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This research proposes using spin-glass theory to diagnose the phase structure of autoencoder latent spaces, offering a physics-based framework to detect ordered and disordered regimes. By driving the system toward the edge-of-stability, the authors demonstrate improved reconstruction-generation trade-offs and enhanced out-of-distribution detection across standard and real-world datasets. The work advocates for a phase-aware evaluation paradigm that complements standard metrics with spin-glass observables to better understand latent representation dynamics.
High-Dimensional Latents Should Be Diagnosed Through Phase Structure
arXiv:2606.02600v1 Announce Type: cross 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.
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.
Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG)
arXiv:2606.02600 [cond-mat.dis-nn]
(or arXiv:2606.02600v1 [cond-mat.dis-nn] for this version)
https://doi.org/10.48550/arXiv.2606.02600 Focus to learn more arXiv-issued DOI via DataCite
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