Cooperation of Experts: Fusing Heterogeneous Information with Large Margin

Jinghui Yuan; Shunyang Huang; Shuo Wang; Zhao Kang; Zhixiang Shen

REVIEW 4 major objections 5 minor 1 cited by

Cooperation of Experts: Fusing Heterogeneous Information with Large Margin

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read CoE fuses heterogeneous networks by pairing per-layer experts with experts on fused layers, combining all opinions through a confidence tensor trained with a large-margin objective, and reports the best accuracy on all nine benchmarks.

desk verdict Solid empirical fusion framework with a real reproducibility gap (G_ij never defined) and an unsound convexity proof; worth review, but needs major revision. read the letter →

arxiv 2505.20853 v4 pith:IDAGKYHB submitted 2025-05-27 cs.LG cs.AI

Shuo Wang , Shunyang Huang , Jinghui Yuan , Zhixiang Shen , Zhao Kang This is my paper · ORCID

classification cs.LGcs.AI

keywords heterogeneousmultiplexnetworksexpertcooperationgraphstructurelearningmutualinformationmaximizationlarge-marginnodeclassificationmultimodalfusionconfidencetensor

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

Fusing heterogeneous information — different relation types over the same nodes, or different modalities describing the same objects — is hard because each view carries its own patterns. The paper proposes Cooperation of Experts (CoE), which encodes all views as layers of a multiplex network and trains two tiers of experts: low-level experts specialize in single layers, while high-level experts learn from layers fused by mutual-information maximization. Instead of gating a few experts per input, CoE lets every expert vote, with influence set by a learnable confidence tensor; a large-margin loss pushes the two most confident outcomes apart so that experts tend to agree on the right answer. The authors claim this cooperation beats a wide range of structure-learning, multiplex, and graph-mixture-of-experts baselines, reaching the top accuracy on all five network and four multimodal benchmarks they test. If the claim holds, cooperative fusion offers a generic recipe for any learning problem where the same objects are described by multiple views or relation types.

What carries the argument

The load-bearing objects are the confidence tensor and the fused network. The confidence tensor $\Theta \in \mathbb{R}^{c \times c \times k}$ assigns each of $k$ experts a per-class credibility weight, so the final prediction is $\mathrm{softmax}(\Theta g_i)$ over the concatenated expert opinions $g_i$; it converts a set of separate classifiers into one cooperative decision. The tensor is driven by the large-margin mechanism, which replaces the hard $\max_2$ (second-largest entry) with a logsumexp approximation, producing a differentiable loss $M$ that widens the gap between the most and second-most confident outcomes. The other load-bearing mechanism is mutual-information fusion: Eq. 3 estimates the information shared by networks through the InfoNCE-style lower bound $I_{\mathrm{lb}}(Z^i;\,Z^j)$ of Eq. 4, while cross-entropy terms serve, by Theorem 4.1, as upper bounds on $-I(G;Y)$. These pieces together generate the fused networks $G_{ij}$ and $G_{\mathrm{tot}}$ on which the high-level experts are trained.

What would settle it

Run the released code on Yelp with the fusion step replaced by elementwise averaging of the two refined adjacency matrices; if accuracy stays within noise of the reported 93.40%, the mutual-information fusion is not the active ingredient and the paper's account of why CoE works is put in doubt.

Watch

Extended reading notes

Core claim

CoE's central claim is that heterogeneous information is best exploited by a two-level division of labor among experts on a heterogeneous multiplex network. Low-level experts each specialize in one refined network layer, and high-level experts are trained on fused networks obtained by maximizing mutual information between layers, so that shared cross-network structure becomes explicit. All experts — not a gated subset — contribute to the final prediction, with their influence calibrated by a confidence tensor $\Theta \in \mathbb{R}^{c \times c \times k}$ that records, for each expert and each true class, how credible that expert's prediction of each class is. The tensor is trained with a combined objective: a cross-entropy term enforcing correctness and a margin term that maximizes the gap between the largest and second-largest fused confidences, pushing experts toward agreement. The paper further argues that the resulting loss is convex in the tensor, Lipschitz continuous, convergent under gradient descent, and covered by a Rademacher-complexity generalization bound in which the margin appears explicitly; on five network and four multimodal benchmarks, CoE is reported to reach the highest accuracy with among the lowest variance.

