GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models

Diffusion models learn a time-indexed score field $\mathbf{s}_θ(\mathbf{x}_t,t)$ that often inherits approximate equivariances (flips, rotations, circular shifts) from in-distribution (ID) data and convolutional backbones. Most diffusion-based out-of-distribution (OOD) detectors exploit score magnitude or local geometry (energies, curvature, covariance spectra) and largely ignore equivariances. We introduce Group-Equivariant Posterior Consistency (GEPC), a training-free probe that measures how consistently the learned score transforms under a finite group $\mathcal{G}$, detecting equivariance breaking even when score magnitude remains unchanged. At the population level, we propose the ideal GEPC residual, which averages an equivariance-residual functional over $\mathcal{G}$, and we derive ID upper bounds and OOD lower bounds under mild assumptions. GEPC requires only score evaluations and produces interpretable equivariance-breaking maps. On OOD image benchmark datasets, we show that GEPC achieves competitive or improved AUROC compared to recent diffusion-based baselines while remaining computationally lightweight. On high-resolution synthetic aperture radar imagery where OOD corresponds to targets or anomalies in clutter, GEPC yields strong target-background separation and visually interpretable equivariance-breaking maps. Code is available at https://github.com/RouzAY/gepc-diffusion/.

Out-of-Distribution Radar Detection with Complex VAEs: Theory, Whitening, and ANMF Fusion

We investigate the detection of weak complex-valued signals immersed in non-Gaussian, range-varying interference, with emphasis on maritime radar scenarios. The proposed methodology exploits a Complex-valued Variational AutoEncoder (CVAE) trained exclusively on clutter-plus-noise to perform Out-Of-Distribution detection. By operating directly on in-phase / quadrature samples, the CVAE preserves phase and Doppler structure and is assessed in two configurations: (i) using unprocessed range profiles and (ii) after local whitening, where per-range covariance estimates are obtained from neighboring profiles. Using extensive simulations together with real sea-clutter data from the CSIR maritime dataset, we benchmark performance against classical and adaptive detectors (MF, NMF, AMF-SCM, ANMF-SCM, ANMF-Tyler). In both configurations, the CVAE yields a higher detection probability Pd at matched false-alarm rate Pfa, with the most notable improvements observed under whitening. We further integrate the CVAE with the ANMF through a weighted log-p fusion rule at the decision level, attaining enhanced robustness in strongly non-Gaussian clutter and enabling empirically calibrated Pfa control under H0. Overall, the results demonstrate that statistical normalization combined with complex-valued generative modeling substantively improves detection in realistic sea-clutter conditions, and that the fused CVAE-ANMF scheme constitutes a competitive alternative to established model-based detectors.

Deinterleaving of Discrete Renewal Process Mixtures with Application to Electronic Support Measures

In this paper, we propose a new deinterleaving method for mixtures of discrete renewal Markov chains. This method relies on the maximization of a penalized likelihood score. It exploits all available information about both the sequence of the different symbols and their arrival times. A theoretical analysis is carried out to prove that minimizing this score allows to recover the true partition of symbols in the large sample limit, under mild conditions on the component processes. This theoretical analysis is then validated by experiments on synthetic data. Finally, the method is applied to deinterleave pulse trains received from different emitters in a RESM (Radar Electronic Support Measurements) context and we show that the proposed method competes favorably with state-of-the-art methods on simulated warfare datasets.