Pith. sign in

REVIEW 3 major objections 3 minor 3 cited by

Learn Beneficial Noise as Graph Augmentation

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

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

Pith's one-line read This paper proves that standard graph contrastive learning with fixed augmentations is equivalent to estimating beneficial noise by point estimation, and then constructs a method that learns that noise instead of fixing it.

desk verdict The proposed augmentation method is usable, but the paper's main theoretical equivalence does not follow as written. read the letter →

arxiv 2505.19024 v1 pith:UWODDV5M submitted 2025-05-25 cs.LG stat.ML

Siqi Huang , Yanchen Xu , Hongyuan Zhang , Xuelong Li This is my paper · ORCID
classification cs.LGstat.ML
keywords graphcontrastivelearningdataaugmentationpositive-incentivenoiselearnablegeneratorInfoNCEmutualinformationtopologicalattribute
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 is trying to show that graph contrastive learning is, at bottom, a noise-estimation problem, and that the common habit of fixing an augmentation (random edge dropping, feature masking) is really a crude point estimate of beneficial noise—noise that lowers the entropy of the target task. It builds a bridge between the InfoNCE loss and information entropy by attaching a Gaussian auxiliary variable to each node, whose variance shrinks as the contrastive loss improves. On that bridge, the standard GCL objective with a fixed augmentation is proven equivalent to minimizing InfoNCE under a Dirac-delta noise estimate. The paper then proposes PiNGDA, which learns the noise distribution on edges and attributes with trainable generators, and reports higher and more stable accuracy than fixed or heuristic augmentations across node, graph, and heterogeneous benchmarks. A reader should care because the result turns a heuristic choice into a principled objective: choose the noise that reduces task entropy, not the noise that happens to work on a given dataset.

What carries the argument

The carrying object is the Gaussian auxiliary variable $\alpha$ with $p(\alpha|u)=\mathcal{N}(0, f(\ell(u;\theta)))$, where $f=\exp$, making the per-node variance $\kappa_\theta(u)^{-1}$ with $\kappa_\theta(u)=\ell_{\mathrm{pos}}(u;\theta)/(\ell_{\mathrm{pos}}(u;\theta)+\ell_{\mathrm{neg}}(u;\theta))$. This converts a per-node contrastive loss into an entropy, so the task entropy becomes $H(T)=\mathbb{E}_u H(\mathcal{N}(0,\kappa_\theta(u)^{-1}))$, and the conditional entropy under a fixed augmentation reduces to the InfoNCE objective. The method side uses a learnable generator $p_\psi(\varepsilon|u)$ for topology (factored Bernoulli with Gumbel-Softmax) and attributes (Gaussian mean and variance with reparameterization), so that the contrastive loss is averaged over learned noise rather than over a single fixed perturbation.

What would settle it

A concrete check: on a fixed graph, sweep random edge-dropping rates and compare the InfoNCE loss of the learned embeddings with their downstream classification accuracy; any rate where lower InfoNCE does not accompany higher accuracy would break the paper's identification of Gaussian task entropy with actual task difficulty.

Watch

Extended reading notes

Core claim

The paper's central claim is that standard GCL with a pre-defined augmentation is equivalent to estimating positive-incentive noise by point estimation. The argument converts the per-node InfoNCE loss into a Gaussian auxiliary variable $p(\alpha|u)=\mathcal{N}(0,\kappa_\theta(u)^{-1})$ with $\kappa_\theta(u)=\ell_{\mathrm{pos}}(u;\theta)/(\ell_{\mathrm{pos}}(u;\theta)+\ell_{\mathrm{neg}}(u;\theta))$, so that maximizing the mutual information $\max_{E,\theta} I(T,E)$ collapses to $\min_\theta -\sum_u \log \kappa_\theta(u,\varepsilon_0)$, exactly the standard contrastive objective when the augmentation is fixed as a Dirac-delta noise $\delta_{\varepsilon_0}(\varepsilon)$. Because heuristic augmentations are unreliable point estimates of the noise that actually reduces task entropy, the paper derives PiNGDA, which replaces the delta with a learned distribution $p_\psi(\varepsilon|u)$: a Bernoulli/Gumbel-Softmax generator for edge dropping and a Gaussian reparameterized generator for attribute noise, and minimizes the expected InfoNCE under that distribution.

Load-bearing premise

The entire argument depends on believing that the spread of a constructed bell-shaped distribution assigned to each node's training loss truly measures how hard the learning task is; if that mapping is false, the equivalence result and PiNGDA's guarantee do not follow.