Load-bearing premise

The whole high-level expert tier rests on the fused networks $G_{ij}$ and $G_{\mathrm{tot}}$, yet the paper never specifies how those fused networks are actually computed: it states only that they are generated by optimizing the mutual-information loss of Eqs. 2–3, with no formula, algorithm, or reference describing the fusion itself.

Editorial extensions

If this is right

On the five multi-relational benchmarks (ACM, DBLP, Yelp, MAG, Amazon), Table 1 reports CoE as the top-accuracy method, with margins from 0.12 to roughly 1.4 points over the best baseline on each dataset.
On the four multimodal benchmarks (ESP, Flickr, IAPR, NUS), where graphs are built from features by KNN because no topology is given, Table 2 also reports CoE as best, so the pipeline transfers from relational data to feature-only data.
The robustness experiments on ACM show CoE degrading more gracefully than GCN, SUBLIME, InfoMGF, and Mowst when edges are randomly added or removed at rates up to 0.9, which the paper attributes to the structure-learning component repairing disrupted topology.
Ablations that remove high-level experts or the structure-learning stage both lower accuracy, with the loss of high-level experts hurting more; this pins the gain on the fusion step rather than on the per-layer encoders alone.
The generalization bound of Eq. 15 grows like $\sqrt{k}$ in the number of experts and shrinks with the margin and the tensor norm, which is the paper's formal reason for expecting the margin mechanism to keep CoE robust as it scales.

Reading between the lines

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

Because the confidence tensor treats each expert as an opaque scorer, the same coordination mechanism should work when the low-level experts are heterogeneous architectures (convolutions, transformers, even non-differentiable predictors); the paper trains all experts with the same graph-convolution backbone, so this untested combination is a natural next step.
The tensor $\Theta$ implicitly encodes each expert's per-class confusion behavior; a reader could use it as a diagnostic to see which classes each expert is trusted on, something the paper does not exploit.
The multimodal experiments construct graphs from raw features, which suggests CoE applies to any multi-view dataset, including temporal or hierarchical views; how the fusion behaves when views are highly redundant or strongly conflicting is left open.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things worth knowing about this paper. First, the fusion operation that creates G_ij—the core of the high-level experts—is never actually defined anywhere in the manuscript. Eq. (2) and (3) reference mutual information terms with G_ij and Z_ij, but no formula, update rule, or reference explains how those fused networks are generated from the refined single networks. That is not a cosmetic omission: the ablation shows removing high-level experts drops Yelp from 93.40 to 68.27. Second, Theorem 5.1 claims L(Θg_i) is convex in (Θg_i), and the proof relies on log-sum-exp being convex and composition with a linear function preserving convexity. But the inner function is S(Θg_i), softmax, not a linear function. The cross-entropy term is convex in the logits, but the margin term γY_i^T S(Θg_i) is not convex in general, so the theorem as stated is false.

What is genuinely new: the two-level expert architecture (low-level per-network, high-level on fused views) combined with a learnable confidence tensor and a margin-based collaboration loss is a reasonable and fairly specific extension of InfoMGF and existing MoE work. The empirical section is unusually thorough: five network benchmarks, four multimodal datasets, a robustness study under edge perturbations, and sensitivity analysis. The code is publicly available. If the fused networks are implemented in that code, then the empirical claims are likely real, and the state-of-the-art numbers—usually by a meaningful margin—deserve attention.

