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

arXiv: https://arxiv.org/abs/2609.28832 · HTML: https://mlsanity.com/paper/2609.28832/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 73 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 30 of 38)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [CutPaste: Self-Supervised Learning for Anomaly Detection and Localization](https://mlsanity.com/paper/2104.04015/) (2021)
- [DRAEM -- A discriminatively trained reconstruction embedding for surface anomaly detection](https://mlsanity.com/paper/2108.07610/) (2021)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [GANomaly: Semi-Supervised Anomaly Detection via Adversarial Training](https://mlsanity.com/paper/1805.06725/) (2018)
- [Deep Joint Rain Detection and Removal from a Single Image](https://mlsanity.com/paper/1609.07769/) (2016)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [Density-aware Single Image De-raining using a Multi-stream Dense Network](https://mlsanity.com/paper/1802.07412/) (2018)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [OCGAN: One-class Novelty Detection Using GANs with Constrained Latent Representations](https://mlsanity.com/paper/1903.08550/) (2019)
- [Image De-raining Using a Conditional Generative Adversarial Network](https://mlsanity.com/paper/1701.05957/) (2017)
- [Natural Synthetic Anomalies for Self-Supervised Anomaly Detection and Localization](https://mlsanity.com/paper/2109.15222/) (2021)
- [Adversarially Learned Anomaly Detection](https://mlsanity.com/paper/1812.02288/) (2018)
- [Old is Gold: Redefining the Adversarially Learned One-Class Classifier Training Paradigm](https://mlsanity.com/paper/2004.07657/) (2020)
- [Deep Structured Energy Based Models for Anomaly Detection](https://mlsanity.com/paper/1605.07717/) (2016)
- [U-shape Transformer for Underwater Image Enhancement](https://mlsanity.com/paper/2111.11843/) (2021)
- [ECG-FM: An Open Electrocardiogram Foundation Model](https://mlsanity.com/paper/2408.05178/) (2024)
- [Guiding Masked Representation Learning to Capture Spatio-Temporal Relationship of Electrocardiogram](https://mlsanity.com/paper/2402.09450/) (2024)
- [Zero-Shot ECG Classification with Multimodal Learning and Test-time Clinical Knowledge Enhancement](https://mlsanity.com/paper/2403.06659/) (2024)
- [Self-Supervised Masking for Unsupervised Anomaly Detection and Localization](https://mlsanity.com/paper/2205.06568/) (2022)
- [Learning Not to Reconstruct Anomalies](https://mlsanity.com/paper/2110.09742/) (2021)
- [ARAE: Adversarially Robust Training of Autoencoders Improves Novelty Detection](https://mlsanity.com/paper/2003.05669/) (2020)
- [Memory Augmented Generative Adversarial Networks for Anomaly Detection](https://mlsanity.com/paper/2002.02669/) (2020)
- [Masked Autoencoders for Unsupervised Anomaly Detection in Medical Images](https://mlsanity.com/paper/2307.07534/) (2023)
- [Autoencoders for Anomaly Detection are Unreliable](https://mlsanity.com/paper/2501.13864/) (2025)

## Abstract (arXiv)

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.