When Does Unsupervised Learning Succeed or Fail? A PoS Perspective on Reconstruction-Based Anomaly Detection

2026-09-23

AI Summary

This study addresses the geometric failure modes in reconstruction-based unsupervised anomaly detection, where anomalous inputs are excessively reconstructed while normal variations are lost. Grounded in the subspace tracking hypothesis, this work reveals that the union of compact normal manifolds constitutes the optimal representation scope. Accordingly, a dynamic push-pull algorithm and nested manifold sculpting technique are proposed to optimize the nonlinear reconstruction mapping via label-free controlled perturbation learning and recursive latent space sculpting. Experimental results demonstrate that the proposed approach significantly enhances detection performance on standard benchmarks and unseen degraded images, while effectively improving downstream classification using pretrained ECG representations. These findings validate the accuracy of the underlying geometric theoretical predictions.

Abstract

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.

Problem

• Unsupervised Learning
• Anomaly Detection
• Reconstruction-based Methods
• Subspace Geometry
• Representation Learning

Innovation

• Unsupervised Anomaly Detection
• Pursuit of Subspaces
• Dynamic Push and Pull
• Nested Manifold Carving
• Latent Geometry