The soft spots are in proportion. The missing G_ij specification is load-bearing: without it the method cannot be reproduced from the text, and the claimed gains are concentrated in exactly that component. The convexity theorem is wrong but not load-bearing for the convergence result (Theorem 5.3 does not use it). The paper also overclaims priority: the “first to emphasize cooperation” line is contradicted by its own citations, including Shi et al. and Yuan et al., which already put non-competitive expert coordination in play.

Who this is for: people working on multiplex graph structure learning or multi-expert fusion will want to look at the code and check the Yelp/Amazon numbers. As a paper, it is not ready in its current form. I would send it to a serious referee, but the verdict would need to be major revision: define G_ij precisely, fix or remove Theorem 5.1, and tone down the novelty claims.

Referee Report

4 major / 5 minor

Summary. The paper proposes Cooperation of Experts (CoE), a framework for node classification on heterogeneous multiplex networks and multimodal data. CoE encodes multi-typed information into multiplex networks, refines each view with graph structure learning, and then trains two levels of experts: low-level experts on individual refined views and high-level experts on fused networks. The experts' predictions are combined through a learnable confidence tensor that is optimized with a margin-based loss intended to encourage agreement among experts. The paper reports state-of-the-art accuracy on five network and four multimodal benchmarks, provides ablation and robustness studies, and states theorems on convexity, Lipschitz continuity, convergence, and generalization. The code is released at a public repository.

Significance. If the method were fully specified and the theory correct, the empirical results would be a useful contribution to multiplex graph learning, and the large-margin cooperation mechanism is a reasonable alternative to gating-based mixture-of-experts. The paper ships code and includes extensive comparisons, which are strengths. However, the current manuscript does not define the fusion operation that drives most of the reported performance gains, and the central convexity theorem is false as stated. These problems prevent the scientific claims from being assessed as written, although the underlying ideas may be salvageable with substantial revision.

major comments (4)

[§4.2, Eqs. (2)-(3)] The fused networks G_ij and G_tot are never defined. The text says that G_ij is generated by "optimizing the loss function above," but Eq. (2) contains I(G'_i; G_ij) as a term, so G_ij appears both as the output of the procedure and as an input to the objective that is supposed to produce it; this is circular unless an independent parameterization or update rule is supplied. Eq. (3) similarly refers to Z_ij without defining an encoder or adjacency matrix for G_ij. This is a load-bearing omission: the ablation in Table 3 shows that removing high-level experts (w/o HE) degrades accuracy substantially (e.g., Yelp from 93.40 to 68.27), so most of the reported gain is attributed to these undefined fused networks. The code link does not repair the missing specification in the manuscript.
[§5, Theorem 5.1 and Appendix D.1] The claim that L(Θg_i) is convex with respect to Θg_i is false as stated. The proof in Appendix D.1 asserts that L2 = γ Σ_i Y_i^T S(Θg_i) is "evidently convex," but the softmax function is not convex in its argument. The term L3 in Eq. (16) is also not a linear transformation of Θg_i composed with log-sum-exp, because S(Θg_i) enters nonlinearly before the exponential. Furthermore, the full loss in Eq. (10) includes contrastive mutual-information terms that are not functions of Θ alone, so the convexity guarantee does not follow from the arguments given. The convergence analysis in Theorem 5.3 relies on this convexity claim, so that result is also unsupported.
[§4.3, Eqs. (6)-(7)] The proposed margin loss does not implement the margin defined in Eq. (12). The second-largest element max2(S(Θg_i)) equals the maximum over incorrect classes max_{y'≠y} S(Θg_i)_{y'} only when the true class y is the top prediction; when y is not the top class, the maximum over incorrect classes is the global maximum, not the second-largest. Equation (7) computes a log-sum-exp over S(Θg_i) - Y_i ⊙ S(Θg_i), which likewise returns the maximum over incorrect classes rather than the second-largest element of the original vector. The proposed "large margin" objective therefore optimizes a different quantity than the margin defined in Eq. (12), and the theoretical results in Section 5 inherit this discrepancy.
[§5, Theorem 5.2 and Appendix D.2] The Lipschitz constant is reported inconsistently: the proof derives the bound 2k√c(1 + γ + γ e^α / c) in Eq. (24), while the theorem statement reads "2√ck(1 + γ + γ/c e^α)", which is ambiguous and does not match the proof. In addition, the derivative expression in Eq. (17) contains unclear notation ("γ−1(...)") that appears to mean γ^{-1}, and the derivation of the bound on ∂L3/∂Θ_pq is not fully justified. Finally, Theorem 5.3 states a gradient-descent convergence rate for Θ, but the paper never specifies the algorithm that optimizes Θ jointly with the expert networks, so it is unclear whether the theorem applies to the actual training procedure.