Editorial extensions

If this is right

  • Every GCL model with a predetermined augmentation is implicitly solving a noise-estimation problem, so the choice of augmentation is a choice of how to point-estimate beneficial noise.
  • Because heuristic augmentations are weak point estimates, training with them is biased; learning the noise distribution instead is the direct fix the theory prescribes.
  • The learned noise generator reduces task entropy by preserving intra-class edges and dropping inter-class edges, which the visualization of learned edge weights shows.
  • PiNGDA is compatible with existing GCL models, improving GRACE and Sp2GCL when plugged into them.
  • The method extends to attribute noise, covering both topology and features rather than only edge operations.

Reading between the lines

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

  • If the loss-to-entropy link is taken literally, per-node values of $\kappa_\theta(u,\varepsilon)$ become a diagnostic for augmentation quality, so one could flag nodes or regions where a fixed augmentation systematically raises entropy.
  • The Gaussian auxiliary variable is a modeling choice; adopting a different noise family for $\alpha$ would change the task-entropy functional and could yield different optimal augmentations, so the derivation is portable in spirit but not in exact form.
  • A testable prediction of the paper's view is that the gains from learned noise should grow on datasets where no single fixed augmentation is near-optimal and shrink where a random drop rate already matches the optimal pi-noise.
  • The same point-estimation reading may apply to fixed augmentations in other contrastive learning settings, such as vision-language alignment, though the paper does not establish this extension.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The paper proposes PiNGDA, a graph contrastive learning (GCL) method that learns to generate beneficial noise for graph augmentations on both topology and node attributes. The central theoretical claim, developed in Section 3.3, is that standard GCL with predefined augmentations is equivalent to estimating positive-incentive noise (pi-noise) via point estimation, established by introducing a Gaussian auxiliary variable whose variance is a monotone function of the per-node contrastive loss. The paper then derives a training objective for PiNGDA by learning a noise distribution instead of fixing a point estimate, and reports experiments on node classification, graph classification, and heterogeneous graphs, along with ablations and efficiency studies.

Significance. If the theoretical equivalence were correct, the paper would provide a principled information-theoretic foundation for learnable graph augmentations and a novel interpretation of GCL. The experimental section is broad, and the proposed method is competitive on several benchmarks, with ablations suggesting that learnable augmentation can help over random or no augmentation. However, the central theoretical derivation is flawed: the claimed reduction of mutual information maximization to the InfoNCE loss drops a theta-dependent entropy term, and the point-estimation interpretation conflicts with the definition of positive-incentive noise. The empirical method may still be useful as a heuristic, but the paper's main advertised contribution—the theoretical bridge between GCL and pi-noise—is unsupported as written.

major comments (3)
  1. [Section 3.3, Eqs. (4)-(13)] The claimed equivalence max_{E,theta} I(T,E) <=> max_theta sum_u log kappa_theta(u, epsilon_0) is not established. From the paper's own definitions, H(T) = E_u H(N(0, kappa_theta(u)^{-1})) = const - (1/2) E_u log kappa_theta(u), which depends on theta through kappa_theta(u). Therefore I(T,E) = H(T) - H(T|E) contains the term -(1/2) E_u log kappa_theta(u), whose gradient with respect to theta is generically nonzero. Equation (13) replaces the mutual information objective with the conditional-entropy term -H(T|E) alone, omitting this theta-dependent term. Unless H(T) is constant in theta, the stationary conditions of I(T,E) and of the InfoNCE loss differ by gradient_theta E_u log kappa_theta(u). The paper does not prove that this term vanishes; indeed, in the same section kappa_theta(u) is defined through the trainable contrastive loss. Thus the reduction of standard GCL to pi-noise point estimation does not follow from Eqs. (4)-(9).
  2. [Section 3.3, Eqs. (6), (10)-(13)] The paper states the optimization principle as max_{E,theta} -H(T|E) in Eq. (6), but then in Eq. (13) refers to 'the original goal to maximize the mutual information.' These objectives are equivalent only if H(T) is independent of theta and E. Under Eq. (5), H(T) is a function of theta via kappa_theta(u). The paper never resolves this inconsistency. If the intended objective is -H(T|E), the link to pi-noise, which is defined through I(T,E)>0, is missing; if the intended objective is I(T,E), then Eq. (13) is missing the H(T) term. This is not a presentation issue; it undermines the central theoretical claim. Additionally, Eqs. (10)-(11) model a predefined augmentation as a Dirac delta p(epsilon|u)=delta_{epsilon_0}(epsilon), making E deterministic; for a deterministic E, I(T,E)=0 by definition, which contradicts the pi-noise definition in Eq. (1) that requires I(T,E)>0. Thus a predefined augmentation cannot be beneficial noise under the paper's own criterion unless an additional latent random variable is introduced, which the derivation does not do.
  3. [Section 3.2, Eq. (5)] The definition of task entropy H(T) as the entropy of an auxiliary Gaussian whose variance is a monotone function of the per-node loss makes the subsequent proof circular. The auxiliary variable alpha is defined through the loss itself, and the entropy of p(alpha|u) is just a deterministic function of the contrastive loss. Minimizing this 'entropy' is therefore equivalent to minimizing the original loss by construction. The paper presents this as an information-theoretic quantification of task complexity, but it is a relabeling of the loss rather than an independent measure of task entropy. Consequently, the derivation in Section 3.3 does not provide an independent justification for why maximizing mutual information should lead to contrastive learning; it recovers the InfoNCE loss because the auxiliary variable was engineered to do so. This concern is foundational and affects the validity of the theoretical framework as a whole.
minor comments (3)
  1. [Abstract] The phrase 'equivalent to estimate the beneficial noise' should be 'equivalent to estimating the beneficial noise' for grammatical consistency.
  2. [Section 5.3.1, Table 1] The claim that 'our method exhibits lower variance' is not uniformly supported by the reported standard deviations; for example, on Cora the std of Ours is 0.25, whereas GCA reports 0.21. The claim should be qualified or supported by a statistical test.
  3. [Appendix A, Eq. (25)] In the second line of Eq. (25), there is a stray 'dα' at the end of the integrand that should be removed for clarity.

Circularity Check

3 steps flagged · score 8.0 of 10

Central claim is definitional: the task entropy H(T) is constructed from the InfoNCE loss, and Eq. (13) drops the θ-dependent H(T) term, so the 'equivalence' of GCL to pi-noise point estimation is a relabeling rather than a derived result.

  1. self definitional [Section 3.2, Eqs. (4)-(5); Section 3.3, Eq. (8)]
    "We define a monotonously increasing mapping function f : R 7→ R+ such that p(α|u) =N(0, f(ℓ(u; θ))). (4) The above definition provides us a natural scheme to define the task entropy of a given task by converting its loss ℓ(u; θ). Formally, H(T ) =Eu∼p(u)H(N(0, f(ℓ(u; θ)))). (5) For GCL, we let f(·)=exp(·) so that p(α|u) =N(0, κθ(u)−1), (8)"

    H(T) is not an independent measure of task complexity; it is the entropy of a Gaussian whose variance is a monotone function of the per-node InfoNCE loss ℓ(u;θ). With f=exp and κθ(u)=ℓpos/(ℓpos+ℓneg), we have ℓ(u;θ)=-log κθ(u), so H(T)=const - (1/2)E_u log κθ(u). Thus the assertion in Section 3.3 that optimizing I(T,E) 'reduces to' minimizing Σ log κθ(u) is guaranteed by this definition: the auxiliary variable was chosen so that its entropy equals the loss. The claimed information-theoretic interpretation is a relabeling of the loss, not a derived property of noise.

  2. other [Section 3.3, Eqs. (11)-(13)]
    "With this assumption, −H(T |E) is equivalent to −H(T |E) ≈ 1 n X u Z p(α|u, ε0) logp(α|u, ε0)dα = L. (11) ... To sum up, the original goal to maximize the mutual information is converted to max E,θ I(T , E) ⇔ max θ 1 n X u log κθ(u, ε0) ⇔ min 1 n X u − log ℓpos(u, ε0; θ) ℓpos(u, ε0; θ) +ℓneg(u, ε0; θ) , (13)"

    Eq. (13) replaces max I(T,E) with max Σ log κθ(u,ε0), but the derivation only computes -H(T|E). Under Eq. (5), H(T)=const - (1/2)E_u log κθ(u) depends on θ and is never subtracted. If the base loss (2) already uses the same point-estimation augmentation ε0, then κθ(u)=κθ(u,ε0), so I(T,E0)=0 identically and the augmentation is not π-noise by Eq. (1); if the κ's are distinct, the stationary condition of the true I differs from InfoNCE by (1/2)∇θ E log κθ(u). Either way, the equivalence in Eq. (13) does not follow from Eqs. (4)-(12); it is obtained by silently discarding one of the two entropies in mutual information.

