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When designing variational autoencoders (VAEs) or other types of latent spacemodels, the dimensionality of the latent space is typically defined upfront. Inthis process, it is possible that the number of dimensions is under- oroverprovisioned for the application at hand. In case the dimensionality is notpredefined, this parameter is usually determined using time- andresource-consuming cross-validation. For these reasons we have developed atechnique to shrink the latent space dimensionality of VAEs automatically andon-the-fly during training using Generalized ELBO with Constrained Optimization(GECO) and the $L_0$-Augment-REINFORCE-Merge ($L_0$-ARM) gradient estimator.The GECO optimizer ensures that we are not violating a predefined upper boundon the reconstruction error. This paper presents the algorithmic details of ourmethod along with experimental results on five different datasets. We find thatour training procedure is stable and that the latent space can be prunedeffectively without violating the GECO constraints.

Dynamic Narrowing of VAE Bottlenecks Using GECO and L0 Regularization