Out-of-Distribution Detection in Heterogeneous Graphs via Energy Propagation

Chen Zhao; Minglai Shao; Tao Yin; Xiaoyan Liu

REVIEW 3 major objections 6 minor 51 references

Out-of-Distribution Detection in Heterogeneous Graphs via Energy Propagation

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read This paper claims that propagating energy scores along meta-paths lets a heterogeneous-graph model reliably flag out-of-distribution nodes, reporting gains over seven baselines on three real-world networks.

desk verdict Useful heterogeneous-graph extension of energy-based OOD detection, but the reported K+1 gains are partly artifacts of test-set threshold selection. read the letter →

arxiv 2505.03774 v1 pith:OPZA73IO submitted 2025-04-29 cs.LG cs.SI

Tao Yin , Chen Zhao , Xiaoyan Liu , Minglai Shao This is my paper · ORCID

classification cs.LGcs.SI

keywords heterogeneousgraphout-of-distributiondetectionenergyscoremeta-pathpropagationneuralnetworksnodeclassificationloss

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

Out-of-distribution detection is well studied for images and homogeneous graphs, but heterogeneous graphs — where nodes and edges come in several types, as in citation, social, and recommender networks — have received little attention. The paper tries to close that gap with OODHG, a method that computes an energy score for each target-type node from the logits of a heterogeneous graph neural network, then refines that score by propagating it along meta-paths that connect same-type nodes. The training objective adds an energy constraint that pushes in-distribution node energies low, making the OOD threshold easier to set. On the DBLP, ACM, and IMDB datasets, the authors report that OODHG outperforms homogeneous-graph OOD detectors and classical softmax- and energy-based baselines on both OOD detection and in-distribution node classification. The takeaway claim is that structural propagation, not just better node features, is what makes the energy signal work in heterogeneous graphs.

What carries the argument

The central object is the meta-path energy-propagation operator. For a meta-path $P_n$ whose first and last node types are the target type, the paper composes row-normalized adjacency matrices $\hat A_{t_i,t_{i+1}}$ between consecutive node types to obtain $\hat A$, a row-normalized adjacency between target-type nodes, and then iterates $\mathbf{E}^{(k,P_n)} = \gamma \mathbf{E}^{(k-1,P_n)} + (1-\gamma)\hat A \mathbf{E}^{(k-1,P_n)}$; the final score for a node is the average over all chosen meta-paths. This operator injects heterogeneous structure into the OOD signal: it lets a target-type node inherit the energy of semantically related same-type neighbors, so the decision rule $-\hat E_i \le \tau$ sees smoothed, structurally aware scores instead of raw per-node logit energies. The squared-hinge energy loss is the second piece of machinery; it directly regularizes the propagated energies during training, pulling in-distribution energies below a margin while leaving OOD energies comparatively high.

What would settle it

Construct a heterogeneous graph in which OOD nodes are deliberately placed so that none of their meta-path neighbors are OOD; if OODHG's detection AUROC on that graph is no better than plain per-node energy scoring, the propagation step fails for non-local OOD patterns.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that energy scores computed from heterogeneous-graph node logits become a reliable OOD detector when they are propagated along meta-paths whose endpoints are the target node type. The proposed OODHG pipeline first learns node embeddings with a heterogeneous graph neural network, computes per-node energy $E_i = -\log \sum_{c=1}^{K} e^{h_i[c]}$, then refines these energies by iteratively mixing with the energies of meta-path neighbors, averages over meta-paths, and thresholds negative energy to separate OOD from ID nodes. A squared-hinge energy loss $\mathcal{L}_E = \frac{1}{N}\sum_i [\max(0, E_i - m_\mathrm{in})]^2$ is added to the cross-entropy classification loss so that ID nodes are pulled below a margin, widening the gap to OOD nodes. The reported experiments on DBLP, ACM, and IMDB show consistent gains over homogeneous-graph OOD detectors and classical softmax/energy baselines, with ablations and density plots indicating that both the propagation step and the energy loss reduce the overlap between ID and OOD energy distributions.

Load-bearing premise

The load-bearing assumption is that out-of-distribution status is locally correlated along the chosen meta-paths: averaging a node's energy with its meta-path neighbors must make OOD nodes stand out rather than blend in.

Editorial extensions

If this is right

On DBLP, ACM, and IMDB, the method with the strongest tested backbone raises OOD detection AUROC by about 2.6, 6.4, and 2.5 percentage points over the best baseline and cuts FPR@95 by 10.2, 32.8, and 3.6 percentage points respectively, according to the paper's tables.
Removing either energy propagation or the energy loss degrades detection performance in the paper's ablations, and the largest gains appear when both components act together.
Detection quality tracks representation quality: the paper compares three heterogeneous graph neural network backbones and reports that the strongest backbone yields the best OOD detection and classification results.
The reported comparisons favor energy-based scoring over softmax confidence in heterogeneous graphs, with the energy baseline already outperforming MSP and ODIN before propagation is added.
The extra cost is modest: with the meta-path adjacency precomputed, propagation contributes $O(k|\Phi|N_\mathrm{target}^2)$ per epoch, so the method does not trade away practical training time for its detection gains.

