Generative adversarial networks (GANs) have been broadly applied to a wide range of application domains since their proposal. In this thesis,  we propose several methods that aim to tackle different existing problems in GANs. Particularly, even though GANs are generally  able to generate high-quality samples, the diversity of the generated set is often sub-optimal. Moreover, the common increase of the number of  models in the original GANs framework, as well as their architectural sizes, introduces additional costs. Additionally, even though challenging, the  proper evaluation of a generated  set is an  important  direction to ultimately improve the generation process in GAN's.

We start by introducing two diversification methods that extend the original GANs framework to multiple adversaries to stimulate sample diversity in a gen- erated set. Then, we introduce  a new post-training  compression  method  based on Monte Carlo methods and importance sampling to quantize and prune the weights and activations of pre-trained neural networks without any additional training. The previous method may be used to reduce the memory and com- putational costs introduced by increasing the number of models in the original GANs framework. Moreover, we use a similar procedure to quantize and prune gradients during training, which also reduces the communication costs between different workers in a distributed training setting.

We introduce several topology-based evaluation methods to assess data gen- eration in different settings, namely  image  generation  and  language  genera- tion. Our methods retrieve both single-valued and double-valued metrics, which, given a real set, may be used to broadly assess a generated set or separately evaluate sample  quality and sample diversity,  respectively. Moreover,  two of our metrics use locality-sensitive hashing to accurately  assess the  generated sets of highly compressed GANs. The analysis of the compression effects in GANs paves the way for their efficient employment in real-world applications.

Given their general applicability, the methods proposed in this thesis may be extended beyond  the  context  of GANs. Hence, they may be generally  applied to enhance existing neural networks and, in particular, generative frameworks.