On Implicit Regularization in $β$-VAEs
This provides theoretical insights into regularization in VAEs, which is incremental for researchers in generative modeling and variational inference.
The paper tackles the problem of understanding how variational inference regularizes learned generative models in VAEs, revealing that the variational family imposes uniqueness and geometric constraints, and derives an implicit regularizer in β-VAEs that unifies them with deterministic autoencoders. The result is empirically verified, showing similar objective values and sample quality.
While the impact of variational inference (VI) on posterior inference in a fixed generative model is well-characterized, its role in regularizing a learned generative model when used in variational autoencoders (VAEs) is poorly understood. We study the regularizing effects of variational distributions on learning in generative models from two perspectives. First, we analyze the role that the choice of variational family plays in imparting uniqueness to the learned model by restricting the set of optimal generative models. Second, we study the regularization effect of the variational family on the local geometry of the decoding model. This analysis uncovers the regularizer implicit in the $β$-VAE objective, and leads to an approximation consisting of a deterministic autoencoding objective plus analytic regularizers that depend on the Hessian or Jacobian of the decoding model, unifying VAEs with recent heuristics proposed for training regularized autoencoders. We empirically verify these findings, observing that the proposed deterministic objective exhibits similar behavior to the $β$-VAE in terms of objective value and sample quality.