minor comments (5)

[Figure 1c] The caption does not define what "+" versus "&" mean beyond a parenthetical; please spell out the fusion operation used for "a&b", "a&c", etc., so the reader can interpret the comparison.
[References] Several citations are incomplete: "Li et al." in Section 2.3 has no year or venue, and Eq. (2) cites "Federici et al." without a bibliographic entry; please complete all references.
[Appendix B] The learning-rate search set "{0.0001, 0.005, 0.001, 0.005, 0.01}" contains a duplicate value and likely omits the intended range; please correct the list.
[Section 5, after Theorem 5.3] The text states that "there must be at least one critical point" among the visited points, but the displayed bound in Eq. (11) only guarantees a point with gradient norm O(1/T); the correct statement is that a point with small gradient exists.
[Eq. (7)] The phrase "by setting the maximum value of the vector to be operated upon to zero" is unclear; please state explicitly how max2 is computed and why the formula in Eq. (7) follows.

Circularity Check

2 steps flagged · score 3.0 of 10

Measured benchmark claims (Tables 1-2) are independent supervised results, but the G_ij fusion is defined only via a self-referential objective (Eq. 2), so high-level-expert gains in Table 3 cannot be decomposed from the text; the margin surrogate equivalence (Eq. 6) is imported from a co-author's prior work.

self definitional [Section 4.2, Eq. (2) (fusion of Gij and Gtot)]
"LE = ... − ΣVi=1 Σj≠i I(G′i; Gij) (2) ... where we fuse G′i and G′j by optimizing the loss function above to generate the fused network Gij. Additionally, an extra high-level expert is trained on Gtot, which is obtained by fusing all refined single networks following the same fusion procedure."

The only definition of the fusion is 'optimizing the loss function above' (Eq. 2), but that objective already contains I(G′i; Gij), i.e., the very network the fusion is said to generate. No parameterization of Gij, no encoder producing Zij, no update rule, and no reference to an existing fusion algorithm is given; the same holds for Gtot ('following the same fusion procedure'). Gij is therefore defined as the output of a self-referential optimization: its value appears inside the objective that is supposed to produce it.
self citation load bearing [Section 4.3, paragraph following Eq. (6)]
"It is worth noting that the definition of margin itself is given by max1(S(Θgi)) − max2(S(Θgi)) ... It is proved that using our defined margin (Eq. 6) leads to the same optimization direction as the original definition while avoiding approximations (Yuan et al., 2024)."

The paper's headline 'novel large margin optimization strategy' rests on Eq. (6), whose asserted equivalence to the true margin is not proven here but delegated: 'It is proved that using our defined margin (Eq. 6) leads to the same optimization direction as the original definition... (Yuan et al., 2024).' The cited first author (J. Yuan) matches co-author Jinghui Yuan of the present paper, making this a self-citation that carries the load of justifying the surrogate. It is only partially load-bearing: Theorem 5.1 (convexity) is proven in-house and the RF/WRF ablation (Table 3) empirically supports the mechanism, so the central empirical claims do not reduce to this citation.

