发表机构
Tampere University; Radboud University（坦佩雷大学; 拉德堡德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从子空间几何视角揭示重建式无监督学习失败机制，提出动态推拉与嵌套流形雕刻方法，在无需异常标签下提升异常检测性能。
AI 中文摘要
基于重建的无监督学习可能以两种相反的方式失败：模型可能过于准确地重建异常，或者丢弃有效的名义变异。利用子空间追求假设，我们通过名义成分诱导的交、并和连接几何来表征这些失败。过度的学习范围产生连接盲性，而容量不足则产生交偏好和名义保真度损失。我们证明了紧凑的名义并集在名义保真范围内是最优的，并且通常需要非线性重建映射。基于这种几何，我们引入了动态推拉，它无需异常标签即可从受控扰动中学习，以及嵌套流形雕刻，它在潜在空间中递归地应用相同的原理。实验证实了在每种测试的推拉配置中潜在几何的预测变化。所提出的方法在标准基准和未见图像退化上改善了基于重建的异常检测，同时也改善了预训练的 ECG 表示用于下游分类。这些结果将重建失败与可识别的几何条件联系起来，并为学习紧凑表示提供了实用机制。
英文摘要
Reconstruction-based unsupervised learning can fail in two opposing ways: a model may reconstruct anomalies too accurately or discard valid nominal variation. Using the Pursuit of Subspaces hypothesis, we characterize these failures through the meet, union, and join geometries induced by the nominal components. Excess learned range produces join blindness, while insufficient capacity produces meet preference and loss of nominal fidelity. We show that the compact nominal union is optimal among nominal faithful ranges and generally requires a nonlinear reconstruction map. Based on this geometry, we introduce Dynamic Push and Pull, which learns from controlled perturbations without anomaly labels, and nested manifold carving, which applies the same principle recursively in latent space. Experiments confirm the predicted changes in latent geometry across every tested Push and Pull configuration. The proposed methods improve reconstruction-based anomaly detection across standard benchmarks and unseen image degradations, while also improving pretrained ECG representations for downstream classification. These results connect reconstruction failures to identifiable geometric conditions and provide practical mechanisms for learning compact representations.
Comments39 pages, 8 figures, and 27 tables, including appendices
