang, Zhenru Wang, Erkun Yang, and Cheng Deng. 2021. Graph Debiased Contrastive Learning with Joint Representation Clustering.. In IJCAI. 3434–3440

2021
[48]

Yanqiao Zhu, Yichen Xu, Feng Yu, Qiang Liu, Shu Wu, and Liang Wang. 2020. Deep graph contrastive representation learning. arXiv preprint arXiv:2006.04131 (2020)

2020 arXiv
[49]

Yanqiao Zhu, Yichen Xu, Feng Yu, Qiang Liu, Shu Wu, and Liang Wang. 2021. Graph contrastive learning with adaptive augmentation. In Proceedings of the Web Conference 2021. 2069–2080

2021
[2000]

Information Retrieval 3 (2000), 127–163

Automating the construction of internet portals with machine learning. Information Retrieval 3 (2000), 127–163

2000
[2020]

arXiv preprint arXiv:2003.01604 (2020)

Self-supervised graph representation learning via global context prediction. arXiv preprint arXiv:2003.01604 (2020)

2020
[2022]

IEEE transactions on knowledge and data engineering 35, 6 (2022), 5879–5900

Graph self-supervised learning: A survey. IEEE transactions on knowledge and data engineering 35, 6 (2022), 5879–5900

2022
[2023]

In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining

B2-sampling: Fusing balanced and biased sampling for graph contrastive learning. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 1489–1500

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Anish Acharya, Sujay Sanghavi, Li Jing, Bhargav Bhushanam, Dhruv Choud- hary, Michael Rabbat, and Inderjit Dhillon. 2022. Positive unlabeled contrastive learning. arXiv preprint arXiv:2206.01206 (2022)

work page Pith review arXiv 2022

[2] [2]

Peng Bao, Hua-Wei Shen, Wei Chen, and Xue-Qi Cheng. 2013. Cumulative effect in information diffusion: empirical study on a microblogging network. PloS one 8, 10 (2013), e76027

work page 2013

[3] [3]

Piotr Bielak, Tomasz Kajdanowicz, and Nitesh V Chawla. 2022. Graph bar- low twins: A self-supervised representation learning framework for graphs. Knowledge-Based Systems 256 (2022), 109631

work page 2022

[4] [4]

Xingping Dong and Jianbing Shen. 2018. Triplet loss in siamese network for object tracking. In Proceedings of the European conference on computer vision (ECCV). 459–474

2018

[5] [5]

Yi Fang, Dongzhe Fan, Daochen Zha, and Qiaoyu Tan. 2024. Gaugllm: Improving graph contrastive learning for text-attributed graphs with large language models. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 747–758

2024

[6] [6]

C Lee Giles, Kurt D Bollacker, and Steve Lawrence. 1998. CiteSeer: An automatic citation indexing system. InProceedings of the third ACM conference on Digital libraries. 89–98

1998

[7] [7]

Shurui Gui, Xiner Li, Limei Wang, and Shuiwang Ji. 2022. Good: A graph out-of- distribution benchmark. Advances in Neural Information Processing Systems 35 (2022), 2059–2073

work page 2022

[8] [8]

Zayd Hammoudeh and Daniel Lowd. 2020. Learning from positive and unlabeled data with arbitrary positive shift. Advances in Neural Information Processing Systems 33 (2020), 13088–13099

work page 2020