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REVIEW 6 major objections 7 minor 47 references

SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps

T0 review · 6 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A spectral-gap subtraction detects out-of-distribution graphs by removing a second-largest-eigenvalue component, improving OOD detection on graph benchmarks.

desk verdict A plausible post-hoc trick—Laplacian spectral gap as a scaling factor for rank-one feature removal—but the theory is missing a proof, the mechanism story is contradictory, and the closest prior baseline is never compared. read the letter →

arxiv 2505.15177 v2 pith:6QXCGZSV submitted 2025-05-21 cs.LG

Jiawei Gu , Ziyue Qiao , Zechao Li This is my paper · ORCID
classification cs.LG MSC 05C5068T07
keywords graph-levelOODdetectionLaplacianspectralgappost-hocfeatureadjustmentgraphneuralnetworksout-of-distributiontheoryparameter-freemethod
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that graph-level out-of-distribution (OOD) detection can be improved by a parameter-free post-hoc feature adjustment driven by the Laplacian spectral gap. The central observation is that OOD graphs often show an anomalous difference between the largest and second-largest Laplacian eigenvalues, so the method subtracts the component of the second-largest eigenvalue, scaled by that gap, from the GNN's high-level features. On five benchmark dataset pairs spanning molecules, social networks, and bioinformatics, SpecGap raises AUC and AUPR and cuts the average FPR95 by 15.40% relative to the best prior method, without retraining or architecture changes. The reader should care because this makes OOD detection a drop-in post-processing step for any trained GNN, provided the spectral-gap distributions of ID and OOD graphs are separable.

What carries the argument

The central object is the Laplacian spectral gap $\Delta\lambda = \lambda_n - \lambda_{n-1}$ of the input graph, together with the corresponding eigenvector $u_{n-1}$. The gap drives the feature adjustment $X' = X - \Delta\lambda\, u_{n-1} v_{n-1}^T$, which projects out the second-largest-eigenvalue component of the feature map; the adjustment's benefit is governed by the distributional separation assumption that a single threshold can split the spectral-gap distributions of ID and OOD graphs with a margin. The separation-gain proof expands the squared Frobenius distance between adjusted ID and OOD features and shows the cross-terms are controlled by the gap difference and the angle between the two eigenvectors.

What would settle it

Construct two graph distributions engineered to have identical distributions of $\lambda_n - \lambda_{n-1}$ but different higher-order structure (e.g., same eigenvalue distribution but different assortativity or community mixing) and run SpecGap on a GNN trained on one of them; if OOD detection still improves, spectral-gap separation is not the cause, and if it does not, the method's dependence on the threshold separation is confirmed.

Watch

Extended reading notes

Core claim

SpecGap's claim is that a graph's Laplacian spectral gap $\Delta\lambda = \lambda_n - \lambda_{n-1}$ is a structural signature of whether the graph belongs to the training distribution, and that removing the second-largest-eigenvalue component of the learned feature map—weighted by $\Delta\lambda$—moves OOD features closer to the in-distribution feature manifold. Concretely, with $X$ the high-level feature matrix, $u_{n-1}$ the eigenvector of $\lambda_{n-1}$, and $v_{n-1}=X^T u_{n-1}$, the adjusted features are $X' = X - \Delta\lambda\, u_{n-1} v_{n-1}^T$. The paper proves a strict increase in the expected Frobenius separation between ID and OOD feature pairs under distributional assumptions on the spectral gap, and empirically the adjustment improves OOD detection across unsupervised, supervised, and transformer GNNs, with the largest gains on datasets where OOD graphs deviate structurally from ID graphs.

Load-bearing premise

The whole mechanism rests on the assumption that the spectral gaps of in-distribution and out-of-distribution graphs are separable by a single threshold with a nontrivial margin, and the paper's independent evidence for this is limited to one motivating figure; the separation-gain proof additionally needs the ID and OOD eigenvectors to have a benign angle and bounded feature norms.

Editorial extensions

If this is right

  • Because SpecGap is parameter-free and post-hoc, any already-trained GNN can gain OOD detection ability without retraining or architecture changes.
  • The method consistently helps across unsupervised, supervised, and transformer GNNs on molecular, social-network, and bioinformatics benchmarks, so the spectral-gap cue is not tied to a particular model family.
  • OOD graphs show consistently higher average spectral gap ratios than ID graphs across all five dataset pairs, so the gap can serve as a cheap structural screening statistic.
  • The feature adjustment yields the largest gains when the base model is weak, suggesting spectral structure supplies information that the learned features miss.

