# Statistical Non-linear Reconstruction Loss for Image Anomaly Detection

arXiv: https://arxiv.org/abs/2607.12866 · HTML: https://mlsanity.com/paper/2607.12866/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 29 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 22 of 22)

- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Real-world Anomaly Detection in Surveillance Videos](https://mlsanity.com/paper/1801.04264/) (2018)
- [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)
- [GANomaly: Semi-Supervised Anomaly Detection via Adversarial Training](https://mlsanity.com/paper/1805.06725/) (2018)
- [SPot-the-Difference Self-Supervised Pre-training for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2207.14315/) (2022)
- [Uninformed Students: Student-Teacher Anomaly Detection with Discriminative Latent Embeddings](https://mlsanity.com/paper/1911.02357/) (2019)
- [Multiresolution Knowledge Distillation for Anomaly Detection](https://mlsanity.com/paper/2011.11108/) (2020)
- [A Unified Model for Multi-class Anomaly Detection](https://mlsanity.com/paper/2206.03687/) (2022)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [Patch SVDD: Patch-level SVDD for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2006.16067/) (2020)
- [OCGAN: One-class Novelty Detection Using GANs with Constrained Latent Representations](https://mlsanity.com/paper/1903.08550/) (2019)
- [Deep Industrial Image Anomaly Detection: A Survey](https://mlsanity.com/paper/2301.11514/) (2023)
- [Deep Learning for Medical Anomaly Detection -- A Survey](https://mlsanity.com/paper/2012.02364/) (2020)
- [Generalized Denoising Auto-Encoders as Generative Models](https://mlsanity.com/paper/1305.6663/) (2013)
- [MambaAD: Exploring State Space Models for Multi-class Unsupervised Anomaly Detection](https://mlsanity.com/paper/2404.06564/) (2024)
- [Hierarchical Vector Quantized Transformer for Multi-class Unsupervised Anomaly Detection](https://mlsanity.com/paper/2310.14228/) (2023)
- [ADTR: Anomaly Detection Transformer with Feature Reconstruction](https://mlsanity.com/paper/2209.01816/) (2022)
- [Learning to Detect Multi-class Anomalies with Just One Normal Image Prompt](https://mlsanity.com/paper/2505.09264/) (2025)
- [Salvaging the Overlooked: Leveraging Class-Aware Contrastive Learning for Multi-Class Anomaly Detection](https://mlsanity.com/paper/2412.04769/) (2024)

## Abstract (arXiv)

Reconstruction-based methods are a cornerstone of unsupervised image anomaly detection, but they remain vulnerable to outlier leakage, where standard mean squared error (MSE) loss drives the model to faithfully reconstruct anomalous patterns. We propose a Non-linear Reconstruction Loss that applies a sigmoid-based squashing function to suppress high-magnitude features, preventing outliers from dominating optimization while preserving sensitivity to normal patterns. In addition, we introduce a statistical calibration scheme that selects the scaling factor k from the confidence interval (CI) of the normal feature distribution, enabling data-driven control of the suppression strength. Our approach achieves competitive or superior anomaly detection performance compared to state-of-the-art methods, reaching 99.0% Image-AUROC and 97.3% Pixel-AUROC on MVTec-AD, and 95.3% Image-AUROC and 99.0% Pixel-AUROC on VisA. These results indicate that non-linear gradient suppression is an effective mechanism for mitigating outlier leakage and improving anomaly localization in unified industrial inspection settings. The implementation is available at https://github.com/mintii13/Statistical-Non-linear-Reconstruction-Loss.git.