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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.09277 |
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| _version_ | 1866914318313848832 |
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| author | Vu, Minh Wan, Xiaoliang Wei, Shuangqing |
| author_facet | Vu, Minh Wan, Xiaoliang Wei, Shuangqing |
| contents | 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 $L_2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09277 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mutual Information Collapse Explains Disentanglement Failure in $β$-VAEs Vu, Minh Wan, Xiaoliang Wei, Shuangqing Machine Learning 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 $L_2$ 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. |
| title | Mutual Information Collapse Explains Disentanglement Failure in $β$-VAEs |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.09277 |