# Bridging Unsupervised and Semi-Supervised Anomaly Detection: A Theoretically-Grounded and Practical Framework with Synthetic Anomalies

arXiv: https://arxiv.org/abs/2506.13955 · HTML: https://mlsanity.com/paper/2506.13955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 53 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 23 of 23)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Deep Anomaly Detection with Deviation Networks](https://mlsanity.com/paper/1911.08623/) (2019)
- [DROCC: Deep Robust One-Class Classification](https://mlsanity.com/paper/2002.12718/) (2020)
- [Why Should Adversarial Perturbations be Imperceptible? Rethink the Research Paradigm in Adversarial NLP](https://mlsanity.com/paper/2210.10683/) (2022)
- [Neural Transformation Learning for Deep Anomaly Detection Beyond Images](https://mlsanity.com/paper/2103.16440/) (2021)
- [Optimal Approximation Rate of ReLU Networks in terms of Width and Depth](https://mlsanity.com/paper/2103.00502/) (2021)
- [Feature Encoding with AutoEncoders for Weakly-supervised Anomaly Detection](https://mlsanity.com/paper/2105.10500/) (2021)
- [Interpretable, Multidimensional, Multimodal Anomaly Detection with Negative Sampling for Detection of Device Failure](https://mlsanity.com/paper/2007.10088/) (2020)
- [AD-LLM: Benchmarking Large Language Models for Anomaly Detection](https://mlsanity.com/paper/2412.11142/) (2024)
- [Perturbation Learning Based Anomaly Detection](https://mlsanity.com/paper/2206.02704/) (2022)
- [NNG-Mix: Improving Semi-supervised Anomaly Detection with Pseudo-anomaly Generation](https://mlsanity.com/paper/2311.11961/) (2023)
- [Training shallow ReLU networks on noisy data using hinge loss: when do we overfit and is it benign?](https://mlsanity.com/paper/2306.09955/) (2023)
- [Bias of Homotopic Gradient Descent for the Hinge Loss](https://mlsanity.com/paper/1907.11746/) (2019)
- [Revisiting Non-separable Binary Classification and its Applications in Anomaly Detection](https://mlsanity.com/paper/2312.01541/) (2023)
- [Learning rates for classification with Gaussian kernels](https://mlsanity.com/paper/1702.08701/) (2017)
- [Learning to Detect Cyber Attacks: Neural Anomaly Detection for Cybersecurity with Theoretical Insights](https://mlsanity.com/paper/2409.08521/) (2024)

## Abstract (arXiv)

Anomaly detection (AD) is a critical task across domains such as cybersecurity and healthcare. In the unsupervised setting, an effective and theoretically-grounded principle is to train classifiers to distinguish normal data from (synthetic) anomalies. We extend this principle to semi-supervised AD, where training data also include a limited labeled subset of anomalies possibly present in test time. We propose a theoretically-grounded and empirically effective framework for semi-supervised AD that combines known and synthetic anomalies during training. To analyze semi-supervised AD, we introduce the first mathematical formulation of semi-supervised AD, which generalizes unsupervised AD. Here, we show that synthetic anomalies enable (i) better anomaly modeling in low-density regions and (ii) optimal convergence guarantees for neural network classifiers -- the first theoretical result for semi-supervised AD. We empirically validate our framework on five diverse benchmarks, observing consistent performance gains. These improvements also extend beyond our theoretical framework to other classification-based AD methods, validating the generalizability of the synthetic anomaly principle in AD.