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We derive this as a consequence of the loss via a Landau stability analysis. We define a latent-rescaling-invariant order parameter that ranks active latent modes and whose collapse thresholds identify which effective variables to inspect first.
In the linear Gaussian case, the collapse spectrum, utility spectrum, and normalized PCA spectrum coincide, and each collapse follows a mean-field law. We test these predictions on the WorldClim dataset.
| Subjects: | Machine Learning (cs.LG); Statistical Mechanics (cond-mat.stat-mech) |
| Cite as: | arXiv:2605.22691 [cs.LG] |
| (or arXiv:2605.22691v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.22691 arXiv-issued DOI via DataCite (pending registration) |
From: Johannes Hirn [view email]
[v1]
Thu, 21 May 2026 16:36:10 UTC (344 KB)
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