Reading between the lines

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

Editorial extension: if OOD status is not locally correlated along the chosen meta-paths — say, OOD nodes are isolated singletons surrounded by in-distribution nodes — the propagation operator would average the signal away; testing the method on graphs with deliberately scattered OOD nodes would expose this dependence.
Editorial extension: the paper tunes the propagation weight, step count, loss weight, margin, and decision threshold per dataset; a learnable or automatically adjusted version of these parameters is an obvious next step that the current results do not cover.
Editorial extension: because the energy loss regularizes only the target node type, the same propagated-energy score could serve as a plug-in OOD signal for other target-type prediction tasks such as link prediction or anomaly detection on heterogeneous graphs, though the paper does not test this.
Editorial extension: the decision threshold is chosen by grid search and best performance is reported; a threshold-free evaluation would clarify how much of the reported gain is intrinsic to the energy score rather than to threshold selection.

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

Here's the short version: this is a clean, incremental extension of energy-based OOD detection to heterogeneous graphs, and the core mechanism—meta-path-constrained energy propagation plus an energy hinge loss—is sensible and well motivated. The ablations show both components help. The main experimental weakness is the threshold protocol: Section 5.1 says they scanned thresholds and reported the best result for each case. That makes the K+1 classification numbers in Table 3 in-sample and inflated. The stress-test note overreaches a bit in saying this also undermines AUROC/AUPR/FPR@95; those are ranking metrics and don't depend on the reported threshold, so Table 2 is largely clean. But Table 3 is a real problem, and the margin m_in and hyperparameters alpha, gamma, K are not disclosed for the main runs, with no code released. These are fixable, not fatal.

What's new: applying energy propagation along meta-paths whose endpoints are the target node type, with row-normalized adjacency products and averaging over paths. That is a straightforward adaptation of prior graph-energy propagation work [36, 39], but it's the right simple recipe for heterogeneous graphs. The paper is clearly written, the equations are correct, and the design choices are explained.

What's soft, in proportion: the threshold fitting is the load-bearing issue for the classification claim. The baselines got the same treatment, so the comparison is not unfair in protocol, but the absolute numbers are optimistic and the claimed margins over Energy could shrink under a proper validation-set threshold. The propagation assumption—that averaging with meta-path neighbors improves the OOD signal—is plausible and the ablations support it, but there's no formal or isolated test of when it fails. The parameter sensitivity analysis on DBLP is nice, but it doesn't give the exact settings used for the main tables.

Who it's for: anyone working on OOD detection in heterogeneous graphs will find a useful baseline and a clear starting point. It deserves a serious referee. I'd send it to review with a request for a validation-based threshold selection protocol, full hyperparameter disclosure, and code. My verdict would be conditional accept: the idea is worth publishing, but the evaluation needs to be re-run honestly.

Referee Report

3 major / 6 minor

Summary. The paper proposes OODHG, a method for out-of-distribution detection in heterogeneous graphs. It uses an HGNN encoder (SeHGNN) to produce logits, computes per-node energy scores (Eq. 3), propagates these scores along user-selected meta-paths (Eqs. 6-7), and averages the propagated scores across paths (Eq. 8). Training combines a classification loss with a squared hinge energy loss that penalizes ID nodes whose energy exceeds a margin (Eqs. 9-11). Experiments on DBLP, ACM, and IMDB compare OODHG with graph-specific baselines (OpenWGL, OODGAT, GNNSafe) and classical energy/softmax detectors (MSP, ODIN, Energy), reporting AUROC, AUPR, FPR@95, and K+1 Micro/Macro-F1. The paper claims consistent superiority in both OOD detection and ID node classification, with ablations suggesting that both energy propagation and the energy loss contribute to the reported gains.

Significance. If the results survive a stricter evaluation protocol, OODHG is a solid and timely contribution: node-level OOD detection in heterogeneous graphs is indeed underexplored, and the proposed mechanism is simple, interpretable, and naturally extends energy-based detection to heterogeneous structure. The use of meta-path-based propagation is coherent with the SeHGNN backbone, and the ablation study in Figure 3 at least isolates the two proposed components. The main weakness is that the quantitative claims rest on an evaluation protocol in which decision thresholds and possibly hyperparameters are selected using test-set labels. The threshold-free AUROC/AUPR results and the qualitative visualizations are encouraging, but they do not by themselves validate the K+1 classification gains or the FPR@95 comparisons. The paper should be judged after a clean held-out evaluation.

major comments (3)

