Effect of The Latent Structure on Clustering with GANs

Generative adversarial networks (GANs) have shown remarkable success in generation of data from natural data manifolds such as images. In several scenarios, it is desirable that generated data is well-clustered, especially when there is severe class imbalance. In this paper, we focus on the problem of clustering in generated space of GANs and uncover its relationship with the characteristics of the latent space. We derive from first principles, the necessary and sufficient conditions needed to achieve faithful clustering in the GAN framework: (i) presence of a multimodal latent space with adjustable priors, (ii) existence of a latent space inversion mechanism and (iii) imposition of the desired cluster priors on the latent space. We also identify the GAN models in the literature that partially satisfy these conditions and demonstrate the importance of all the components required, through ablative studies on multiple real world image datasets. Additionally, we describe a procedure to construct a multimodal latent space which facilitates learning of cluster priors with sparse supervision.

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.