Learning Hyperspherical Time-Frequency Representations for Time-Series Out-of-Distribution Detection

Long-tailed out-of-distribution (LT-OOD) detection is often addressed with specialized training, including auxiliary out-of-distribution (OOD) data, abstention heads, contrastive objectives, energy losses, or gradient-conflict control. We show that these training mechanisms can obscure a simpler issue: frozen long-tailed representations may already contain useful OOD evidence, but raw Mahalanobis distance is distorted by frequency-coupled feature radius and poorly supported tail covariance. We propose Hyperspherical Pooled Mahalanobis (HPM), a post-hoc detector that normalizes features onto the unit sphere and replaces class-specific covariance with a pooled, ridge-regularized metric while keeping class means as semantic anchors. In CIFAR-LT experiments and an ImageNet-100-LT near-OOD boundary analysis, HPM improves raw Mahalanobis scoring; for Prior-Calibrated ERM (PC-ERM), it raises AUROC from 46.49 to 85.67 on CIFAR-10-LT and from 50.40 to 78.35 on CIFAR-100-LT. This simple PC-ERM+HPM pipeline also achieves the best Log Efficiency Score (LES; 3.08) on CIFAR-100-LT, retaining roughly 95% of the best CIFAR-100-LT AUROC observed among the compared post-hoc scores at substantially lower training-time cost. These results argue for evaluating representation quality, detector geometry, and training complexity as separate factors in LT-OOD detection.

We introduce MM++ (Multilayer Mahalanobis++), a strictly post-hoc, and scale-invariant framework for Out-of-Distribution (OOD) detection. To address the trade-off between scale invariance and hierarchical expressivity, MM++ constructs a principled joint feature space. It first identifies discriminative intermediate layers by measuring entropy density drops, which mark the boundaries of sharp semantic compression. By fusing these selected layers with the terminal representation, the framework captures latent cross-layer correlations while mitigating early-layer noise. Crucially, a Ledoit-Wolf regularized tied covariance matrix stabilizes this unified space, enabling reliable distance estimation. Requiring no auxiliary OOD data, classifier fine-tuning, or architectural modifications, MM++ delivers robust performance across distinct architectures for both near- and far-OOD detection.

Reliable detection of out-of-distribution (OOD) samples is crucial for the safe deployment of machine learning models. Neural networks often produce overconfident predictions for inputs that deviate from their training data, leading to significant degradation in performance. While many OOD detection methods focus on the final output layer, they neglect the rich hierarchical information present in intermediate network layers. This paper introduces a novel approach that leverages sparse autoencoders (SAEs) to learn interpretable features from these intermediate activations. We find that in-distribution (ID) and OOD data activate distinct sets of these sparse features. We propose a new OOD score derived from the cosine similarity between the sparse feature activations of a test sample and the mean activations of ID classes. Our post-hoc detection method not only achieves state-of-the-art performance on standard OOD detection benchmarks, but yields interpretable insights into how distribution shift affects learned representations.