[Section 5.1] The threshold selection procedure invalidates the K+1 classification comparisons in Table 3 and potentially affects the FPR@95 comparisons in Table 2. The text states that the energy threshold was explored between 1 and 2 with step 0.05, the softmax threshold between 0.5 and 0.9, and that 'the corresponding best performance for each case' was reported. This selects the decision threshold using test-set labels, so the Micro-F1 and Macro-F1 numbers in Table 3 (e.g., DBLP Micro-F1 91.37 vs 88.97 for Energy) are in-sample estimates of the best achievable threshold for each method, not evaluations of a fixed decision rule. The issue is material on IMDB, where the reported gains are small (e.g., Micro-F1 51.94 vs 50.52). Please recompute all threshold-dependent metrics using thresholds selected on a validation split, or report threshold-free metrics (AUROC, AUPR) as the primary comparison. If FPR@95 is computed by the standard procedure of fixing TPR at 95% from the score distribution, state this explicitly; otherwise it inherits the same test-set fitting problem.
[Section 5.1 and Section 5.5] The selection of hyperparameters alpha, gamma, K, and especially the margin m_in is not described with a clear protocol. Section 5.1 reports dataset-specific values of m_in (-3, -2, -3), and Section 5.5 presents a parameter sensitivity analysis only on DBLP. If any of these hyperparameters were chosen by test-set performance, then even the threshold-independent AUROC/AUPR entries in Table 2 are partly in-sample, because a model trained with test-tuned m_in is not a model selected by a valid model-selection procedure. Please specify for each hyperparameter whether it is a fixed default, selected on a validation split, or selected by sensitivity analysis, and provide evidence that the reported rankings are stable under reasonable variations of these hyperparameters.
[Section 5.1, Baseline Methods] For the graph-based baselines OpenWGL, OODGAT, and GNNSafe, the text says heterogeneous graphs are converted into homogeneous views using different meta-paths and that 'the best performance' is reported. If that best is selected on the test set, the baselines also benefit from in-sample meta-path selection, making the comparison asymmetric: OODHG is evaluated as a single configuration while each baseline is allowed to pick its best meta-path view. Please report the protocol explicitly, e.g., validation-based meta-path selection, averaging over all meta-paths, or a fixed meta-path set shared by all methods.

minor comments (6)

[Algorithm 1 and Figure 2] The decision rule is given as '-E_i <= tau' in Algorithm 1 but as '-E_i < tau' in Figure 2 and in Eq. (4); make the inequality consistent.
[Eq. (8)] Equation (8) mixes vector and scalar notation: E^(k,P_n)_i is used for the propagated energy of node i under path P_n, while E_i is defined as the final scalar energy. Please define all symbols explicitly before Eq. (6).
[Section 5.5 and Figure 6(d)] The text refers to 'Marginal Hyperparameters m_in' and contains the typo 'm_in m' in the margin hyperparameter paragraph; Figure 6(d) also uses inconsistent formatting for m_in. Please correct these typos.
[References] Reference [22] appears to be a duplicate of reference [13]: both are titled 'Supervised algorithmic fairness in distribution shifts: A survey' with the same arXiv identifier. Please merge or correct.
[Section 5.1, IMDB preprocessing] The IMDB multi-label conversion, retaining only the first two labels and binarizing them, is a large simplification that is acknowledged in the text; please state explicitly that the same conversion is applied to all compared methods and discuss whether this preprocessing favors any particular detector.
[Section 5.4] The visualization analysis in Figures 4 and 5 is qualitative only; since the paper already computes quantitative metrics, a small table reporting overlap or separation before and after energy propagation would make the claim more precise.

Circularity Check

1 steps flagged · score 6.0 of 10

Test-set threshold selection makes the K+1 F1 comparisons in-sample; core energy-propagation AUROC/AUPR claim remains independent.

fitted input called prediction [Section 5.1, Implementation Details (threshold selection paragraph); see also Table 3 and Section 5.2]
"To compute the F1 score, a threshold τ needs to be set. We employed a straightforward approach for threshold selection: for the energy score threshold, we explored values between 1 and 2 with a step size of 0.05, while for the softmax score threshold, values from 0.5 to 0.9 were tested in increments of 0.05. We reported the corresponding best performance for each case."

The K+1 classification metrics (Micro-F1, Macro-F1) are computed after the decision threshold τ is chosen on the test set by grid search, and the paper reports 'the corresponding best performance for each case.' Thus the headline Table 3 numbers are in-sample maxima over thresholds by construction, not predictions under a fixed protocol. The claim that OODHG 'consistently outperforms' baselines in ID classification is therefore partly forced by reporting each method's best-case threshold rather than by the energy-propagation mechanism. The AUROC/AUPR columns are threshold-independent and still provide independent support; the circularity is confined to the threshold-dependent classification/F1 claims.

full rationale

The central mechanism — meta-path energy propagation (Eqs. 6–8) and the energy hinge loss (Eq. 11) — is not circular: it is an independently defined transformation of SeHGNN logits, and the AUROC/AUPR columns in Table 2 are threshold-independent, so the main OOD-detection ranking does not reduce to the fitted parameters. The ablations in Figure 3 also show AUROC/AUPR gains from EP and L_E under a consistent protocol. However, the K+1 classification results in Table 3 are computed after choosing each method's decision threshold on the test set: Section 5.1 states that thresholds were explored on the reported ranges and the best performance for each case was reported. The Micro-F1 and Macro-F1 numbers are therefore in-sample maxima over thresholds by construction, not fixed-protocol predictions; the claimed classification gains may partly reflect threshold optimism rather than the energy-propagation mechanism. The paper's own remark that 'the straightforward method for selecting τ may prevent the selection of an optimal τ value' (Section 5.2) does not repair this issue. No load-bearing self-citation chain or uniqueness argument is used; the cited prior works are external baselines or background. Because part of the headline comparison reduces to a test-set-fitted threshold while the core energy-propagation result still has independent AUROC/AUPR support, the circularity score is 6 rather than higher.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The method relies on several dataset-specific choices: an energy threshold, a margin, a loss weight, propagation step count, and the meta-path set. At least the threshold is fitted on the test set; the other values are unreported or tuned per dataset. No new physical or mathematical entities are introduced.

