We view disentanglement learning as discovering an underlying structure that equivariantly reflects the factorized variations shown in data. Traditionally, such a structure is fixed to be a vector space with data variations represented by translations along individual latent dimensions. We argue this simple structure is suboptimal since it requires the model to learn to discard the properties (e.g. different scales of changes, different levels of abstractness) of data variations, which is an extra work than equivariance learning. Instead, we propose to encode the data variations with groups, a structure not only can equivariantly represent variations, but can also be adaptively optimized to preserve the properties of data variations. Considering it is hard to conduct training on group structures, we focus on Lie groups and adopt a parameterization using Lie algebra. Based on the parameterization, some disentanglement learning constraints are naturally derived. A simple model named Commutative Lie Group VAE is introduced to realize the group-based disentanglement learning. Experiments show that our model can effectively learn disentangled representations without supervision, and can achieve state-of-the-art performance without extra constraints.

通过将数据变化编码为Lie群的结构，我们提出了一种利用变换等变地表示变化的不受限制的、自适应优化的组结构，实现了无监督的解缠结学习，并在不增加额外约束的情况下取得了最先进的性能。

可交换李群变分自编码器用于分离学习