Reading between the lines

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

  • A testable extension is to apply the same Laplacian-gap subtraction to node-level OOD detection or link-prediction features; if the mechanism is about global connectivity, its effect should fade on tasks dominated by local neighborhood patterns.
  • The separation-gain theorem depends on the angle between the eigenvectors of ID and OOD graphs staying bounded; an empirical check of that angle distribution across datasets would show where the proof holds and where it silently fails.
  • Since the adjustment uses only the graph's own Laplacian, SpecGap could be combined with any scoring function; a natural next test is whether the benefit persists when OOD graphs are constructed adversarially to match the ID spectral gap distribution.
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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

6 major / 7 minor

Summary. This paper proposes SpecGap, a parameter-free post-hoc feature adjustment for graph-level out-of-distribution (OOD) detection. Given a graph with Laplacian eigenvalues 0 = λ1 ≤ ... ≤ λn, the method computes the spectral gap Δλ = λn − λn−1 and the eigenvector u_{n−1} of λn−1, and updates the GNN feature matrix as X′ = X − Δλ u_{n−1} v_{n−1}^T with v_{n−1} = X^T u_{n−1}, after which the GNN forward pass continues unchanged. The authors claim state-of-the-art performance, including an average FPR95 reduction of 15.40% over the previous best approach, supported by experiments on five ID/OOD dataset pairs (ENZYMES-PROTEIN, IMDBM-IMDBB, BZR-COX2, TOX21-SIDER, BBBP-BACE), multiple architectures (GCL, JOAO, GIN, PPGN, GraphiT, SAN), and ablations over the adjustment formula, feature projection, number of eigenvalues, application position, and Laplacian variant. Appendix B provides a distribution-based theoretical analysis: assumptions (D1)–(D2) on the separability of ID and OOD spectral gaps, and Theorem 1 asserting that the adjustment strictly increases the expected ID–OOD Frobenius separation.

Significance. If the reported empirical results are reproducible, SpecGap is a practically attractive contribution: the method is simple, requires no retraining, and the tables show consistent AUC/AUPR improvements and FPR95 reductions across unsupervised, supervised, and transformer architectures. The ablation structure (Tables 3–6, Figures 3–4) and the Lanczos-based efficiency analysis (Appendix C.2) are useful, and the authors explicitly try to avoid assuming that ID spectral gaps are always larger than OOD gaps. However, the paper does not yet ship code (release is promised upon acceptance), reports no error bars, and its theoretical support is not usable in its current form: the proof of the central Theorem 1 is missing, the mechanism is described in two contradictory ways, and assumption (D1) is essentially the paper's motivating observation. The significance therefore rests entirely on the unverified empirical tables, and the paper needs a RankFeat comparison and a proper statistical treatment before the claims can be assessed.