full rationale

This paper's measured claims are independent of its inputs, so this is not a case of benchmark numbers being produced by construction. The confidence tensor Θ and margin surrogate are trained against training labels via cross-entropy and margin losses (Eqs. 8-10), and accuracies in Tables 1-2 are held-out test measurements; no parameter is fitted to reproduce the reported tables. The mutual-information layer is standard and externally supported: Theorem 4.1 (cross-entropy upper-bounds -I(G;Y)) cites Sun et al. 2022 and Li et al. 2024b, and the InfoNCE lower bound (Eq. 4) cites Liang et al. 2024 and Federici et al., none of whom overlap with the present author list. Theorems 5.1-5.3 are proven in Appendix D using in-paper arguments, and the Section 5 generalization bound uses the classical margin definition with standard Rademacher machinery, not the citation-attributed surrogate. Two flagged items prevent a zero score. First, Section 4.2's fusion of G_ij is specified only as 'optimizing the loss function above,' yet Eq. (2) already contains I(G′i; Gij); with no parameterization, encoder for Z_ij, or algorithmic reference, G_ij is defined self-referentially, and the MI term as written is trivially maximized by copying an input. This is a genuine definitional circularity in a supporting construction, and because the Table 3 ablation attributes large accuracy gains to high-level experts consuming this unnamed G_ij (Yelp drops 93.40 → 68.27 without them), the derivation cannot be verified from the manuscript. Second, the equivalence claim for the margin surrogate (Eq. 6) is imported from Yuan et al. 2024, whose first author matches co-author Jinghui Yuan; the in-house convexity proof and the RF/WRF ablation keep this from being load-bearing. Minor self-citations to InfoMGF (Shen, Wang, Kang, 2024b) for GSL post-processing are shared with the external SUBLIME reference and are not load-bearing. Overall: no load-bearing circularity in the measured results; partial definitional self-reference in the fusion step; score 3.

Assumptions & free parameters 5 free parameters · 6 assumptions · 2 invented entities

The central claim (SOTA fusion) rests on several assumptions: the validity of MI lower bounds, the existence of an unspecified fusion procedure, and a false convexity assertion in the theoretical analysis. The learned confidence tensor and fused networks are internal constructs with no external falsifiable predictions.

free parameters (5)

alpha (logsumexp smoothness) = 100
Chosen by hand for all datasets; controls the smooth approximation of max2.
gamma (margin threshold) = 100
Chosen by hand; appears in the ramp loss margin and in the Lipschitz bound.
K (KNN neighbors) = 10 or 15
Tuned per dataset from {5,10,15,20,30}; used in graph construction.
tau_c (contrastive temperature) = 0.2
Fixed constant in the contrastive mutual information estimator.
eta (balance between C and M) = not reported
Hyperparameter in the total loss L = C - eta*M + ...; no value is given in the hyperparameter table.

assumptions (6)

domain assumption Cross-entropy loss L_cls(Z,Y) is an upper bound of -I(G;Y)
Used in Theorem 4.1 to replace mutual information with classification loss, citing Sun et al. 2022.
domain assumption Ilb(Z_i; Z_j) as defined in Eq. (4) is a valid lower bound of I(Z_i; Z_j)
Standard InfoNCE bound from Liang et al. 2024.
ad hoc to paper The fused network G_ij is produced by optimizing the mutual information objective
This is the central fusion step but no explicit construction is provided; the paper assumes such a network exists.
ad hoc to paper The softmax cross-entropy loss L1 = -Y^T log(S(Theta g)) is convex with respect to Theta g
Used to prove Theorem 5.1, but softmax is not convex in logits, so the axiom is false.
standard math The logsumexp approximation with large alpha gives a smooth surrogate for max2
Standard smooth max approximation.
domain assumption The margin direction of Eq. (6) is equivalent to max1-max2 (Yuan et al. 2024)
The authors rely on a prior result without proof.

invented entities (2)

fused network G_ij
purpose: Captures shared information between networks i and j for high-level experts.
The paper states G_ij is generated by optimizing the mutual information loss but provides no construction; its existence is assumed for the method to work.
confidence tensor Theta
purpose: Assigns credibility weights to each expert per class confusion, enabling cooperation.
A learnable parameter; not an external entity but a new architectural component.

