Deep neural networks are vulnerable to backdoor attacks, where malicious behaviors are implanted during training. While existing defenses can effectively purify compromised models, they typically require labeled data or specific training procedures, making them difficult to apply beyond supervised learning settings. Notably, recent studies have shown successful backdoor attacks across various learning paradigms, highlighting a critical security concern. To address this gap, we propose Two-stage Symmetry Connectivity (TSC), a novel backdoor purification defense that operates independently of data format and requires only a small fraction of clean samples. Through theoretical analysis, we prove that by leveraging permutation invariance in neural networks and quadratic mode connectivity, TSC amplifies the loss on poisoned samples while maintaining bounded clean accuracy. Experiments demonstrate that TSC achieves robust performance comparable to state-of-the-art methods in supervised learning scenarios. Furthermore, TSC generalizes to self-supervised learning frameworks, such as SimCLR and CLIP, maintaining its strong defense capabilities. Our code is available at https://github.com/JiePeng104/TSC.

Graph anomaly detection aims to identify the abnormal nodes in a graph that deviate from the majority of nodes, which is critical in fields such as finance and social network analysis. Due to the unbearable costs of labeling anomalies, existing methods are mainly tackled from unsupervised or semi-supervised manners. Unfortunately, most proposed methods either lack prior knowledge of the anomalies or neglect the potential relation between labeled and unlabeled nodes, with limited improvement. In this paper, we propose a novel Semi-supervised learning framework for graph Anomaly Detection via Multi-view Contrastive Learning (SADMCL for abbreviation), which uses very few labels to promote detection performance. To be specific, we employ multi-view contrastive learning, i.e., sample-sample contrast, sample-instance contrast, and normal-anomaly contrast, to generate the representations with significant discrimination between normal and abnormal nodes, as well as the instances that respond to the normal features. By comparing the learned representations and the instances, we comprehensively calculate the anomaly score for each node and infer its label. Extensive experiments conducted on four real-world datasets demonstrate that our approach outperforms current state-of-the-art anomaly detection algorithms when provided with few labeled samples.