We develop a generalised notion of disentanglement in Variational Auto-Encoders (VAEs) by casting it as a \emph{decomposition} of the latent representation, characterised by i) enforcing an appropriate level of overlap in the latent encodings of the data, and ii) regularisation of the average encoding to a desired structure, represented through the prior. We motivate this by showing that a) the $\beta$-VAE disentangles purely through regularisation of the overlap in latent encodings, and through its average (Gaussian) encoder variance, and b) disentanglement, as independence between latents, can be cast as a regularisation of the aggregate posterior to a prior with specific characteristics. We validate this characterisation by showing that simple manipulations of these factors, such as using rotationally variant priors, can help improve disentanglement, and discuss how this characterisation provides a more general framework to incorporate notions of decomposition beyond just independence between the latents.

本文提出了VAEs的解耦合方法，即分解潜在表示，通过先验中有结构的聚合编码和适当的重叠来满足。这种分解不仅能实现特定的解耦，还可通过引入先验来实现其他更丰富类型的约束，并通过控制先验和潜在空间分布来改善解耦效果。此外，还介绍了另一套训练目标和先验选择来控制分解和解耦，并对β-VAE在控制潜在空间重叠方面的性质进行了分析。

变分自编码器中的解缠纷问题