Real trained VAE latent spaces organize into measurably distinct ordered, disordered, and glassy phases, and shifting toward a more ordered phase improves anomaly detection

Spin-glass overlap-distribution diagnostics (order parameters, susceptibility) are applied to real trained VAE/autoencoder latent spaces on CIFAR-10, CelebA64, Mars Rover Mastcam, and Galaxy Zoo 64 real image data, projected onto a hypersphere [ascarate-etal-2026-high-dimensional-latents-phase-structure] The latent space organizes into measurably distinct ordered, disordered, and glassy phase regimes rather than varying along a single smooth curvature or dimension number [ascarate-etal-2026-high-dimensional-latents-phase-structure] A hyperspherical-compression intervention that shifts the latent regime toward greater order improves downstream anomaly-detection AUROC on real data: Mars Rover Mastcam kNN-AUROC rises from 0.66 to 0.76, and Galaxy Zoo 64 kNN-AUROC rises from 0.74 to 0.79 [ascarate-etal-2026-high-dimensional-latents-phase-structure]