Towards Latent Space Optimality for Auto-Encoder Based Generative Models

The field of neural generative models is dominated by the highly successful Generative Adversarial Networks (GANs) despite their challenges, such as training instability and mode collapse. Auto-Encoders (AE) with regularized latent space provides an alternative framework for generative models, albeit their performance levels have not reached that of GANs. In this work, we identify one of the causes for the under-performance of AE-based models and propose a remedial measure. Specifically, we hypothesize that the dimensionality of the AE model's latent space has a critical effect on the quality of the generated data. Under the assumption that nature generates data by sampling from a "true" generative latent space followed by a deterministic non-linearity, we show that the optimal performance is obtained when the dimensionality of the latent space of the AE-model matches with that of the "true" generative latent space. Further, we propose an algorithm called the Latent Masked Generative Auto-Encoder (LMGAE), in which the dimensionality of the model's latent space is brought closer to that of the "true" generative latent space, via a novel procedure to mask the spurious latent dimensions. We demonstrate through experiments on synthetic and several real-world datasets that the proposed formulation yields generation quality that is better than the state-of-the-art AE-based generative models and is comparable to that of GANs.