Industrial image anomaly detection is a challenging problem owing to extreme class imbalance and the scarcity of labeled defective samples, particularly in few-shot settings. We propose BayPrAnoMeta, a Bayesian generalization of Proto-MAML for few-shot industrial image anomaly detection. Unlike existing Proto-MAML approaches that rely on deterministic class prototypes and distance-based adaptation, BayPrAnoMeta replaces prototypes with task-specific probabilistic normality models and performs inner-loop adaptation via a Bayesian posterior predictive likelihood. We model normal support embeddings with a Normal-Inverse-Wishart (NIW) prior, producing a Student-$t$ predictive distribution that enables uncertainty-aware, heavy-tailed anomaly scoring and is essential for robustness in extreme few-shot settings. We further extend BayPrAnoMeta to a federated meta-learning framework with supervised contrastive regularization for heterogeneous industrial clients and prove convergence to stationary points of the resulting nonconvex objective. Experiments on the MVTec AD benchmark demonstrate consistent and significant AUROC improvements over MAML, Proto-MAML, and PatchCore-based methods in few-shot anomaly detection settings.

翻译：工业图像异常检测是一个具有挑战性的问题，其原因在于极端的类别不平衡以及标记缺陷样本的稀缺性，在少样本场景下尤其如此。我们提出了BayPrAnoMeta，一种用于少样本工业图像异常检测的Proto-MAML的贝叶斯泛化方法。与现有依赖确定性类别原型和基于距离的适应的Proto-MAML方法不同，BayPrAnoMeta将原型替换为任务特定的概率正态性模型，并通过贝叶斯后验预测似然进行内循环适应。我们使用正态-逆Wishart（NIW）先验对正常支持嵌入进行建模，产生一个Student-$t$预测分布，该分布能够实现不确定性感知、重尾的异常评分，这对于极端少样本场景下的鲁棒性至关重要。我们进一步将BayPrAnoMeta扩展到一个具有监督对比正则化的联邦元学习框架，以适用于异构工业客户端，并证明了该框架能收敛于由此产生的非凸目标函数的稳定点。在MVTec AD基准测试上的实验表明，在少样本异常检测场景下，该方法相较于MAML、Proto-MAML以及基于PatchCore的方法，取得了持续且显著的AUROC提升。