High-Dimensional Latents Should Be Diagnosed Through Phase Structure

• URL: http://arxiv.org/abs/2606.02600v1
• Date: Sat, 23 May 2026 06:17:23 GMT
• Title: High-Dimensional Latents Should Be Diagnosed Through Phase Structure
• Abstract summary: We study autoencoder and variational-autoencoder latent spaces through the lens of spin-glass theory.<n>We formalize a latent-space spin-glass dictionary for a fixed decoder.<n>We show that driving the latent system toward the edge-of-stability of the topological trivialization regime has concrete downstream consequences.
• Score: 56.362776482614976
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study autoencoder and variational-autoencoder latent spaces through the lens of spin-glass theory. The paper has two components. First, we formalize a latent-space spin-glass dictionary: for a fixed decoder, the reconstruction term together with a hyperspherical coordinates prior induces a Hamiltonian on the latent sphere, where latent coordinates play the role of continuous spins and the prior acts as an external magnetic field. This allows us to import operational spin-glass diagnostics -- overlap distributions, susceptibility, and block-spin coarse-graining -- to detect ordered, disordered, and edge-of-stability phases in trained latent representations. Second, we show that deliberately driving the latent system toward the edge-of-stability of the topological trivialization regime has concrete downstream consequences. In generation, hyperspherical compression improves the reconstruction-generation trade-off on CIFAR-10 and CelebA64, yielding lower self-FID while preserving or improving reconstruction. In anomaly detection, the same semi-ordered latent geometry improves both fully unsupervised and conditional OOD detection, including real-world Mars Rover and Galaxy Zoo datasets, as well as CIFAR-10/100 and Imagenette-based OOD benchmarks. We therefore advocate a phase-aware evaluation paradigm for AEs/VAEs, in which spin-glass observables complement standard ML metrics and expose the latent regimes that underlie downstream success or failure in many cases.

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