1 more flagged steps
  1. renaming known result [Section 3.3, Eq. (13) and conclusion paragraph]
    "which is the same as the standard contrastive learning paradigm. In conclusion, the standard contrastive learning paradigm is equivalent to optimizing a contrastive learning module with a point estimation of the π-noise, where the predefined data augmentation is the point estimation."

    Because κθ(u,ε0) is exactly the softmax ratio inside InfoNCE, max Σ log κθ ⇔ min InfoNCE is a notational identity. The auxiliary Gaussian was engineered so that -H(T|E) equals the standard contrastive loss up to constants, and this identity is then presented as a proof that GCL performs point estimation of π-noise. The novel terminology ('task entropy', 'point estimation of π-noise') names the loss rather than explaining it; the equivalence is the renaming.

full rationale

The circularity is concentrated in the paper's theoretical bridge (Section 3). Eq. (5) defines the task entropy H(T) as the entropy of a Gaussian whose variance is a monotone function of the very InfoNCE loss that appears in the objective, so the later 'reduction' of GCL to π-noise point estimation is built into the definition. Eq. (13) then asserts max I ⇔ max Σ log κθ(u,ε0) while only -H(T|E) has been computed; the θ-dependent H(T) term is dropped. Under the paper's own equations, a predefined augmentation used to define the base loss gives κθ(u)=κθ(u,ε0) and hence I(T,E0)=0, contradicting Eq. (1); with distinct κ's, the stationary conditions differ. The claimed theoretical guarantee for PiNGDA therefore rests on a relabeling plus an omitted term rather than on a derived equivalence. The PiNGDA method itself—a trainable edge/attribute noise generator evaluated against external baselines in Section 5—is not circular and could be useful for empirical reasons, but it does not rescue the paper's stated information-theoretic proof. The self-citations to the same group's π-noise papers (Li 2022; Zhang et al. 2024; Huang et al. 2025) are present, but even setting those aside, the definitional circularity in Eqs. (4)-(13) is decisive.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The central derivation depends on a small set of choices: the pi-noise definition, the monotone loss-to-variance mapping, the Dirac-delta treatment of fixed augmentations, and the single-view simplification. None of these is independently validated; the first two come from the authors' prior framework and the paper's own definitions.

free parameters (3)
  • Temperature tau = 0.3 or 0.5 per dataset (Table 9)
    Chosen by grid search to maximize average accuracy; controls sharpness of the InfoNCE loss and affects the noise generator's training.
  • Noise generator learning rates = 1e-4 for edges, 1e-3 for features (Appendix B.4)
    Tuned hyperparameters for the edge-dropping and attribute-noise modules; they determine how much the learned augmentation changes during training.
  • Training epochs = 500 to 2000 depending on dataset (Table 9)
    Selected per dataset by grid search; longer training generally improves representation quality but also risks overfitting.
assumptions (5)
  • domain assumption Pi-noise definition: I(T,E) > 0 iff H(T) > H(T|E) (Eq. 1)
    Adopted from Li (2022) as the definition of beneficial noise; the paper relies on this to call learned augmentations beneficial.
  • ad hoc to paper Task entropy can be represented by the entropy of an auxiliary Gaussian whose variance is a monotone function of the per-node loss (Eqs. 4-5)
    The mapping f = exp is chosen by the authors; there is no argument that this Gaussian entropy equals any intrinsic task entropy.
  • domain assumption A predefined augmentation acts as a Dirac delta point estimate of noise (Eq. 10)
    Used to derive the equivalence; holds for deterministic augmentation functions but ignores stochastic augmentation behavior.
  • domain assumption Only one augmented view is used for contrast; extension to multiple views is asserted without derivation
    Stated without loss of generality in Section 3.3; standard GCL often uses two augmented views, and the proof does not explicitly cover that case.
  • domain assumption Minimizing InfoNCE loss reduces task uncertainty
    The paper conflates the contrastive pretext-task loss with downstream task complexity; this link is assumed, not proven.
invented entities (1)
  • Gaussian auxiliary variable alpha
    purpose: Converts the GCL loss into an entropy quantity to define task entropy and bridge GCL with pi-noise.
    Defined via Eq. 4 as N(0, f(ell(u;theta))); it carries no information beyond the loss and has no falsifiable handle outside the derivation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Learn Beneficial Noise as Graph Augmentation." pith.science (2026). https://pith.science/paper/UWODDV5M