free parameters (6)

Energy threshold tau = DBLP: 1.45, ACM: 1.35, IMDB: 1.95
Selected by searching a range [1,2] with step 0.05 and reporting best performance per dataset (Section 5.1). This fits the decision threshold to the test set and directly affects K+1 classification results.
Margin hyperparameter m_in = DBLP: -3, ACM: -2, IMDB: -3
Dataset-specific margin in the energy hinge loss (Eq. 11). Reported in Section 5.1; not clear whether tuned on validation or test.
Loss weight alpha = not reported for main experiments
Weight balancing classification and energy losses (Eq. 9). Parameter analysis on DBLP shows sensitivity, but the values used in Tables 2 and 3 are not given.
Propagation weight gamma = not reported for main experiments
Balance between self and neighbor energy in Eq. 6. Sensitivity analyzed on DBLP (Fig. 6a/6b), but main-run values are absent.
Propagation steps K = not reported for main experiments
Number of energy propagation iterations in Eq. 6. Sensitivity analyzed on DBLP, but main-run values are absent.
Meta-path sets = DBLP: {APA}; ACM: 11 meta-paths; IMDB: 14 meta-paths
Candidate meta-paths are filtered by hop count and endpoint target type (Section 4.3), a design choice that affects propagation. Not a fitted scalar, but a free selection.

assumptions (4)

standard math Meta-path adjacency matrix is computed as the product of row-normalized type-wise adjacency matrices (Eq. 7).
Matrix multiplication for meta-path reachability is standard linear algebra.
domain assumption Energy scores of structurally related nodes are informative about a node's OOD status.
The entire energy propagation mechanism (Eq. 6) assumes OOD-ness is correlated across nodes connected via meta-paths. Motivated by prior work [39,36] but not proven.
ad hoc to paper Meta-paths with both endpoints of the target type are the correct propagation channels.
Introduced in Section 4.3 to restrict propagation to target-type nodes; no theoretical justification beyond analogy to message passing.
ad hoc to paper The threshold can be selected by searching a fixed range on the test set.
Section 5.1 reports best performance over a threshold grid; this assumes test-set tuning is an acceptable evaluation protocol.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Out-of-Distribution Detection in Heterogeneous Graphs via Energy Propagation." pith.science (2026). https://pith.science/paper/OPZA73IO

@misc{pith2026250503774,
  author       = {Pith},
  title        = {Pith review of: Out-of-Distribution Detection in Heterogeneous Graphs via Energy Propagation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OPZA73IO}},
  note         = {Machine review of arXiv:2505.03774}
}

read the original abstract

Graph neural networks (GNNs) are proven effective in extracting complex node and structural information from graph data. While current GNNs perform well in node classification tasks within in-distribution (ID) settings, real-world scenarios often present distribution shifts, leading to the presence of out-of-distribution (OOD) nodes. OOD detection in graphs is a crucial and challenging task. Most existing research focuses on homogeneous graphs, but real-world graphs are often heterogeneous, consisting of diverse node and edge types. This heterogeneity adds complexity and enriches the informational content. To the best of our knowledge, OOD detection in heterogeneous graphs remains an underexplored area. In this context, we propose a novel methodology for OOD detection in heterogeneous graphs (OODHG) that aims to achieve two main objectives: 1) detecting OOD nodes and 2) classifying all ID nodes based on the first task's results. Specifically, we learn representations for each node in the heterogeneous graph, calculate energy values to determine whether nodes are OOD, and then classify ID nodes. To leverage the structural information of heterogeneous graphs, we introduce a meta-path-based energy propagation mechanism and an energy constraint to enhance the distinction between ID and OOD nodes. Extensive experimental findings substantiate the simplicity and effectiveness of OODHG, demonstrating its superiority over baseline models in OOD detection tasks and its accuracy in ID node classification.

Figures

Figures reproduced from arXiv: 2505.03774 by the authors.

**Figure 1.** An illustration of OOD detection in heterogeneous graphs. The target nodes are authors, and during the training stage, we only utilize a subset of nodes from the ID classes (ID Class1 and ID Class2, as depicted in the figure). The task involves two main objectives: 1) detecting OOD nodes, and 2) classifying ID nodes. generalization [14] and OOD detection [38], these efforts have predominantly concentrated on image d… view at source ↗

**Figure 2.** The overall framework of OODHG. Given a heterogeneous graph , HGNN outputs the logits 𝐻 of the nodes and computes the energy scores for target type nodes. Energy propagation is performed under different meta-paths, and the average is taken as the final energy score. During the training phase, the final energy scores of target nodes in the training set are calculated for energy loss, while the classification probabi… view at source ↗

**Figure 3.** Ablation study on three datasets. compared to OODHG. These experimental results not only validate the effectiveness of our model but also underscore its robustness and superiority in handling complex graphstructured data. Additionally, it is worth noting that among all the baseline methods, the Energy-based approach performs notably well in the OOD detection task, suggesting that energy-based models are better sui… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: The visualized results of the energy scores on three datasets. propagation. However, after energy propagation, this overlap is greatly reduced, and the peak density of the ID and OOD distributions increases noticeably, indicating a clearer distinction between the two. …

