We focus on a specific use case in anomaly detection where the distribution of normal samples is supported by a lower-dimensional manifold. Here, regularized autoencoders provide a popular approach by learning the identity mapping on the set of normal examples, while trying to prevent good reconstruction on points outside of the manifold. Typically, this goal is implemented by controlling the capacity of the model, either directly by reducing the size of the bottleneck layer or implicitly by imposing some sparsity (or contraction) constraints on parts of the corresponding network. However, neither of these techniques does explicitly penalize the reconstruction of anomalous signals often resulting in poor detection. We tackle this problem by adapting a self-supervised learning regime that exploits discriminative information during training but focuses on the submanifold of normal examples. Informally, our training objective regularizes the model to produce locally consistent reconstructions, while replacing irregularities by acting as a filter that removes anomalous patterns. To support this intuition, we perform a rigorous formal analysis of the proposed method and provide a number of interesting insights. In particular, we show that the resulting model resembles a non-linear orthogonal projection of partially corrupted images onto the submanifold of uncorrupted samples. On the other hand, we identify the orthogonal projection as an optimal solution for a number of regularized autoencoders including the contractive and denoising variants. We support our theoretical analysis by empirical evaluation of the resulting detection and localization performance of the proposed method. In particular, we achieve a new state-of-the-art result on the MVTec AD dataset -- a challenging benchmark for visual anomaly detection in the manufacturing domain.

翻译：我们聚焦于异常检测中的一个特定应用场景，其中正常样本的分布由低维流形支撑。在此框架下，正则化自编码器通过学习正常样本集合上的恒等映射，同时尝试阻止流形外点上的良好重构，成为一种流行方法。通常，这一目标通过直接减小瓶颈层尺寸或隐式地对网络相应部分施加稀疏（或收缩）约束来控制模型容量来实现。然而，这两种技术均未显式惩罚异常信号的重构，往往导致检测性能不佳。我们通过采用一种自监督学习机制来解决此问题，该机制在训练过程中利用判别信息，但聚焦于正常样本的子流形。非正式地说，我们的训练目标通过正则化模型以产生局部一致的重构，同时通过充当过滤异常模式的滤波器来替换不规则性。为支撑这一直觉，我们对所提方法进行了严谨的形式化分析，并提供了若干有趣见解。特别地，我们证明所得模型类似于将部分损坏图像非线性正交投影到未损坏样本子流形上。另一方面，我们将正交投影识别为包括收缩与去噪变体在内的多种正则化自编码器的优化解。我们通过所提方法的检测与定位性能实证评估来支持理论分析。具体而言，我们在MVTec AD数据集（制造业领域视觉异常检测的一项具有挑战性的基准）上取得了最新最优结果。