major comments (6)
  1. [Appendix B.4 (Theorem 1)] The central theoretical claim is unproven. Theorem 1 asserts that, under (D1)–(D2), E||X′_ID − X′_OOD||_F ≥ E||X_ID − X_OOD||_F + Γ for some Γ > 0, with the proof deferred to 'Appendix A'; Appendix A of the manuscript, however, is the Related Work section, and no derivation of Theorem 1 appears anywhere in the paper. The proof sketch that is present is not a proof: it expands the squared Frobenius norm while the theorem concerns the norm itself; it never bounds the cross term written as '−2⟨. . .⟩'; it asserts positivity of the second term's mean, which follows merely from the two rank-1 terms differing with positive probability and does not imply a net gain once the cross term is included; and it never defines Γ in terms of the parameters in (D1)–(D2), the feature statistics, or the angle between u_{n−1,ID} and u_{n−1,OOD}. Assumption (D2) is never invoked quantitatively, and no assumption is stated on the joint distribution of the GNN features X with (Δλ, u_{n−1}), which is needed for the claimed expectation to be meaningful. Since Theorem 1 is the basis for the paper's claim of 'comprehensive theoretical analyses', this missing derivation is load-bearing.
  2. [Section 2.2 / 3.2 vs. Theorem 1] The paper explains the mechanism of SpecGap in two mutually contradictory ways. Sections 2.2 and 3.2, together with Figure 1(c), state that the adjustment 'brings OOD samples closer to the ID distribution', while Theorem 1 in Appendix B.4 claims that the adjustment strictly increases the expected ID–OOD separation by a positive margin Γ. These are opposite effects: decreasing the distance between ID and OOD samples typically makes distance-based OOD scoring less discriminative, so the two statements cannot both serve as the explanation for the observed improvements. The manuscript never reconciles this tension, leaving the interpretability of the reported gains unresolved.
  3. [Section 2.2, Eqs. (4)–(5)] Equations (4)–(5) are dimensionally inconsistent as written. The feature matrix is defined in Section 2.2 as X ∈ R^{C×HW}, while the Laplacian eigenvector is u_{n−1} ∈ R^n because L is n×n; hence the projection v_{n−1} = X^T u_{n−1} is undefined unless HW = n or C = n, and neither equality is stated or generally holds for a GNN feature map. The PyTorch-style implementation in Appendix D instead applies the update to the node-feature matrix x ∈ R^{n×d}, which is a different object from the R^{C×HW} feature map used in the main text. A single consistent convention for X (per-node feature matrix or spatial feature map) is needed before the method and the downstream claims in Eqs. (6)–(7) can be evaluated.
  4. [Section 3.2, Figure 2] The headline empirical claims cannot be verified from the reported numbers. First, RankFeat (Song et al., 2022), the most closely related method — a rank-1 feature removal for OOD detection that SpecGap generalizes by scaling with the spectral gap and by choosing a Laplacian eigenvector direction — is cited in Appendix A.3 but is never included in Tables 1–2, Table 7, or Figure 2. Second, the comparison against AAGOD, OCGIN, GLocalKD, and GOOD-D in Figure 2 is presented only as bar charts without numeric values, so the improvements over these methods are not quantified in the text. Third, the abstract's claim of 'reducing the average FPR95 by 15.40% compared to the previous best approach' is not accompanied by any description of the aggregation over datasets, baselines, or metrics, making the principal quantitative claim of the paper impossible to check.
  5. [Appendix B.2–B.3 vs. Table 9] The theoretical framework is circular as presented, and it also conflicts with the paper's own measurements of the direction of the effect. Assumption (D1) in Appendix B.2 — the existence of a threshold τ with margin ε separating the ID and OOD spectral-gap distributions — is essentially the motivating observation of Figure 1(b); Theorem 1 then shows that a gap-based adjustment improves separation only under that assumption, so the empirical gains in Tables 1–2 do not provide independent evidence for the spectral-gap mechanism. Furthermore, the baseline detector in Section B.3 ('if ∆λ(G) > τ, then ŷ = ID'), together with the direction of (D1), presupposes that ID gaps tend to exceed OOD gaps, whereas Table 9 reports that the average spectral gap ratio is higher for OOD than for ID on all five dataset pairs, and Figure 1(a) states that OOD samples show 'larger and more varied spectral gaps'. The paper does not address this contradiction between the direction assumed in the theory and the direction observed in its own data.
  6. [Tables 1–2, 7] None of the experiments in Tables 1–2, 5–7, and Figures 2–4 report standard deviations, confidence intervals, or the number of random seeds, and the code is promised only 'upon acceptance'; several reported gains are small in absolute terms (e.g., TOX21-SIDER with GCL_S: AUC 68.04 to 73.41; BBBP-BACE with GCL_L: AUC 46.74 to 52.05). The claims of consistent, state-of-the-art improvement therefore cannot currently be assessed for statistical reliability, and the experiments are not reproducible by the community.
minor comments (7)
  1. [Section 3.2] The sentence 'The substantial and consistent performance improvements achieved by SpecGap across a diverse range of graph neural network architectures and datasets.' is grammatically incomplete because it lacks a finite verb.
  2. [Appendix D] The provided pseudo-code applies SpecGap to the initial node features before the first GNN layer, which does not match Section 3.1's statement that SpecGap is applied to the final layer's feature map (or after the self-attention layer for Transformers), nor Table 5's finding that the best position is after the first layer; the implementation and the reported configuration should be aligned.
  3. [Table 7] Table 7 reports FPR95 as fractions (e.g., 0.215) while Tables 1–2 report percentages (e.g., 93.33); the units should be made uniform across all tables.
  4. [Eq. (15)] The stated Lanczos convergence bound in Eq. (15) has an unspecified constant C and does not match the standard form of Ritz-value error bounds; since this bound is not used elsewhere in the paper, citing a standard reference would be cleaner than presenting a nonstandard expression.
  5. [References] The reference list contains the same paper twice as [Liu et al., 2020a] and [Liu et al., 2020b] with different author lists; the duplicate entry should be removed.
  6. [Figure 6] The caption of Figure 6 describes x-, y-, and z-axes, but the displayed panels are heatmaps with a color bar; the axis description and the colorbar label should be clarified.
  7. [Appendix C.2] The section begins with 'In the subsection, we provide a detailed analysis'; this should read 'In this subsection, ...'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the benchmark results are external measurements and Theorem 1 is a conditional statement whose flaws are an omitted proof and an internal contradiction, not a circular reduction.

