Toward Robust Signed Graph Learning through Joint Input-Target Denoising

TL;DR

The paper addresses robustness in signed graph neural networks under noise in both input structure and supervision signals. It introduces RIDGE, a framework that extends the Graph Information Bottleneck (GIB) with target-space denoising (GIB-TD) and employs a reparameterization-based, variational objective to denoise inputs $\tilde{\mathcal{G}}$ and targets $\tilde{Y}$, while learning effective representations $H$ for link-sign prediction. RIDGE combines feature masking, substructure sampling, and tractable bounds on mutual information, yielding a loss $\mathcal{L} = \mathcal{L}_{cls} + \alpha \mathcal{L}_{KL}^{Y} + \beta \mathcal{L}_{KL}^{\mathcal{G}}$, with $\mathcal{L}_{KL}^{Y}$ and $\mathcal{L}_{KL}^{\mathcal{G}}$ derived from variational bounds. The approach demonstrates strong robustness on four real-world signed-graph datasets, outperforming baselines under random and adversarial noise, and scales efficiently to larger graphs. By avoiding strict balance-theory assumptions and grounding robustness in information-theoretic principles, RIDGE offers a principled and practical pathway for reliable signed graph learning in noisy real-world applications.

Abstract

Signed Graph Neural Networks (SGNNs) are widely adopted to analyze complex patterns in signed graphs with both positive and negative links. Given the noisy nature of real-world connections, the robustness of SGNN has also emerged as a pivotal research area. Under the supervision of empirical properties, graph structure learning has shown its robustness on signed graph representation learning, however, there remains a paucity of research investigating a robust SGNN with theoretical guidance. Inspired by the success of graph information bottleneck (GIB) in information extraction, we propose RIDGE, a novel framework for Robust sI gned graph learning through joint Denoising of Graph inputs and supervision targEts. Different from the basic GIB, we extend the GIB theory with the capability of target space denoising as the co-existence of noise in both input and target spaces. In instantiation, RIDGE effectively cleanses input data and supervision targets via a tractable objective function produced by reparameterization mechanism and variational approximation. We extensively validate our method on four prevalent signed graph datasets, and the results show that RIDGE clearly improves the robustness of popular SGNN models under various levels of noise.

Figures (19)

• Figure 1: Framework overview of RIDGE. RIDGE extends the GIB theory with the ability of target space denoising, referred to as GIB-TD, in which $Y_c$ denotes the clean subset extracted from the noisy label set $\tilde{Y}$. Given a signed graph with random noise, RIDGE is capable of deriving robust representations by combating the noise inherent in the input and target spaces using the reparameterization mechanism and variational approximation.
• Figure 2: Two common unbalanced triangles in signed graphs and their corresponding ego-trees. Positive edges are shown in black, while negative edges are depicted in red.
• Figure 3: t-SNE visualization of the node features produced by Truncated-SVD of the two unbalanced triangles in Fig \ref{['fig:unbalance_case']}.
• Figure 4: Hyper-parameter sensitivity on Bitcoin_OTC.
• Figure 5: Loss curves of RIDGE with 25% random noise. Due to the scale difference, we normalize the curves to 0-1.

Theorems & Definitions (4)

• proposition 1
• proposition 2
• proposition 3
• proposition 4