Mutual Information Collapse Explains Disentanglement Failure in β-VAEs

The β-VAE is a foundational framework for unsupervised disentanglement, using β to regulate the trade-off between latent factorization and reconstruction fidelity. Empirically, however, disentanglement performance exhibits a pervasive non-monotonic trend: benchmarks such as MIG and SAP typically peak at intermediate β and collapse as regularization increases. We demonstrate that this collapse is a fundamental information-theoretic failure, where strong Kullback-Leibler pressure promotes marginal independence at the expense of the latent channel's semantic informativeness. By formalizing this mechanism in a linear-Gaussian setting, we prove that for β > 1, stationarity-induced dynamics trigger a spectral contraction of the encoder gain, driving latent-factor mutual information to zero. To resolve this, we introduce the λβ-VAE, which decouples regularization pressure from informational collapse via an auxiliary L2 reconstruction penalty λ. Extensive experiments on dSprites, Shapes3D, and MPI3D-real confirm that λ > 0 stabilizes disentanglement and restores latent informativeness over a significantly broader range of β, providing a principled theoretical justification for dual-parameter regularization in variational inference backbones.