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Cite this review

Pith. "Pith review of Cooperation of Experts: Fusing Heterogeneous Information with Large Margin." pith.science (2026). https://pith.science/paper/IDAGKYHB

@misc{pith2026250520853,
  author       = {Pith},
  title        = {Pith review of: Cooperation of Experts: Fusing Heterogeneous Information with Large Margin},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IDAGKYHB}},
  note         = {Machine review of arXiv:2505.20853}
}

read the original abstract

Fusing heterogeneous information remains a persistent challenge in modern data analysis. While significant progress has been made, existing approaches often fail to account for the inherent heterogeneity of object patterns across different semantic spaces. To address this limitation, we propose the Cooperation of Experts (CoE) framework, which encodes multi-typed information into unified heterogeneous multiplex networks. By overcoming modality and connection differences, CoE provides a powerful and flexible model for capturing the intricate structures of real-world complex data. In our framework, dedicated encoders act as domain-specific experts, each specializing in learning distinct relational patterns in specific semantic spaces. To enhance robustness and extract complementary knowledge, these experts collaborate through a novel large margin mechanism supported by a tailored optimization strategy. Rigorous theoretical analyses guarantee the framework's feasibility and stability, while extensive experiments across diverse benchmarks demonstrate its superior performance and broad applicability. Our code is available at https://github.com/strangeAlan/CoE.

Figures

Figures reproduced from arXiv: 2505.20853 by the authors.

**Figure 1.** (a) and (b) present the classification results on different networks from the ACM and Yelp datasets, representing the diverse and intricate patterns within networks. (c) “+” symbol denotes directly adding the networks, while “&” represents the fusion procedure used in CoE. tegrates such complex information across all networks? To address this, we propose Cooperation of Experts (CoE), a novel architecture specificall… view at source ↗

**Figure 2.** The overall framework of the proposed CoE. Specifically, CoE first encodes various information into heterogeneous multiplex networks, followed by network fusion through mutual information maximization. Subsequently, two-level experts are trained on single and fused networks respectively. Expert collaboration is enabled by a confidence tensor, which is optimized via a large margin mechanism. Graph Convolution (SGC) (… view at source ↗

**Figure 3.** Robustness analysis on ACM. The experimental results, presented in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Sensitivity analysis on critical hyper-parameters. 7. Conclusion In this work, we propose and analyze a novel paradigm for fusing diverse information through heterogeneous multiplex networks. Our approach introduces an expert mechanism into network learning and provide…

**Figure 5.** Figure 5: Sensitivity analysis on K. Subsequent to the research on α and γ, an investigation into the sensitivity of the number of neighbors K is conducted. The values of K span a set of {5, 10, 15, 20, 25}. As depicted in [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

16 extracted references · 15 canonical work pages · cited by 1 Pith paper

[1]

It is evident that |gq| ≤1, |δmp| ≤1, and |S(Θg)pgq| ≤1

(17) Where I(j ̸= m) is the indicator function, which is 0 when j = m and 1 otherwise. It is evident that |gq| ≤1, |δmp| ≤1, and |S(Θg)pgq| ≤1. Therefore, the following inequality holds: ∂L1 ∂Θpq ≤ |gqδmp| + |S(Θg)pgq| ≤2 (18) Similarly, we have: ∂L2 ∂Θpq ≤ γ|S(Θg)m| · |gqδmp − S(Θg)pgq| ≤2γ (19) Based on the fact that | Pc j=1 eαS(Θg)j − eαS(Θg)m + 1| ≤c...

work page 2022
[5]

Hdmi: High-order deep multiplex infomax

Jing, B., Park, C., and Tong, H. Hdmi: High-order deep multiplex infomax. In Proceedings of the Web Conference 2021, pp. 2414–2424,

work page 2021
[6]