**Figure 5.** Figure 5: Visualization of energy distribution of one class of nodes on three datasets. number of steps being essential for achieving the best performance. Loss Function Weight Coefficient. Figures 6c presents the results evaluating the impact of 𝛼 on model performance using AU…

**Figure 6.** Figure 6: Hyperparameter analysis on DBLP. (a)(b)Analysis of propagation weight coefficient 𝛾 and propagation steps K. (c)Analysis of the loss function weight coefficient 𝛼. (d)Analysis of Marginal Hyperparameters 𝑚𝑖𝑛. OODHG OpenWGLOODGAT GNNSafe MSP ODIN Energy 0.000 0.025 0.05…

**Figure 7.** Figure 7: AUROC and time consumption of OODHG and baseline methods on the DBLP dataset. nodes. Our extensive experimental evaluations demonstrate that OODHG consistently outperforms state-of-the-art baseline methods, underscoring the critical role of meta-pathguided propagatio…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 32 canonical work pages

[1]

Decou- pledgraphenergy-basedmodelfornodeout-of-distributiondetection on heterophilic graphs

Chen, Y., Luo, Y., Song, Y., Dai, P., Tang, J., Cao, X., 2025. Decou- pledgraphenergy-basedmodelfornodeout-of-distributiondetection on heterophilic graphs. arXiv preprint arXiv:2502.17912

arXiv 2025
[2]

Evidence-based out-of-distribution detection on multi-label graphs

Ding, R., Zhao, X., Zhao, C., Shao, M., Chen, Z., Chen, H., 2025. Evidence-based out-of-distribution detection on multi-label graphs . : Preprint submitted to Elsevier Page 12 of 14

work page 2025
[3]

Magnn: Metapath aggregatedgraphneuralnetworkforheterogeneousgraphembedding, in: Proceedings of the web conference 2020, pp

Fu, X., Zhang, J., Meng, Z., King, I., 2020. Magnn: Metapath aggregatedgraphneuralnetworkforheterogeneousgraphembedding, in: Proceedings of the web conference 2020, pp. 2331–2341. doi:10. 1145/3366423.3380297

arXiv 2020
[4]

Inductive representation learning on large graphs

Hamilton, W., Ying, Z., Leskovec, J., 2017. Inductive representation learning on large graphs. Advances in neural information process- ing systems 30. URL:https://proceedings.neurips.cc/paper_files/ paper/2017/file/5dd9db5e033da9c6fb5ba83c7a7ebea9-Paper.pdf

work page 2017
[5]

Aspect-level deepcollaborativefilteringviaheterogeneousinformationnetworks., in: IJCAI, pp

Han, X.,Shi, C., Wang,S., Philip, S.Y.,Song, L., 2018. Aspect-level deepcollaborativefilteringviaheterogeneousinformationnetworks., in: IJCAI, pp. 3393–3399. doi:10.5555/3304222

doi:10.5555/3304222 2018
[6]

He, Z., Zhao, C., Shao, M., Lin, Y., Li, D., Tian, Q., 2025. Gdda: Semantic ood detection on graphs under covariate shift via score- based diffusion models, in: ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE. pp. 1–5

work page 2025
[7]

A baseline for detecting mis- classified and out-of-distribution examples in neural networks, in: International Conference on Learning Representations

Hendrycks, D., Gimpel, K., 2017. A baseline for detecting mis- classified and out-of-distribution examples in neural networks, in: International Conference on Learning Representations. URL:https: //openreview.net/forum?id=Hkg4TI9xl

work page 2017
[8]

Hofmann, C., Schmid, S., Lehner, B., Klotz, D., Hochreiter, S.,

work page

Show all 51 references

[9]

Semi-supervised classification with graph convolutional networks, in: International Conference on Learning Representations

Kipf, T.N., Welling, M., 2017. Semi-supervised classification with graph convolutional networks, in: International Conference on Learning Representations. URL: https://openreview.net/forum?id= SJU4ayYgl

2017
[10]

Doc: Deep open classification of text documents

Lei, S., Hu, X., Bing, L., 2017. Doc: Deep open classification of text documents. Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing doi:10.18653/v1/d17-1314

2017 doi
[11]

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

Li, Z., Wu, Q., Nie, F., Yan, J., 2022. Graphde: A generative framework for debiased learning and out-of- distribution detection on graphs. Advances in Neural Information Processing Systems 35, 30277–30290. URL: https://proceedings.neurips.cc/paper_files/paper/2022/file/ c3426...

