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.

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