arXiv:2609.09698v1 Announce Type: cross Abstract: Graph Neural Networks (GNNs) have achieved remarkable success across diverse applications, yet they remain highly vulnerable to adversarial attacks that maliciously perturb graph structure. Existing defenses often lack rigorous theoretical grounding, rely on attack-specific heuristics, or require costly retraining procedures such as adversarial training. To address these limitations, we propose Kernel-Complexity Edge Sanitization (KCES), a training-free and model-agnostic framework for defending against structural attacks. KCES is built upon Graph Kernel Complexity (GKC), a principled metric derived from the graph Gram matrix that appears in a generalization upper bound on the GNN test error. From this bound, we define an edge-specific KC score that quantifies each edge's structural influence via its induced change in GKC. KCES then identifies and prunes high-KC edges, which are empirically enriched with adversarial perturbations under structural attacks, to mitigate their harmful impact. Computationally efficient and scalable, KCES operates as a lightweight preprocessing step without retraining and can be seamlessly integrated with existing defenses. Extensive experiments demonstrate that KCES consistently outperforms representative robust baselines across diverse attack settings and scales effectively to large graphs. Supported by theoretical analysis and extensive empirical validation, KCES provides a principled and efficient framework for securing GNNs. Our code is available at https://github.com/karpning/KCScore.

arXiv:2603.12581v1 Announce Type: cross Abstract: Although diffusion models have achieved remarkable progress in multi-modal magnetic resonance imaging (MRI) translation tasks, existing methods still tend to suffer from anatomical inconsistencies or degraded texture details when handling arbitrary missing-modality scenarios. To address these issues, we propose a latent diffusion-based multi-modal MRI translation framework, termed MSG-LDM. By leveraging the available modalities, the proposed method infers complete structural information, which preserves reliable boundary details. Specifically, we introduce a style--structure disentanglement mechanism in the latent space, which explicitly separates modality-specific style features from shared structural representations, and jointly models low-frequency anatomical layouts and high-frequency boundary details in a multi-scale feature space. During the structure disentanglement stage, high-frequency structural information is explicitly incorporated to enhance feature representations, guiding the model to focus on fine-grained structural cues while learning modality-invariant low-frequency anatomical representations. Furthermore, to reduce interference from modality-specific styles and improve the stability of structure representations, we design a style consistency loss and a structure-aware loss. Extensive experiments on the BraTS2020 and WMH datasets demonstrate that the proposed method outperforms existing MRI synthesis approaches, particularly in reconstructing complete structures. The source code is publicly available at https://github.com/ziyi-start/MSG-LDM.