2022
[12]

Enhancing the reliability of out- of-distribution image detection in neural networks, in: International Conference on Learning Representations

Liang, S., Li, Y., Srikant, R., 2018. Enhancing the reliability of out- of-distribution image detection in neural networks, in: International Conference on Learning Representations. URL:https://openreview. net/forum?id=H1VGkIxRZ

2018
[13]

arXiv preprint arXiv:2402.01327 doi:10.48550/arXiv.2402.01327

Lin,Y.,Li,D.,Zhao,C.,Wu,X.,Tian,Q.,Shao,M.,2024.Supervised algorithmic fairness in distribution shifts: A survey. arXiv preprint arXiv:2402.01327 doi:10.48550/arXiv.2402.01327

2024 doi arXiv
[14]

Towards out-of-distribution generalization: A survey

Liu, J., Shen, Z., He, Y., Zhang, X., Xu, R., Yu, H., Cui, P., 2021. Towards out-of-distribution generalization: A survey. arXiv preprint arXiv:2108.13624 doi:10.48550/arXiv.2108.13624

2021 doi arXiv
[15]

Energy- based out-of-distribution detection

Liu, W., Wang, X., Owens, J., Li, Y., 2020. Energy- based out-of-distribution detection. Advances in neural information processing systems 33, 21464–21475. URL: https://proceedings.neurips.cc/paper_files/paper/2020/file/ f5496252609c43eb8a3d147ab9b9c006-Paper.pdf

2020
[16]

Good-d: On unsupervised graph out-of-distribution detection, in: Proceedings of the Sixteenth ACM International Conference on Web Search and Data Mining, pp

Liu, Y., Ding, K., Liu, H., Pan, S., 2023. Good-d: On unsupervised graph out-of-distribution detection, in: Proceedings of the Sixteenth ACM International Conference on Web Search and Data Mining, pp. 339–347. doi:10.1145/3539597.357044

2023
[17]

Hetero- geneous graph neural networks for malicious account detection, in: Proceedingsofthe27thACMinternationalconferenceoninformation and knowledge management, pp

Liu, Z., Chen, C., Yang, X., Zhou, J., Li, X., Song, L., 2018. Hetero- geneous graph neural networks for malicious account detection, in: Proceedingsofthe27thACMinternationalconferenceoninformation and knowledge management, pp. 2077–2085. doi:10.1145/3269206. 3272010

2018 doi
[18]

Lv,Q.,Ding,M.,Liu,Q.,Chen,Y.,Feng,W.,He,S.,Zhou,C.,Jiang, J., Dong, Y., Tang, J., 2021. Are we really making much progress? revisiting, benchmarking and refining heterogeneous graph neural networks, in: Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & dat...

2021
[19]

Ma,X.,Zhao,C.,Shao,M.,Lin,Y.,2025.Hypergraph-baseddynamic graph node classification, in: ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE. pp. 1–5

2025
[20]

A uni- fied energy-based framework for unsupervised learning, in: Artificial Intelligence and Statistics, PMLR

Ranzato, M., Boureau, Y.L., Chopra, S., LeCun, Y., 2007. A uni- fied energy-based framework for unsupervised learning, in: Artificial Intelligence and Statistics, PMLR. pp. 371–379. URL: https:// proceedings.mlr.press/v2/ranzato07a.html

2007
[21]

Toward open set recognition

Scheirer,W.J.,deRezendeRocha,A.,Sapkota,A.,Boult,T.E.,2013. Toward open set recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 35, 1757–1772. doi:10.1109/TPAMI.2012. 256

2013 doi
[22]

arXiv preprint arXiv:2402.01327

Shao,M.,Li,D.,Zhao,C.,Wu,X.,Lin,Y.,Tian,Q.,2024.Supervised algorithmic fairness in distribution shifts: A survey. arXiv preprint arXiv:2402.01327

2024 arXiv
[23]

Learning on graphs with out-of- distribution nodes, in: Proceedings of the 28th ACM SIGKDD Con- ference on Knowledge Discovery and Data Mining, pp

Song, Y., Wang, D., 2022. Learning on graphs with out-of- distribution nodes, in: Proceedings of the 28th ACM SIGKDD Con- ference on Knowledge Discovery and Data Mining, pp. 1635–1645. doi:10.1145/3534678.3539457

2022
[24]

Graph posterior network: Bayesian predictive uncertainty for node classification

Stadler, M., Charpentier, B., Geisler, S., Zügner, D., Günnemann, S., 2021. Graph posterior network: Bayesian predictive uncertainty for node classification. Advances in Neural Information Processing Systems 34, 18033–18048. URL: https://proceedings.neurips.cc/paper_files/pape...

2021
[25]

Graph structure learning with variational information bottleneck, in: Proceedings of the AAAI Conference on Artificial Intelligence, pp

Sun, Q., Li, J., Peng, H., Wu, J., Fu, X., Ji, C., Philip, S.Y., 2022. Graph structure learning with variational information bottleneck, in: Proceedings of the AAAI Conference on Artificial Intelligence, pp. 4165–4174. doi:10.1609/aaai.v36i4.20335

2022 doi
[26]

Pathsim:Metapath- basedtop-ksimilaritysearchinheterogeneousinformationnetworks

Sun,Y.,Han,J.,Yan,X.,Yu,P.S.,Wu,T.,2011. Pathsim:Metapath- basedtop-ksimilaritysearchinheterogeneousinformationnetworks. Proceedings of the VLDB Endowment 4, 992–1003. doi:10.14778/ 3402707.3402736

2011
[27]

Mldgg: Meta-learning for domain generalization on graphs

Tian,Q.,Zhao,C.,Shao,M.,Wang,W.,Lin,Y.,Li,D.,2024. Mldgg: Meta-learning for domain generalization on graphs. arXiv preprint arXiv:2411.12913