We also select 4 multimodal datasets where the topological structure is not given

Following (Shen et al., 2024a), here we extract MAG from the original OGBN-MAG (Wang et al., 2020), remaining the nodes from the four largest classes. We also select 4 multimodal datasets where the topological structure is not given. For a fair comparison, we adopt the identical data processing approach as described in (Mao et al.,

work page 2020
[8]

Towards unsupervised deep graph structure learning

Liu, Y ., Zheng, Y ., Zhang, D., Chen, H., Peng, H., and Pan, S. Towards unsupervised deep graph structure learning. In Proceedings of the ACM Web Conference 2022 , pp. 1392–1403,

work page 2022
[10]

Graph structure estimation neural networks

Wang, R., Mou, S., Wang, X., Xiao, W., Ju, Q., Shi, C., and Xie, X. Graph structure estimation neural networks. In Proceedings of the web conference 2021, pp. 342–353,

work page 2021
[13]

Graph- revised convolutional network

Yu, D., Zhang, R., Jiang, Z., Wu, Y ., and Yang, Y . Graph- revised convolutional network. In Machine Learning and Knowledge Discovery in Databases: European Confer- ence, ECML PKDD 2020, Ghent, Belgium, September 14– 18, 2020, Proceedings, Part III, pp. 378–393. Springer,

work page 2020
[14]

A Margin-Maximizing Fine-Grained Ensemble Method

Yuan, J., Chen, H., Luo, R., and Nie, F. A margin- maximizing fine-grained ensemble method. arXiv preprint arXiv:2409.12849,

work page Pith review arXiv
[2015]

Wang, X., Ji, H., Shi, C., Wang, B., Ye, Y ., Cui, P., and Yu, P. S. Heterogeneous graph attention network. In The world wide web conference, pp. 2022–2032,

work page 2022

Show all 16 references

[2016]

Pc-conv: Unifying homophily and heterophily with two-fold filtering

Li, B., Pan, E., and Kang, Z. Pc-conv: Unifying homophily and heterophily with two-fold filtering. In Proceedings of the AAAI conference on artificial intelligence, volume 38, pp. 13437–13445, 2024a. Li, J., Su, Q., Yang, Y ., Jiang, Y ., Wang, C., and Xu, H. Adaptive gating i...

2023
[2019]

Magnn: Metapath aggregated graph neural network for heterogeneous graph embedding

Fu, X., Zhang, J., Meng, Z., and King, I. Magnn: Metapath aggregated graph neural network for heterogeneous graph embedding. In Proceedings of the web conference 2020, pp. 2331–2341,

2020
[2020]

Addressing heterophily in graph anomaly detection: A perspective of graph spectrum

Gao, Y ., Wang, X., He, X., Liu, Z., Feng, H., and Zhang, Y . Addressing heterophily in graph anomaly detection: A perspective of graph spectrum. In Proceedings of the ACM Web Conference 2023, pp. 1528–1538,

2023
[2021]

Learning robust representations via multi-view in- formation bottleneck

Federici, M., Dutta, A., Forr´e, P., Kushman, N., and Akata, Z. Learning robust representations via multi-view in- formation bottleneck. In International Conference on Learning Representations. Franceschi, L., Niepert, M., Pontil, M., and He, X. Learning discrete structures fo...

