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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.
The key idea of the state-of-the-art VAE-based unsupervised representation disentanglement methods is to minimize the total correlation of the latent variable distributions. However, it has been proved that VAE-based unsupervised disentanglement can
Recent work by Locatello et al. (2018) has shown that an inductive bias is required to disentangle factors of interest in Variational Autoencoder (VAE). Motivated by a real-world problem, we propose a setting where such bias is introduced by providin
Disentangling data into interpretable and independent factors is critical for controllable generation tasks. With the availability of labeled data, supervision can help enforce the separation of specific factors as expected. However, it is often expe
Learning rich representation from data is an important task for deep generative models such as variational auto-encoder (VAE). However, by extracting high-level abstractions in the bottom-up inference process, the goal of preserving all factors of va
Learning interpretable and disentangled representations is a crucial yet challenging task in representation learning. In this work, we focus on semi-supervised disentanglement learning and extend work by Locatello et al. (2019) by introducing another