full rationale

The paper's central empirical claim (average FPR95 reduction of 15.40%) is an external benchmark measurement, not a quantity derived from the spectral-gap assumption; no fitted parameter is renamed as a prediction, and no self-citation is load-bearing. The theoretical chain is conditional: assumption (D1) states ID and OOD spectral-gap distributions are partially separable, and Theorem 1 (Appendix B.4) asserts that under (D1)-(D2) SpecGap increases average ID-OOD Frobenius separation. A conditional implication from D1 to a separation gain is not, by itself, circular; the conclusion is not the same proposition as D1. Two in-scope flaws should nevertheless be flagged but they do not constitute circularity: (i) the proof of Theorem 1 is omitted—the manuscript says 'A detailed step-by-step derivation is provided in Appendix A,' but Appendix A is the Related Work section and contains no such derivation; (ii) Figure 1(c) states SpecGap 'brings OOD samples closer to the ID distribution,' which conflicts with Theorem 1's claim of strictly larger ID-OOD separation. The absence of a RankFeat comparison is an empirical completeness concern, not a circular-reasoning concern. Because the loaded derivation does not reduce to its own inputs by construction, the circularity score is 0.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

No new entities are postulated. The load-bearing inputs are the two distributional assumptions D1 and D2 plus several hyperparameter-style design choices selected through ablations. These carry much of the paper's explanatory weight and are not independently established.

free parameters (4)
  • Number of top eigenvalues used (k) = 2
    Ablation in Figure 3 on ENZYMES-PROTEIN shows AUC peaks at 2 eigenvalues; this design choice is selected post hoc and used everywhere.
  • Application position in the GNN = after first layer (per Table 5); main text Section 3.1 says final layer
    Table 5 shows after first layer is best, but Section 3.1 says SpecGap is applied to the final layer's feature map. The deployed configuration is ambiguous.
  • Laplacian variant = Normalized Laplacian (Table 6)
    Ablation on BZR-COX2 shows normalized Laplacian is best, while Section 2 defines L = D - A as unnormalized. The evaluated variant differs from the specified algorithm.
  • Feature projection method = Eigenvector-based (Figure 4)
    Chosen over random projection or no projection based on ablation on IMDBM-IMDBB.
assumptions (3)
  • ad hoc to paper (D1) There exists tau and epsilon > 0 such that P_ID(Delta_lambda <= tau) <= alpha - epsilon and P_OOD(Delta_lambda >= tau) <= alpha - epsilon.
    Introduced in Appendix B.2 as the core assumption. It is the paper's motivating observation restated as an axiom and is not independently evidenced.
  • domain assumption (D2) Spectral gap distributions have bounded variance or sub-Gaussian tails.
    Used in Theorem 1 to prevent pathological overlap; no justification is given for real-world graphs.
  • domain assumption The feature matrix X and Laplacian eigenvector u_{n-1} have compatible dimensions, with X's rows corresponding to graph vertices.
    Section 2.2 writes X in R^{C x HW} but the code uses node features with X^T u_{n-1}; the product is only defined if the feature dimension matches the number of vertices.