@misc{pith2026250519024,
  author       = {Pith},
  title        = {Pith review of: Learn Beneficial Noise as Graph Augmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UWODDV5M}},
  note         = {Machine review of arXiv:2505.19024}
}
read the original abstract

Although graph contrastive learning (GCL) has been widely investigated, it is still a challenge to generate effective and stable graph augmentations. Existing methods often apply heuristic augmentation like random edge dropping, which may disrupt important graph structures and result in unstable GCL performance. In this paper, we propose Positive-incentive Noise driven Graph Data Augmentation (PiNGDA), where positive-incentive noise (pi-noise) scientifically analyzes the beneficial effect of noise under the information theory. To bridge the standard GCL and pi-noise framework, we design a Gaussian auxiliary variable to convert the loss function to information entropy. We prove that the standard GCL with pre-defined augmentations is equivalent to estimate the beneficial noise via the point estimation. Following our analysis, PiNGDA is derived from learning the beneficial noise on both topology and attributes through a trainable noise generator for graph augmentations, instead of the simple estimation. Since the generator learns how to produce beneficial perturbations on graph topology and node attributes, PiNGDA is more reliable compared with the existing methods. Extensive experimental results validate the effectiveness and stability of PiNGDA.

Figures

Figures reproduced from arXiv: 2505.19024 by the authors.

Figure 1
Figure 1. This figure illustrates the PiNGDA framework, which consists of a [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Comparison in terms of training time of one epoch, and memory costs between different graph representation [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Visualization of noise in graph data. Nodes are selected from the graph which are colored according to their labels, [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The effect of the temperature τ [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: The effect of the hidden dim. of node classification with variable temperature τ and hidden dim. We can observe that our PiNGDA is not very sensitive to temperature and hidden dim. For small graphs, smaller temperature leads to better performance. 15 [PITH_FULL_IMAGE:…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

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

  1. TableZoomer: A Collaborative Agent Framework for Large-scale Table Question Answering

    cs.CL 2025-09 conditional novelty 5.0 of 10

    TableZoomer compresses tables into schemas, zooms to query-relevant regions, and executes generated Python to answer questions, lifting Qwen3-8B accuracy by 19.34 points on DataBench and 25 points on TableBench Fact Checking.

  2. Skill-Nav: Enhanced Navigation with Versatile Quadrupedal Locomotion via Waypoint Interface

    cs.RO 2025-06 conditional novelty 5.0 of 10

    A waypoint-based interface between planners and a trained quadrupedal locomotion policy enables navigation over diverse obstacles in simulation and on a real robot.

  3. AnchorFormer: Differentiable Anchor Attention for Efficient Vision Transformer

    cs.CV 2025-05 conditional novelty 4.0 of 10

    A vision transformer reduces self-attention complexity from O(n^2) to O(mn) by using m learnable anchor tokens and a two-step Markov transition between anchors and tokens.

Reference graph

Works this paper leans on

19 extracted references · 9 canonical work pages · cited by 3 Pith papers

  1. [3]

    Hierarchical Graph Convolutional Networks for Semi-supervised Node Classification

    Hu, F., Zhu, Y ., Wu, S., Wang, L., and Tan, T. Hierarchical graph convolutional networks for semi-supervised node classification. arXiv preprint arXiv:1902.06667,

    work page Pith review arXiv 1902

  2. [5]

    Kingma, D. P. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114,

    arXiv

  3. [6]

    We evaluate our proposed framework in the semi-supervised learning setting on graph classification on the benchmark TUDataset (Morris et al., 2020)

    For all datasets, we randomly split the datasets, where 10%, 10%, and the rest 80% of nodes are selected for the training, validation, and test set, respectively. We evaluate our proposed framework in the semi-supervised learning setting on graph classification on the benchmark TUDataset (Morris et al., 2020). The detailed statistics of the datasets are s...

    work page 2020

  4. [7]

    C.-C., Lei, Y ., and Yang, B

    10 Pei, H., Wei, B., Chang, K. C.-C., Lei, Y ., and Yang, B. Geom-gcn: Geometric graph convolutional networks. arXiv preprint arXiv:2002.05287,

    arXiv 2002

  5. [8]

    Dropout: a simple way to prevent neural networks from overfitting

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

    work page 1929

  6. [9]

