Neural Information Processing Systems http://nips.cc/

Signed graphs model complex relationships through positive and negative edges, with widespread real-world applications. Given the sensitive nature of such data, selective removal mechanisms have become essential for privacy protection. While graph unlearning enables the removal of specific data influences from Graph Neural Networks (GNNs), existing methods are designed for conventional GNNs and overlook the unique heterogeneous properties of signed graphs. When applied to Signed Graph Neural Networks (SGNNs), these methods lose critical sign information, degrading both model utility and unlearning effectiveness. To address these challenges, we propose Certified Signed Graph Unlearning (CSGU), which provides provable privacy guarantees while preserving the sociological principles underlying SGNNs. CSGU employs a three-stage method: (1) efficiently identifying minimal influenced neighborhoods via triangular structures, (2) applying sociological theories to quantify node importance for optimal privacy budget allocation, and (3) performing importance-weighted parameter updates to achieve certified modifications with minimal utility degradation. Extensive experiments demonstrate that CSGU outperforms existing methods, achieving superior performance in both utility preservation and unlearning effectiveness on SGNNs.

Samples of brain signals collected by EEG sensors have inherent anti-correlations that are well modeled by negative edges in a finite graph. To differentiate epilepsy patients from healthy subjects using collected EEG signals, we build lightweight and interpretable transformer-like neural nets by unrolling a spectral denoising algorithm for signals on a balanced signed graph -- graph with no cycles of odd number of negative edges. A balanced signed graph has well-defined frequencies that map to a corresponding positive graph via similarity transform of the graph Laplacian matrices. We implement an ideal low-pass filter efficiently on the mapped positive graph via Lanczos approximation, where the optimal cutoff frequency is learned from data. Given that two balanced signed graph denoisers learn posterior probabilities of two different signal classes during training, we evaluate their reconstruction errors for binary classification of EEG signals. Experiments show that our method achieves classification performance comparable to representative deep learning schemes, while employing dramatically fewer parameters.

We consider graphs where edges and their signs are added independently at random from among all pairs of nodes. We establish strong concentration inequalities for adjacency and Laplacian matrices obtained from this family of random graph models. Then, we apply our results to study graphs sampled from the signed stochastic block model. Namely, we take a two-community setting where edges within the communities have positive signs and edges between the communities have negative signs and apply a random sign perturbation with probability $0< s <1/2$. In this setting, our findings include: first, the spectral gap of the corresponding signed Laplacian matrix concentrates near $2s$ with high probability; and second, the sign of the first eigenvector of the Laplacian matrix defines a weakly consistent estimator for the balanced community detection problem, or equivalently, the $\pm 1$ synchronization problem. We supplement our theoretical contributions with experimental data obtained from the models under consideration.

Signed Graph Neural Networks (SGNNs) are powerful tools for signed graph representation learning but struggle with limited generalization and heavy dependence on labeled data. While recent advancements in "graph pre-training and prompt tuning" have reduced label dependence in Graph Neural Networks (GNNs) and improved their generalization abilities by leveraging pre-training knowledge, these efforts have focused exclusively on unsigned graphs. The scarcity of publicly available signed graph datasets makes it essential to transfer knowledge from unsigned graphs to signed graph tasks. However, this transfer introduces significant challenges due to the graph-level and task-level divergences between the pre-training and downstream phases. To address these challenges, we propose Signed Graph Prompt Tuning (SGPT) in this paper. Specifically, SGPT employs a graph template and a semantic prompt to segregate mixed link semantics in the signed graph and then adaptively integrate the distinctive semantic information according to the needs of downstream tasks, thereby unifying the pre-training and downstream graphs. Additionally, SGPT utilizes a task template and a feature prompt to reformulate the downstream signed graph tasks, aligning them with pre-training tasks to ensure a unified optimization objective and consistent feature space across tasks. Finally, extensive experiments are conducted on popular signed graph datasets, demonstrating the superiority of SGPT over state-of-the-art methods.

Graphs are ubiquitous for modeling complex systems involving structured data and relationships. Consequently, graph representation learning, which aims to automatically learn low-dimensional representations of graphs, has drawn a lot of attention in recent years. The overwhelming majority of existing methods handle unsigned graphs. However, signed graphs appear in an increasing number of application domains to model systems involving two types of opposed relationships. Several authors took an interest in signed graphs and proposed methods for providing vertex-level representations, but only one exists for whole-graph representations, and it can handle only fully connected graphs. In this article, we tackle this issue by proposing two approaches to learning whole-graph representations of general signed graphs. The first is a SG2V, a signed generalization of the whole-graph embedding method Graph2vec that relies on a modification of the Weisfeiler--Lehman relabelling procedure. The second one is WSGCN, a whole-graph generalization of the signed vertex embedding method SGCN that relies on the introduction of master nodes into the GCN. We propose several variants of both these approaches. A bottleneck in the development of whole-graph-oriented methods is the lack of data. We constitute a benchmark composed of three collections of signed graphs with corresponding ground truths. We assess our methods on this benchmark, and our results show that the signed whole-graph methods learn better representations for this task. Overall, the baseline obtains an F-measure score of 58.57, when SG2V and WSGCN reach 73.01 and 81.20, respectively. Our source code and benchmark dataset are both publicly available online.

Signed Graph Neural Networks (SGNNs) have been shown to be effective in analyzing complex patterns in real-world situations where positive and negative links coexist. However, SGNN models suffer from poor explainability, which limit their adoptions in critical scenarios that require understanding the rationale behind predictions. To the best of our knowledge, there is currently no research work on the explainability of the SGNN models. Our goal is to address the explainability of decision-making for the downstream task of link sign prediction specific to signed graph neural networks. Since post-hoc explanations are not derived directly from the models, they may be biased and misrepresent the true explanations. Therefore, in this paper we introduce a Self-Explainable Signed Graph transformer (SE-SGformer) framework, which can not only outputs explainable information while ensuring high prediction accuracy. Specifically, We propose a new Transformer architecture for signed graphs and theoretically demonstrate that using positional encoding based on signed random walks has greater expressive power than current SGNN methods and other positional encoding graph Transformer-based approaches. We constructs a novel explainable decision process by discovering the $K$-nearest (farthest) positive (negative) neighbors of a node to replace the neural network-based decoder for predicting edge signs. These $K$ positive (negative) neighbors represent crucial information about the formation of positive (negative) edges between nodes and thus can serve as important explanatory information in the decision-making process. We conducted experiments on several real-world datasets to validate the effectiveness of SE-SGformer, which outperforms the state-of-the-art methods by improving 2.2\% prediction accuracy and 73.1\% explainablity accuracy in the best-case scenario.

Like Graph Neural Networks (GNNs), Signed Graph Neural Networks (SGNNs) are also up against fairness issues from source data and typical aggregation method. In this paper, we are pioneering to make the investigation of fairness in SGNNs expanded from GNNs. We identify the issue of degree bias within signed graphs, offering a new perspective on the fairness issues related to SGNNs. To handle the confronted bias issue, inspired by previous work on degree bias, a new Model-Agnostic method is consequently proposed to enhance representation of nodes with different degrees, which named as Degree Debiased Signed Graph Neural Network (DD-SGNN) . More specifically, in each layer, we make a transfer from nodes with high degree to nodes with low degree inside a head-to-tail triplet, which to supplement the underlying domain missing structure of the tail nodes and meanwhile maintain the positive and negative semantics specified by balance theory in signed graphs. We make extensive experiments on four real-world datasets. The result verifies the validity of the model, that is, our model mitigates the degree bias issue without compromising performance($\textit{i.e.}$, AUC, F1). The code is provided in supplementary material.