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Cite this review

Pith. "Pith review of SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps." pith.science (2026). https://pith.science/paper/6QXCGZSV

@misc{pith2026250515177,
  author       = {Pith},
  title        = {Pith review of: SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6QXCGZSV}},
  note         = {Machine review of arXiv:2505.15177}
}
abstract

The task of graph-level out-of-distribution (OOD) detection is crucial for deploying graph neural networks in real-world settings. In this paper, we observe a significant difference in the relationship between the largest and second-largest eigenvalues of the Laplacian matrix for in-distribution (ID) and OOD graph samples: \textit{OOD samples often exhibit anomalous spectral gaps (the difference between the largest and second-largest eigenvalues)}. This observation motivates us to propose SpecGap, an effective post-hoc approach for OOD detection on graphs. SpecGap adjusts features by subtracting the component associated with the second-largest eigenvalue, scaled by the spectral gap, from the high-level features (i.e., $\mathbf{X}-\left(\lambda_n-\lambda_{n-1}\right) \mathbf{u}_{n-1} \mathbf{v}_{n-1}^T$). SpecGap achieves state-of-the-art performance across multiple benchmark datasets. We present extensive ablation studies and comprehensive theoretical analyses to support our empirical results. As a parameter-free post-hoc method, SpecGap can be easily integrated into existing graph neural network models without requiring any additional training or model modification.

Figures

Figures reproduced from arXiv: 2505.15177 by the authors.

Figure 1
Figure 1. SpecGap: Spectral Gap-based OOD Detection. (a) Orig [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Performance comparison of OOD detection methods before and after applying SpecGap. Each subplot represents a different dataset [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Impact of the number of largest eigenvalues used in Spec [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Comparison of different feature projection methods in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: An example ID vs. OOD spectral gap distribution from [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Spectral distributions of graph embeddings. Top row: ID samples before (left) and after (right) SpecGap processing. Bottom row: [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Evolution of spectral gap ratios during GNN training for [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]

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Reference graph

Works this paper leans on

47 extracted references · 35 canonical work pages

  1. [1]

    Spectral graph theory

    [Chung and Graham, 1997] Fan RK Chung and Fan Chung Graham. Spectral graph theory . Number

    work page 1997

  2. [3]

    the correct side

    The projection vn−1 = X T un−1. Then define X ′ = X − ∆λ un−1 (vn−1)T . While prior literature sometimes assumes ∆λID is consis- tently larger, we do not impose that restriction here. Instead, we rely on the difference in∆λ distributions and (potentially) in un−1 distributions to yield improved separation in the X ′ space. Separation Analysis in Feature S...

    work page 2021

  3. [7]

    Expander graphs and their applications

    [Hoory et al., 2006] Shlomo Hoory, Nathan Linial, and Avi Wigderson. Expander graphs and their applications. Bul- letin of the American Mathematical Society , 43(4):439– 561,

    work page 2006

  4. [11]

    A comprehensive survey on deep graph representation learning

    [Ju et al., 2024] Wei Ju, Zheng Fang, Yiyang Gu, Zequn Liu, Qingqing Long, Ziyue Qiao, Yifang Qin, Jianhao Shen, Fang Sun, Zhiping Xiao, et al. A comprehensive survey on deep graph representation learning. Neural Networks, page 106207,

    work page 2024

  5. [12]

    Semi-supervised classification with graph convolutional networks

    [Kipf and Welling, 2016] Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907,

    arXiv 2016

  6. [13]

    Rethinking graph transformers with spectral atten- tion

    [Kreuzer et al., 2021] Devin Kreuzer, Dominique Beaini, Will Hamilton, Vincent L ´etourneau, and Prudencio Tossou. Rethinking graph transformers with spectral atten- tion. Advances in Neural Information Processing Systems, 34:21618–21629,

    work page 2021

  7. [17]

    Good-d: On unsupervised graph out-of- distribution detection

    [Liu et al., 2023] Yixin Liu, Kaize Ding, Huan Liu, and Shirui Pan. Good-d: On unsupervised graph out-of- distribution detection. In Proceedings of the Sixteenth ACM International Conference on Web Search and Data Mining, pages 339–347,

    work page 2023

  8. [18]

    Towards self- interpretable graph-level anomaly detection

    [Liu et al., 2024] Yixin Liu, Kaize Ding, Qinghua Lu, Fuyi Li, Leo Yu Zhang, and Shirui Pan. Towards self- interpretable graph-level anomaly detection. Advances in Neural Information Processing Systems, 36,

    work page 2024

Show all 47 references
  1. [19]

