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A Scalable Inter-edge Correlation Modeling in CopulaGNN for Link Sign Prediction

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Signed Graph Representation LearningGraph Neural NetworkGaussian CopulaLink Sign PredictionLinear Convergence
Abstract:

Link sign prediction on a signed graph is a task to determine whether the relationship represented by an edge is positive or negative. Since the presence of negative edges violates the graph homophily assumption that adjacent nodes are similar, regular graph methods have not been applicable without auxiliary structures to handle them. We aim to directly model the latent statistical dependency among edges with the Gaussian copula and its corresponding correlation matrix, extending CopulaGNN (Ma et al., 2021). However, a naive modeling of edge-edge relations is computationally intractable even for a graph with moderate scale. To address this, we propose to 1) represent the correlation matrix as a Gramian of edge embeddings, significantly reducing the number of parameters, and 2) reformulate the conditional probability distribution to dramatically reduce the inference cost. We theoretically verify scalability of our method by proving its linear convergence. Also, our extensive experiments demonstrate that it achieves significantly faster convergence than baselines, maintaining competitive prediction performance to the state-of-the-art models.

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Overview

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
23
Contribution Candidate Papers Compared
4
Refutable Paper

Research Landscape Overview

Core task: link sign prediction on signed graphs. The field has evolved into a rich landscape organized around several major branches. Graph Neural Network Architectures for Sign Prediction form a dense branch, encompassing works like Signed Graph Convolutional[14], Signed Graph Attention[16], and more recent innovations such as GegenNet[3] and Decoupled Sign Prediction[5], which explore specialized aggregation and message-passing schemes tailored to positive and negative edges. Social Theory-Driven Approaches leverage structural balance and status theory, while Network Embedding and Representation Learning methods such as Signed Latent Factors[13] and Sparse Network Embedding[33] focus on low-dimensional representations. Temporal and Dynamic Signed Networks address evolution over time with models like Continuous-Time Dynamic[17] and Dynamise[45]. Classical and Hybrid Machine Learning Approaches include Random Forest Prediction[22] and Graph Kernel Prediction[20], and Specialized Problem Settings tackle domains from bipartite graphs to protein interactions. Advanced Statistical and Probabilistic Models represent a smaller but methodologically distinct branch, exploring probabilistic dependencies and higher-order correlations beyond standard neural architectures. Recent work has increasingly focused on balancing expressiveness with interpretability and robustness. Many studies explore trade-offs between capturing complex signed network structures and maintaining computational efficiency or theoretical guarantees. CopulaGNN[0] sits within the Advanced Statistical and Probabilistic Models branch, employing copula-based dependency modeling to capture nuanced statistical relationships among edge signs. This approach contrasts with mainstream GNN methods like GegenNet[3] or Decoupled Sign Prediction[5], which rely on neural message-passing, by instead leveraging probabilistic frameworks to model joint distributions of link signs. While GNN architectures dominate the landscape with their flexibility and scalability, CopulaGNN[0] offers a complementary perspective grounded in statistical theory, potentially providing stronger guarantees on dependency structures and interpretability in settings where probabilistic reasoning is paramount.

Claimed Contributions

Gramian-based correlation matrix for inter-edge dependencies

The authors introduce a novel parameterization of the correlation matrix as a Gramian of edge embeddings (R = ν(QQ^T + εI_n)). This approach dramatically reduces memory consumption from O(|V|^4) to O(|V|^2 d) while maintaining sufficient representational power to capture inter-edge correlations in signed graphs.

4 retrieved papers
Woodbury reformulation for efficient conditional sampling

The authors apply the Woodbury matrix identity to reformulate the conditional probability distribution used during inference. This reformulation transforms the inversion of a large m×m correlation matrix into the inversion of a much smaller d×d matrix, significantly reducing computational cost and memory usage at inference time.

9 retrieved papers
Can Refute
Theoretical proof of linear convergence

The authors provide a theoretical analysis demonstrating that their loss function satisfies both L-smoothness and the μ-PL condition, which guarantees linear convergence during gradient descent optimization. This theoretical result validates that explicit inter-edge correlation modeling accelerates convergence speed.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Gramian-based correlation matrix for inter-edge dependencies

The authors introduce a novel parameterization of the correlation matrix as a Gramian of edge embeddings (R = ν(QQ^T + εI_n)). This approach dramatically reduces memory consumption from O(|V|^4) to O(|V|^2 d) while maintaining sufficient representational power to capture inter-edge correlations in signed graphs.

Contribution

Woodbury reformulation for efficient conditional sampling

The authors apply the Woodbury matrix identity to reformulate the conditional probability distribution used during inference. This reformulation transforms the inversion of a large m×m correlation matrix into the inversion of a much smaller d×d matrix, significantly reducing computational cost and memory usage at inference time.

Contribution

Theoretical proof of linear convergence

The authors provide a theoretical analysis demonstrating that their loss function satisfies both L-smoothness and the μ-PL condition, which guarantees linear convergence during gradient descent optimization. This theoretical result validates that explicit inter-edge correlation modeling accelerates convergence speed.

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