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arXiv 2602.09277stat.MLcs.LG
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互信息崩溃解释了β-VAEs中的解耦失败

Mutual Information Collapse Explains Disentanglement Failure in $β$-VAEs

Department of Mathematics, Miami University, Oxford, OH, USA;Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA;Division of Electrical \& Computer Engineering, Louisiana State University, Baton Rouge, LA, USA

Minh Vu, Xiaoliang Wan, Shuangqing Wei

AI总结:

β-VAE中解耦失败源于互信息崩溃,通过引入λβ-VAE和L2正则化惩罚解决信息论失效问题。

摘要:

β-VAE是无监督解耦的基础框架,使用β来调节潜在因子分解与重建保真度之间的权衡。然而,经验上,解耦性能表现出普遍的非单调趋势:诸如MIG和SAP等基准通常在中间β值时达到峰值,随着正则化增加而崩溃。我们证明这种崩溃是一种信息论上的失败,强的Kullback-Leibler压力会以牺牲潜在通道语义信息量为代价促进边缘独立性。通过在线性高斯设置中正式化这一机制,我们证明对于β>1,站稳性诱导的动力学触发编码器增益的谱收缩,使潜在因子互信息趋于零。为了解决这一问题,我们引入了λβ-VAE,通过辅助的L2重建惩罚λ将正则化压力与信息崩溃解耦。在dSprites、Shapes3D和MPI3D-real上的广泛实验表明,λ>0可以稳定解耦并恢复潜在信息量,使其在显著更宽的β范围内恢复,为变分推断骨干中的双参数正则化提供了原理性理论依据。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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