    Deep graph-level anomaly de- tection by glocal knowledge distillation

    [Ma et al., 2022] Rongrong Ma, Guansong Pang, Ling Chen, and Anton van den Hengel. Deep graph-level anomaly de- tection by glocal knowledge distillation. InProceedings of the fifteenth ACM international conference on web search and data mining, pages 704–714,

    2022

  2. [20]

    Towards graph-level anomaly detection via deep evolutionary mapping

    [Ma et al., 2023] Xiaoxiao Ma, Jia Wu, Jian Yang, and Quan Z Sheng. Towards graph-level anomaly detection via deep evolutionary mapping. InProceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 1631–1642,

    2023

  3. [21]

    Provably powerful graph networks

    [Maron et al., 2019] Haggai Maron, Heli Ben-Hamu, Hadar Serviansky, and Yaron Lipman. Provably powerful graph networks. Advances in neural information processing sys- tems, 32,

    2019

  4. [22]

    Graphit: Encod- ing graph structure in transformers

    [Mialon et al., 2021] Gr´egoire Mialon, Dexiong Chen, Mar- got Selosse, and Julien Mairal. Graphit: Encod- ing graph structure in transformers. arXiv preprint arXiv:2106.05667,

    2021 arXiv

  5. [23]

    A new method to predict anomaly in brain network based on graph deep learning

    [Mirakhorli et al., 2020] Jalal Mirakhorli, Hamidreza Amin- davar, and Mojgan Mirakhorli. A new method to predict anomaly in brain network based on graph deep learning. Reviews in the Neurosciences, 31(6):681–689,

    2020

  6. [24]

    Tudataset: A collection of bench- mark datasets for learning with graphs

    [Morris et al., 2020] Christopher Morris, Nils M Kriege, Franka Bause, Kristian Kersting, Petra Mutzel, and Mar- ion Neumann. Tudataset: A collection of bench- mark datasets for learning with graphs. arXiv preprint arXiv:2007.08663,

    2020 arXiv

  7. [25]

    Semi-supervised domain adaptation in graph transfer learning

    [Qiao et al., 2023] Ziyue Qiao, Xiao Luo, Meng Xiao, Hao Dong, Yuanchun Zhou, and Hui Xiong. Semi-supervised domain adaptation in graph transfer learning. In Proceed- ings of the Thirty-Second International Joint Conference on Artificial Intelligence, pages 2279–2287,

    2023

  8. [26]

    Information filtering and in- terpolating for semi-supervised graph domain adaptation

    [Qiao et al., 2024] Ziyue Qiao, Meng Xiao, Weiyu Guo, Xiao Luo, and Hui Xiong. Information filtering and in- terpolating for semi-supervised graph domain adaptation. Pattern Recognition, 153:110498,

    2024

  9. [27]

    Towards contin- uous reuse of graph models via holistic memory diversi- fication

    [Qiao et al., 2025] Ziyue Qiao, Junren Xiao, Qingqiang Sun, Meng Xiao, Xiao Luo, and Hui Xiong. Towards contin- uous reuse of graph models via holistic memory diversi- fication. In The Thirteenth International Conference on Learning Representations,

    2025

  10. [29]

    Optimizing ood detection in molecular graphs: A novel approach with diffusion mod- els

    [Shen et al., 2024] Xu Shen, Yili Wang, Kaixiong Zhou, Shirui Pan, and Xin Wang. Optimizing ood detection in molecular graphs: A novel approach with diffusion mod- els. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining , pages 2640– 2650,

    2024

  11. [30]

    Rankfeat: Rank-1 feature removal for out-of-distribution detection

    [Song et al., 2022] Yue Song, Nicu Sebe, and Wei Wang. Rankfeat: Rank-1 feature removal for out-of-distribution detection. Advances in Neural Information Processing Systems, 35:17885–17898,

    2022

  12. [31]

    Spectral graph the- ory and its applications

    [Spielman, 2007] Daniel A Spielman. Spectral graph the- ory and its applications. 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS’07) , pages 29– 38,

    2007

  13. [33]

    Large margin deep networks for out- of-distribution detection

    [Wang et al., 2021] Ruoqi Wang, Lingxi Xie, Matthew Geiger, and Qi Lin. Large margin deep networks for out- of-distribution detection. International Conference on Ma- chine Learning (ICML),