    Specifically, we carry out grid search for the hyper-parameters on the following search space: • Number of training epochs: {500, 1000, 1500, 2000, 3000}

    For the learnable noise generators, we use separate optimizers with learning rates of 0.0001 for edges and 0.001 for features, and apply a weight decay of 0.0001 to both. Specifically, we carry out grid search for the hyper-parameters on the following search space: • Number of training epochs: {500, 1000, 1500, 2000, 3000}. • Learning rate for training: {...

    work page 2000

  7. [12]

    Graph contrastive learning automated

    You, Y ., Chen, T., Shen, Y ., and Wang, Z. Graph contrastive learning automated. In International Conference on Ma- chine Learning, pp. 12121–12132. PMLR, 2021a. You, Y ., Chen, T., Shen, Y ., and Wang, Z. Graph contrastive learning automated. In International Conference on Ma- chine Learning, pp. 12121–12132. PMLR, 2021b. Zhang, H., Huang, S., and Li, X...

    arXiv

  8. [13]

    Data augmentation of contrastive learning is estimating positive-incentive noise

    11 Zhang, H., Xu, Y ., Huang, S., and Li, X. Data augmentation of contrastive learning is estimating positive-incentive noise. arXiv preprint arXiv:2408.09929,

    arXiv

Show all 19 references
  1. [14]

    Graph contrastive learning with adaptive augmentation

    Zhu, Y ., Xu, Y ., Yu, F., Liu, Q., Wu, S., and Wang, L. Graph contrastive learning with adaptive augmentation. In Proceedings of the Web Conference 2021, pp. 2069– 2080,

    2021

  2. [16]

    The detailed statistics of the datasets are summarized in Table

    and ogbn-arxiv (Hu et al., 2020). The detailed statistics of the datasets are summarized in Table

    2020

  3. [256]

    Dataset Graphs Avg

    Additionally, we utilize a projection head, consisting of a 256-dimensional fully connected layer with ReLU activation, followed by a 256-dimensional 13 Table 7: Statistics of datasets used in graph classification experiments. Dataset Graphs Avg. Nodes Avg. Edges Classes NCI1 ...

    2000

  4. [2016]

    Inductive repre- sentation learning on large graphs

    Hamilton, W., Ying, Z., and Leskovec, J. Inductive repre- sentation learning on large graphs. Advances in neural information processing systems, 30, 2017a. Hamilton, W. L., Ying, R., and Leskovec, J. Representation learning on graphs: Methods and applications. arXiv preprint a...

    arXiv

  5. [2019]

    How powerful are graph neural networks? arXiv preprint arXiv:1810.00826,

    Xu, K., Hu, W., Leskovec, J., and Jegelka, S. How powerful are graph neural networks? arXiv preprint arXiv:1810.00826,

    arXiv

  6. [2020]

    and Cho, K

    Falcon, W. and Cho, K. A framework for contrastive self- supervised learning and designing a new approach. arXiv preprint arXiv:2009.00104,

    2009 arXiv

  7. [2021]

    Representa- tion learning with contrastive predictive coding

    van den Oord, A., Li, Y ., and Vinyals, O. Representa- tion learning with contrastive predictive coding. arXiv preprint arXiv:1807.03748,

    arXiv

  8. [2022]

    Adversarial graph augmentation to improve graph contrastive learn- ing, 2021a

    Suresh, S., Li, P., Hao, C., and Neville, J. Adversarial graph augmentation to improve graph contrastive learn- ing, 2021a. Suresh, S., Li, P., Hao, C., and Neville, J. Adversarial graph augmentation to improve graph contrastive learning. Advances in Neural Information Process...

    arXiv

  9. [2023]

    and Cangea, C

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

    2007 arXiv

  10. [2024]

    Derivation of Eq

    12 Appendix A. Derivation of Eq. (12) We can expand the density of N (0, κθ(u, ε)−1) and substitute it into L, L = 1 n X u log C + 1 2 log κθ(u, ε0) − 1 2 , (23) where the details can be found in Appendix A as p(α|u, ε0) =C p κθ(u, ε0) exp(− α2 2 · κθ(u, ε0)) =⇒ log p(α|u, ε0)...

    2008

  11. [2025]

    Categorical repa- rameterization with gumbel-softmax

    Jang, E., Gu, S., and Poole, B. Categorical repa- rameterization with gumbel-softmax. arXiv preprint arXiv:1611.01144,

    arXiv

Pith tools

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