$β$-VAEs as Effective Theories: Tolerance-Dependent Dimension
In a $β$-VAE, increasing the regularization strength acts as a spectral cutoff by collapsing low-utility latent coordinates. In the linear Gaussian VAE, the collapse order matches the ranking of reconstruction utilities exactly, because both are set by the PCA spectrum. We ask which parts of this picture survive in fully connected nonlinear VAEs trained on WorldClim. We find that nonlinear interactions shift and broaden collapse onsets, so thresholds no longer coincide exactly with utilities. However, the common ordering is preserved over the resolved ranks, so the spectral cutoff still acts as a utility cutoff and the effective-description logic carries through. The resulting effective-d...
| Authors | Johannes Hirn |
|---|---|
| Primary category | cs.LG |
| Published | 11 August 2026 |
| Last updated at source | 11 August 2026 |
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