    2021

  14. [34]

    Goodat: Towards test-time graph out-of-distribution detection

    [Wang et al., 2024] Luzhi Wang, Dongxiao He, He Zhang, Yixin Liu, Wenjie Wang, Shirui Pan, Di Jin, and Tat-Seng Chua. Goodat: Towards test-time graph out-of-distribution detection. In Proceedings of the AAAI Conference on Arti- ficial Intelligence, volume 38, pages 15537–15545,

    2024

  15. [35]

    A com- prehensive survey on graph neural networks

    [Wu et al., 2020] Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and Philip S Yu. A com- prehensive survey on graph neural networks. IEEE trans- actions on neural networks and learning systems, 32(1):4– 24,

    2020

  16. [36]

    Energy-based out-of-distribution de- tection for graph neural networks

    [Wu et al., 2023] Qitian Wu, Yuxuan Chen, Chenghao Yang, and Junchi Yan. Energy-based out-of-distribution de- tection for graph neural networks. arXiv preprint arXiv:2302.02914,

    2023 arXiv

  17. [37]

    Graph learning: A survey

    [Xia et al., 2021] Feng Xia, Ke Sun, Shuo Yu, Abdul Aziz, Liangtian Wan, Shirui Pan, and Huan Liu. Graph learning: A survey. IEEE Transactions on Artificial Intelligence , 2(2):109–127,

    2021

  18. [38]

    How powerful are graph neural net- works? arXiv preprint arXiv:1810.00826,

    [Xu et al., 2018] Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural net- works? arXiv preprint arXiv:1810.00826,

    2018 arXiv

  19. [40]

    Openood: Benchmarking generalized out-of-distribution detection

    [Yang et al., 2022] Jingkang Yang, Pengyun Wang, Dejian Zou, Zitang Zhou, Kunyuan Ding, Wenxuan Peng, Haoqi Wang, Guangyao Chen, Bo Li, Yiyou Sun, et al. Openood: Benchmarking generalized out-of-distribution detection. Advances in Neural Information Processing Systems , 35:325...

    2022

  20. [41]

    Graph con- trastive learning with augmentations

    [You et al., 2020] Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, and Yang Shen. Graph con- trastive learning with augmentations. Advances in neural information processing systems, 33:5812–5823,

    2020

  21. [42]

    Graph contrastive learning auto- mated

    [You et al., 2021] Yuning You, Tianlong Chen, Yang Shen, and Zhangyang Wang. Graph contrastive learning auto- mated. In International Conference on Machine Learning, pages 12121–12132. PMLR,

    2021

  22. [43]

    Dual-discriminative graph neural network for imbalanced graph-level anomaly detection

    [Zhang et al., 2022] Ge Zhang, Zhenyu Yang, Jia Wu, Jian Yang, Shan Xue, Hao Peng, Jianlin Su, Chuan Zhou, Quan Z Sheng, Leman Akoglu, et al. Dual-discriminative graph neural network for imbalanced graph-level anomaly detection. Advances in Neural Information Processing System...

    2022

  23. [44]

    On using classification datasets to evaluate graph outlier detection: Peculiar observations and new insights

    [Zhao and Akoglu, 2023] Lingxiao Zhao and Leman Akoglu. On using classification datasets to evaluate graph outlier detection: Peculiar observations and new insights. Big Data, 11(3):151–180,

    2023

  24. [45]

    gap-only

    A Related Work Our work on graph-level out-of-distribution (OOD) detection is related to several research areas in machine learning and graph theory. We organize the related work into three main categories: general OOD detection, graph-level OOD detec- tion, and spectral metho...

    2016

  25. [47]

    fixed” data-level Laplacian and “learned

    Across both supervised and unsupervised learning paradigms, SpecGap consistently improves the OOD detection performance of the base models across all three metrics: AUC, AUPR, and FPR95. In the supervised setting, SpecGap enhances GraphiT’s performance with average improvement...

