Title: Diagnosing High-Dimensional Latents via Phase Structure

Abstract

This study examines the latent spaces of autoencoders and variational autoencoders by applying the framework of spin-glass theory. The research is divided into two primary contributions. First, we establish a spin-glass dictionary for latent spaces: given a fixed decoder, the combination of a reconstruction term and a hyperspherical coordinate prior generates a Hamiltonian on the latent sphere. In this model, latent coordinates function as continuous spins, while the prior serves as an external magnetic field. This theoretical grounding enables the application of established spin-glass diagnostics—such as overlap distributions, susceptibility, and block-spin coarse-graining—to identify ordered, disordered, and edge-of-stability phases within trained latent representations.

Second, we demonstrate that intentionally steering the latent system toward the edge-of-stability of the topological trivialization regime yields tangible benefits for downstream tasks. In generative modeling, this hyperspherical compression enhances the trade-off between reconstruction and generation on CIFAR-10 and CelebA64, resulting in reduced self-FID scores without compromising, and often improving, reconstruction quality. Similarly, in anomaly detection, this semi-ordered latent geometry boosts performance in both fully unsupervised and conditional out-of-distribution (OOD) detection. These improvements were validated across real-world datasets, including Mars Rover and Galaxy Zoo, as well as standard OOD benchmarks like CIFAR-10/100 and Imagenette. Consequently, we propose a phase-aware evaluation paradigm for autoencoders and variational autoencoders, where spin-glass observables supplement conventional machine learning metrics to reveal the latent regimes that determine success or failure in various applications.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC