# Interpretable Multi-Hypersphere Deep Anomaly Detection for Open-set Supervised Anomaly Detection

arXiv: https://arxiv.org/abs/2609.23008 · HTML: https://mlsanity.com/paper/2609.23008/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 19 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [A Unified Model for Multi-class Anomaly Detection](https://mlsanity.com/paper/2206.03687/) (2022)
- [EfficientAD: Accurate Visual Anomaly Detection at Millisecond-Level Latencies](https://mlsanity.com/paper/2303.14535/) (2023)
- [MedIAnomaly: A comparative study of anomaly detection in medical images](https://mlsanity.com/paper/2404.04518/) (2024)
- [Multi-Class Anomaly Detection](https://mlsanity.com/paper/2110.15108/) (2021)
- [Interpretable Maximum Margin Deep Anomaly Detection](https://mlsanity.com/paper/2603.07073/) (2026)

## Abstract (arXiv)

Multi-class open-set anomaly detection requires a model to characterize the normal acceptance domain formed by multiple heterogeneous subdistributions using only class-labeled samples from known normal classes, and to identify previously unseen anomalies at test time. Existing single-hypersphere methods cannot explicitly represent class-specific locations and acceptance ranges, while current multi-hypersphere or multi-class approaches do not fully integrate inter-class boundary constraints, learnable acceptance ranges, and interpretable decisions. To address these limitations, we propose Interpretable Multi-Hypersphere Deep Anomaly Detection (IMHD-AD). IMHD-AD constructs an independent hypersphere for each known normal class in a shared feature space. With target-inside and non-target-outside constraints, IMHD-AD embeds the class-specific hypersphere centers and radii directly into the final network layer and jointly optimizes them with the shared representation. The minimum signed boundary score across hyperspheres simultaneously determines open-set acceptance or rejection and provides a faithful geometric explanation of each decision. On MNIST, Fashion-MNIST, and CIFAR-10, IMHD-AD achieves the highest AUC in 28 of 30 open-set comparisons. A two-dimensional synthetic study further shows that model architecture must balance the compactness of known normal classes against the separability of unknown anomalies.