2024 arXiv
[28]

Graphattentionnetworks,in:InternationalConference on Learning Representations

Veličković, P., Cucurull, G., Casanova, A., Romero, A., Liò, P., Ben- gio,Y.,2018. Graphattentionnetworks,in:InternationalConference on Learning Representations. URL: https://openreview.net/forum? id=rJXMpikCZ

2018
[29]

1225–1234

Wang,D.,Cui,P.,Zhu,W.,2016.Structuraldeepnetworkembedding, in: Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 1225–1234. doi:10. 1145/2939672.2939753

2016
[30]

Feature-space semantic invari- ance:Enhancedooddetectionforopen-setdomaingeneralization,in: 2024 IEEE International Conference on Big Data (BigData), IEEE

Wang, H., Zhao, C., Chen, F., 2024a. Feature-space semantic invari- ance:Enhancedooddetectionforopen-setdomaingeneralization,in: 2024 IEEE International Conference on Big Data (BigData), IEEE. pp. 8244–8246

2024
[31]

Madod: Generalizing ood detectiontounseendomainsviag-invariancemeta-learning,in:2024 IEEE International Conference on Big Data (BigData), IEEE

Wang, H., Zhao, C., Chen, F., 2024b. Madod: Generalizing ood detectiontounseendomainsviag-invariancemeta-learning,in:2024 IEEE International Conference on Big Data (BigData), IEEE. pp. 1134–1143

2024
[32]

Layer adaptive deep neural networks for out-of-distribution detection, in: Pacific-Asia ConferenceonKnowledgeDiscoveryandDataMining,Springer.pp

Wang, H., Zhao, C., Zhao, X., Chen, F., 2022a. Layer adaptive deep neural networks for out-of-distribution detection, in: Pacific-Asia ConferenceonKnowledgeDiscoveryandDataMining,Springer.pp. 526–538
[33]

A survey on heterogeneous graph embedding: methods, techniques, applicationsandsources

Wang, X., Bo, D., Shi, C., Fan, S., Ye, Y., Philip, S.Y., 2022b. A survey on heterogeneous graph embedding: methods, techniques, applicationsandsources. IEEETransactionsonBigData9,415–436. doi:10.1109/TBDATA.2022.3177455

2022
[34]

Heterogeneous graph attention network, in: The world wide web conference, pp

Wang, X., Ji, H., Shi, C., Wang, B., Ye, Y., Cui, P., Yu, P.S., 2019. Heterogeneous graph attention network, in: The world wide web conference, pp. 2022–2032. doi:10.1145/3308558.3313562

2019
[35]

Wu,M.,Pan,S.,Zhu,X.,2020.Openwgl:Open-worldgraphlearning, in:2020IEEEinternationalconferenceondatamining(icdm),IEEE. pp. 681–690. doi:10.1109/ICDM50108.2020.00077

2020
[36]

Energy-based out-of- distribution detection for graph neural networks, in: The Eleventh International Conference on Learning Representations

Wu, Q., Chen, Y., Yang, C., Yan, J., 2023. Energy-based out-of- distribution detection for graph neural networks, in: The Eleventh International Conference on Learning Representations. URL:https: //openreview.net/forum?id=zoz7Ze4STUL. : Preprint submitted to Elsevier Page 13 of 14

2023
[37]

How powerful are graph neural networks?, in: International Conference on Learning Representations

Xu, K., Hu, W., Leskovec, J., Jegelka, S., 2019. How powerful are graph neural networks?, in: International Conference on Learning Representations. URL:https://openreview.net/forum?id=ryGs6iA5Km

2019
[38]

Generalized out-of- distribution detection: A survey

Yang, J., Zhou, K., Li, Y., Liu, Z., 2021. Generalized out-of- distribution detection: A survey. arXiv preprint arXiv:2110.11334 doi:10.1007/s11263-024-02117-4

2021 arXiv
[39]

Graph open-set recognition via entropymessage passing,in: 2023IEEE InternationalConference on DataMining(ICDM),IEEE.pp.1469–1474

Yang, L., Lu, B., Gan, X., 2023a. Graph open-set recognition via entropymessage passing,in: 2023IEEE InternationalConference on DataMining(ICDM),IEEE.pp.1469–1474. doi: 10.1109/ICDM58522. 2023.00193

2023
[40]

Simple and efficient heterogeneous graph neural network, in: Proceedings of the AAAI Conference on Artificial Intelligence, pp

Yang, X., Yan, M., Pan, S., Ye, X., Fan, D., 2023b. Simple and efficient heterogeneous graph neural network, in: Proceedings of the AAAI Conference on Artificial Intelligence, pp. 10816–10824. doi:10.1609/aaai.v37i9.26283

doi
[41]

Graph trans- formernetworks

Yun, S., Jeong, M., Kim, R., Kang, J., Kim, H.J., 2019. Graph trans- formernetworks. Advancesinneuralinformationprocessingsystems

2019
[42]

Heterogeneous graph neural network, in: Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining, pp

Zhang, C., Song, D., Huang, C., Swami, A., Chawla, N.V., 2019a. Heterogeneous graph neural network, in: Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining, pp. 793–803. doi:10.1145/3292500.3330961
[43]

