Deep latentvariable models learn representations of highdimensional data in an unsupervised manner. A number of recent efforts have focused on learning representations that disentangle statistically independent axes of variation by introducing modifications to the standard objective function. These approaches generally assume a simple diagonal Gaussian prior and as a result are not able to reliably disentangle discrete factors of variation. We propose a twolevel hierarchical objective to control relative degree of statistical independence between blocks of variables and individual variables within blocks. We derive this objective as a generalization of the evidence lower bound, which allows us to explicitly represent the tradeoffs between mutual information between data and representation, KL divergence between representation and prior, and coverage of the support of the empirical data distribution. Experiments on a variety of datasets demonstrate that our objective can not only disentangle discrete variables, but that doing so also improves disentanglement of other variables and, importantly, generalization even to unseen combinations of factors
RateRegularization and Generalization in Variational Autoencoders
Variational autoencoders (VAEs) optimize an objective that comprises a reconstruction loss (the distortion) and a KL term (the rate). The rate is an upper bound on the mutual information, which is often interpreted as a regularizer that controls the degree of compression. We here examine whether inclusion of the rate term also improves generalization. We perform ratedistortion analyses in which we control the strength of the rate term, the network capacity, and the difficulty of the generalization problem. Lowering the strength of the rate term paradoxically improves generalization in most settings, and reducing the mutual information typically leads to underfitting. Moreover, we show that generalization performance continues to improve even after the mutual information saturates, indicating that the gap on the bound (i.e. the KL divergence relative to the inference marginal) affects generalization. This suggests that the standard spherical Gaussian prior is not an inductive bias that typically improves generalization, prompting further work to understand what choices of priors improve generalization in VAEs.
 Editors:
 Banerjee, A.; Fukumizu, K.
 Award ID(s):
 1901117
 Publication Date:
 NSFPAR ID:
 10280434
 Journal Name:
 Proceedings of The 24th International Conference on Artificial Intelligence and Statistics
 Volume:
 130
 Page Range or eLocationID:
 38803888
 Sponsoring Org:
 National Science Foundation
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