  26. [1997]

    Convolutional neural net- works on graphs with fast localized spectral filtering

    [Defferrard et al., 2016] Micha¨el Defferrard, Xavier Bres- son, and Pierre Vandergheynst. Convolutional neural net- works on graphs with fast localized spectral filtering. In Advances in neural information processing systems, pages 3844–3852,

    2016

  27. [2006]

    Open graph benchmark: Datasets for machine learning on graphs

    [Hu et al., 2020] Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec. Open graph benchmark: Datasets for machine learning on graphs. Advances in neural informa- tion processing systems, 33:22118–22133,

    2020

  28. [2007]

    Graph attention networks

    [Veliˇckovi´c et al., 2017] Petar Veliˇckovi´c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. Graph attention networks. arXiv preprint arXiv:1710.10903,

    2017 arXiv

  29. [2010]

    A data-centric framework to endow graph neural networks with out-of- distribution detection ability

    [Guo et al., 2023] Yuxin Guo, Cheng Yang, Yuluo Chen, Jixi Liu, Chuan Shi, and Junping Du. A data-centric framework to endow graph neural networks with out-of- distribution detection ability. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mini...

    2023

  30. [2016]

    Lee, and Yuval Peres

    [Ding et al., 2010] Jian Ding, James R. Lee, and Yuval Peres. Spectral properties of large random d-regular graphs. Annals of Probability, 38(3):1247–1285,

    2010

  31. [2017]

    A baseline for detecting misclassified and out-of- distribution examples in neural networks

    [Hendrycks and Gimpel, 2016] Dan Hendrycks and Kevin Gimpel. A baseline for detecting misclassified and out-of- distribution examples in neural networks. In International Conference on Learning Representations,

    2016

  32. [2018]

    Generalized out-of-distribution detec- tion: A survey

    [Yang et al., 2021] Jingkang Yang, Kaiyang Zhou, Yixuan Li, and Ziwei Liu. Generalized out-of-distribution detec- tion: A survey. arXiv preprint arXiv:2110.11334,

    2021 arXiv

  33. [2019]

    Graphde: A generative framework for debiased learn- ing and out-of-distribution detection on graphs

    [Li et al., 2022] Zenan Li, Qitian Wu, Fan Nie, and Junchi Yan. Graphde: A generative framework for debiased learn- ing and out-of-distribution detection on graphs. Advances in Neural Information Processing Systems , 35:30277– 30290,

    2022

  34. [2020]

    Praga: Prototype-aware graph adaptive aggregation for spatial multi-modal omics analysis

    [Huang et al., 2024] Xinlei Huang, Zhiqi Ma, Dian Meng, Yanran Liu, Shiwei Ruan, Qingqiang Sun, Xubin Zheng, and Ziyue Qiao. Praga: Prototype-aware graph adaptive aggregation for spatial multi-modal omics analysis. In AAAI 2025,

    2024

  35. [2021]

    Label efficient semi- supervised learning via graph filtering

    [Li et al., 2019] Qimai Li, Xiao-Ming Wu, Han Liu, Xiao- tong Zhang, and Zhichao Guan. Label efficient semi- supervised learning via graph filtering. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pat- tern Recognition, pages 9582–9591,

    2019

  36. [2022]

    Enhancing the reliability of out-of-distribution image detection in neural networks

    [Liang et al., 2017] Shiyu Liang, Yixuan Li, and Rayadurgam Srikant. Enhancing the reliability of out-of-distribution image detection in neural networks. In International Conference on Learning Representations ,

    2017

  37. [2023]

    Inductive representation learning on large graphs

    [Hamilton et al., 2017] Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In Advances in neural information processing sys- tems, pages 1024–1034,

    2017

  38. [2024]

    Drugood: Out-of- distribution dataset curator and benchmark for ai-aided drug discovery–a focus on affinity prediction problems with noise annotations

    [Ji et al., 2023] Yuanfeng Ji, Lu Zhang, Jiaxiang Wu, Bingzhe Wu, Lanqing Li, Long-Kai Huang, Tingyang Xu, Yu Rong, Jie Ren, Ding Xue, et al. Drugood: Out-of- distribution dataset curator and benchmark for ai-aided drug discovery–a focus on affinity prediction problems with no...

    2023

  39. [2025]

    Raising the bar in graph-level anomaly detection

    [Qiu et al., 2022] Chen Qiu, Marius Kloft, Stephan Mandt, and Maja Rudolph. Raising the bar in graph-level anomaly detection. arXiv preprint arXiv:2205.13845,

    2022 arXiv

Pith tools

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