URL: https://proceedings.neurips.cc/paper_files/paper/2019/ file/9d63484abb477c97640154d40595a3bb-Paper.pdf

2019
[44]

Link prediction based on graph neu- ral networks

Zhang, M., Chen, Y., 2018. Link prediction based on graph neu- ral networks. Advances in neural information processing systems

2018
[45]

Star-gcn: stacked and reconstructed graph convolutional networks for recommender systems,in:Proceedingsofthe28thInternationalJointConferenceon Artificial Intelligence, pp

Zhang, J., Shi, X., Zhao, S., King, I., 2019b. Star-gcn: stacked and reconstructed graph convolutional networks for recommender systems,in:Proceedingsofthe28thInternationalJointConferenceon Artificial Intelligence, pp. 4264–4270. doi:10.24963/ijcai.2019/592

doi
[46]

Rank-based multi-task learning for fair regression, in: 2019 IEEE International Conference on Data Mining (ICDM), IEEE

Zhao, C., Chen, F., 2019. Rank-based multi-task learning for fair regression, in: 2019 IEEE International Conference on Data Mining (ICDM), IEEE. pp. 916–925

2019
[47]

URL: https://proceedings.neurips.cc/paper_files/paper/2018/ file/53f0d7c537d99b3824f0f99d62ea2428-Paper.pdf

2018
[48]

Fairness-aware multi-task and meta learning

Zhao, C., 2021. Fairness-aware multi-task and meta learning. Ph.D. thesis

2021
[50]

Open set action recognitionviamulti-labelevidentiallearning,in:Proceedingsofthe IEEE/CVF conference on computer vision and pattern recognition, pp

Zhao, C., Du, D., Hoogs, A., Funk, C., 2023. Open set action recognitionviamulti-labelevidentiallearning,in:Proceedingsofthe IEEE/CVF conference on computer vision and pattern recognition, pp. 22982–22991

2023
[51]

Uncertainty aware semi-supervised learning on graph data

Zhao, X., Chen, F., Hu, S., Cho, J.H., 2020. Uncertainty aware semi-supervised learning on graph data. Advances in Neural Information Processing Systems 33, 12827–12836. URL: https://proceedings.neurips.cc/paper_files/paper/2020/file/ 968c9b4f09cbb7d7925f38aea3484111-Paper.pdf...

2020
[2024]

arXiv preprint arXiv:2405.08766

Energy-based hopfield boosting for out-of-distribution detec- tion. arXiv preprint arXiv:2405.08766

arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

Decou- pledgraphenergy-basedmodelfornodeout-of-distributiondetection on heterophilic graphs

Chen, Y., Luo, Y., Song, Y., Dai, P., Tang, J., Cao, X., 2025. Decou- pledgraphenergy-basedmodelfornodeout-of-distributiondetection on heterophilic graphs. arXiv preprint arXiv:2502.17912

arXiv 2025

[2] [2]

Evidence-based out-of-distribution detection on multi-label graphs

Ding, R., Zhao, X., Zhao, C., Shao, M., Chen, Z., Chen, H., 2025. Evidence-based out-of-distribution detection on multi-label graphs . : Preprint submitted to Elsevier Page 12 of 14

work page 2025

[3] [3]

Magnn: Metapath aggregatedgraphneuralnetworkforheterogeneousgraphembedding, in: Proceedings of the web conference 2020, pp

Fu, X., Zhang, J., Meng, Z., King, I., 2020. Magnn: Metapath aggregatedgraphneuralnetworkforheterogeneousgraphembedding, in: Proceedings of the web conference 2020, pp. 2331–2341. doi:10. 1145/3366423.3380297

arXiv 2020

[4] [4]

Inductive representation learning on large graphs

Hamilton, W., Ying, Z., Leskovec, J., 2017. Inductive representation learning on large graphs. Advances in neural information process- ing systems 30. URL:https://proceedings.neurips.cc/paper_files/ paper/2017/file/5dd9db5e033da9c6fb5ba83c7a7ebea9-Paper.pdf

work page 2017

[5] [5]

Aspect-level deepcollaborativefilteringviaheterogeneousinformationnetworks., in: IJCAI, pp

Han, X.,Shi, C., Wang,S., Philip, S.Y.,Song, L., 2018. Aspect-level deepcollaborativefilteringviaheterogeneousinformationnetworks., in: IJCAI, pp. 3393–3399. doi:10.5555/3304222

doi:10.5555/3304222 2018

[6] [6]

He, Z., Zhao, C., Shao, M., Lin, Y., Li, D., Tian, Q., 2025. Gdda: Semantic ood detection on graphs under covariate shift via score- based diffusion models, in: ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE. pp. 1–5

work page 2025

[7] [7]

A baseline for detecting mis- classified and out-of-distribution examples in neural networks, in: International Conference on Learning Representations

Hendrycks, D., Gimpel, K., 2017. A baseline for detecting mis- classified and out-of-distribution examples in neural networks, in: International Conference on Learning Representations. URL:https: //openreview.net/forum?id=Hkg4TI9xl

work page 2017

[8] [8]

Hofmann, C., Schmid, S., Lehner, B., Klotz, D., Hochreiter, S.,

work page