1972
[2022]

Gagsl: Global-augmented graph structure learn- ing via graph information bottleneck

Li, S., Song, J., Zhang, B., Ruan, G., Xie, J., and Wang, C. Gagsl: Global-augmented graph structure learn- ing via graph information bottleneck. arXiv preprint arXiv:2411.04356, 2024b. Li, Z., Sun, X., Luo, Y ., Zhu, Y ., Chen, D., Luo, Y ., Zhou, X., Liu, Q., Wu, S., Wang, L...

arXiv
[2023]

doi: 10.1109/TIP.2023. 3240863. Xie, X., Li, B., Pan, E., Guo, Z., Kang, Z., and Chen, W. One node one model: Featuring the missing-half for graph clustering. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 21688–21696,

2023 doi
[2024]

Multiplex graph representation learning via bi-level optimization

9 Cooperation of Experts: Fusing Heterogeneous Information with Large Margin Huang, Y ., Mo, Y ., Liu, Y ., Nie, C., Wen, G., and Zhu, X. Multiplex graph representation learning via bi-level optimization. In Proceedings of the Thirty-Third Inter- national Joint Conference on A...
[2025]

Balanced multi-relational graph clustering

Shen, Z., He, H., and Kang, Z. Balanced multi-relational graph clustering. In Proceedings of the 32nd ACM In- ternational Conference on Multimedia, pp. 4120–4128, 2024a. Shen, Z., Wang, S., and Kang, Z. Beyond redundancy: Information-aware unsupervised multiplex graph struc- t...

arXiv

Pith tools

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

[1] [1]

It is evident that |gq| ≤1, |δmp| ≤1, and |S(Θg)pgq| ≤1

(17) Where I(j ̸= m) is the indicator function, which is 0 when j = m and 1 otherwise. It is evident that |gq| ≤1, |δmp| ≤1, and |S(Θg)pgq| ≤1. Therefore, the following inequality holds: ∂L1 ∂Θpq ≤ |gqδmp| + |S(Θg)pgq| ≤2 (18) Similarly, we have: ∂L2 ∂Θpq ≤ γ|S(Θg)m| · |gqδmp − S(Θg)pgq| ≤2γ (19) Based on the fact that | Pc j=1 eαS(Θg)j − eαS(Θg)m + 1| ≤c...

work page 2022

[2] [5]

Hdmi: High-order deep multiplex infomax

Jing, B., Park, C., and Tong, H. Hdmi: High-order deep multiplex infomax. In Proceedings of the Web Conference 2021, pp. 2414–2424,

work page 2021

[3] [6]

We also select 4 multimodal datasets where the topological structure is not given

Following (Shen et al., 2024a), here we extract MAG from the original OGBN-MAG (Wang et al., 2020), remaining the nodes from the four largest classes. We also select 4 multimodal datasets where the topological structure is not given. For a fair comparison, we adopt the identical data processing approach as described in (Mao et al.,

work page 2020

[4] [8]

Towards unsupervised deep graph structure learning

Liu, Y ., Zheng, Y ., Zhang, D., Chen, H., Peng, H., and Pan, S. Towards unsupervised deep graph structure learning. In Proceedings of the ACM Web Conference 2022 , pp. 1392–1403,

work page 2022

[5] [10]

Graph structure estimation neural networks

Wang, R., Mou, S., Wang, X., Xiao, W., Ju, Q., Shi, C., and Xie, X. Graph structure estimation neural networks. In Proceedings of the web conference 2021, pp. 342–353,

work page 2021

[6] [13]

Graph- revised convolutional network

Yu, D., Zhang, R., Jiang, Z., Wu, Y ., and Yang, Y . Graph- revised convolutional network. In Machine Learning and Knowledge Discovery in Databases: European Confer- ence, ECML PKDD 2020, Ghent, Belgium, September 14– 18, 2020, Proceedings, Part III, pp. 378–393. Springer,

work page 2020

[7] [14]

A Margin-Maximizing Fine-Grained Ensemble Method

Yuan, J., Chen, H., Luo, R., and Nie, F. A margin- maximizing fine-grained ensemble method. arXiv preprint arXiv:2409.12849,

work page Pith review arXiv

[8] [2015]

Wang, X., Ji, H., Shi, C., Wang, B., Ye, Y ., Cui, P., and Yu, P. S. Heterogeneous graph attention network. In The world wide web conference, pp. 2022–2032,

work page 2022