Graph Neural Networks (GNNs) are vulnerable to backdoor attacks. Existing defenses primarily rely on detecting structural anomalies, distributional outliers, or perturbation-induced prediction instability, which struggle to handle the more subtle, feature-based attacks that do not introduce obvious topological changes. Our empirical analysis reveals that both structure-based and feature-based attacks not only cause early loss convergence of target nodes but also induce a class-coherent loss drift, where this early convergence gradually spreads to nearby clean nodes, leading to significant distribution overlap. To address this issue, we propose LoSplit, the first training-time defense framework in graph that leverages this early-stage loss drift to accurately split target nodes. Our method dynamically selects epochs with maximal loss divergence, clusters target nodes via Gaussian Mixture Models (GMM), and applies a Decoupling-Forgetting strategy to break the association between target nodes and malicious label. Extensive experiments on multiple realworld datasets demonstrate the effectiveness of our approach, significantly reducing attack success rates while maintaining high clean accuracy across diverse backdoor attack strategies.

Collaborative filtering (CF) methods are now facing the challenge of data sparsity in recommender systems. In order to reduce the effect of data sparsity, researchers proposed contrastive learning methods to extract self-supervised signals from raw data. Contrastive learning methods address this problem by graph augmentation and maximizing the consistency of node representations between different augmented graphs. However, these methods tends to unintentionally distance the target node from its path nodes on the interaction path, thus limiting its effectiveness. In this regard, we propose a solution that uses paths as samples in the contrastive loss function. In order to obtain the path samples, we design a path sampling method.

We develop practical and theoretically grounded membership inference attacks (MIAs) against both independent and identically distributed (i.i.d.) data and graphstructured data. Building on the Bayesian decision-theoretic framework of [1], we derive the Bayes-optimal membership inference rule for node-level MIAs against graph neural networks, addressing key open questions about optimal query strategies in the graph setting. We introduce BASE and G-BASE, tractable approximations of the Bayes-optimal membership inference. G-BASE achieves superior performance compared to previously proposed classifier-based node-level MIA attacks. BASE, which is also applicable to non-graph data, matches or exceeds the performance of prior state-of-the-art MIAs, such as LiRA and RMIA, at a significantly lower computational cost. Finally, we show that BASE and RMIA are equivalent under a specific hyperparameter setting, providing a principled, Bayes-optimal justification for the RMIA attack.

The task of geometry problem solving has been a long-standing focus in the automated mathematics community and draws growing attention due to its complexity for both symbolic and neural models. Although prior studies have explored various effective approaches for enhancing problem solving performances, two fundamental challenges remain unaddressed, which are essential to the application in practical scenarios. First, the multi-step reasoning gap between the initial geometric conditions and ultimate problem goal leads to a great search space for solution exploration. Second, obtaining multiple interpretable and shorter solutions remains an open problem. In this work, we introduce the Causal-Reasoning Geometry Problem Solver to overcome these challenges.

Graph Neural Networks (GNNs) are vulnerable to backdoor attacks. Existing defenses primarily rely on detecting structural anomalies, distributional outliers, or perturbation-induced prediction instability, which struggle to handle the more subtle, feature-based attacks that do not introduce obvious topological changes. Our empirical analysis reveals that both structure-based and feature-based attacks not only cause early loss convergence of target nodes but also induce a class-coherent loss drift, where this early convergence gradually spreads to nearby clean nodes, leading to significant distribution overlap. To address this issue, we propose LoSplit, the first training-time defense framework in graph that leverages this early-stage loss drift to accurately split target nodes. Our method dynamically selects epochs with maximal loss divergence, clusters target nodes via Gaussian Mixture Models (GMM), and applies a Decoupling-Forgetting strategy to break the association between target nodes and malicious label. Extensive experiments on multiple real-world datasets demonstrate the effectiveness of our approach, significantly reducing attack success rates while maintaining high clean accuracy across diverse backdoor attack strategies.

Collaborative filtering (CF) methods are now facing the challenge of data sparsity in recommender systems. In order to reduce the effect of data sparsity, researchers proposed contrastive learning methods to extract self-supervised signals from raw data. Contrastive learning methods address this problem by graph augmentation and maximizing the consistency of node representations between different augmented graphs. However, these methods tends to unintentionally distance the target node from its path nodes on the interaction path, thus limiting its effectiveness. In this regard, we propose a solution that uses paths as samples in the contrastive loss function. In order to obtain the path samples, we design a path sampling method.

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

Deep neural networks are ubiquitously adopted in many applications, such as computer vision, natural language processing, and graph analytics. However, well-trained neural networks can make prediction errors after deployment as the world changes.