In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

In this article we use rate-distortion theory, a branch of information theory devoted to the problem of lossy compression, to shed light on an important problem in latent variable modeling of data: is there room to improve the model? One way to address this question is to find an upper bound on the probability (equivalently a lower bound on the negative log likelihood) that the model can assign to some data as one varies the prior and/or the likelihood function in a latent variable model. The core of our contribution is to formally show that the problem of optimizing priors in latent variable models is exactly an instance of the variational optimization problem that information theorists solve when computing rate-distortion functions, and then to use this to derive a lower bound on negative log likelihood. Moreover, we will show that if changing the prior can improve the log likelihood, then there is a way to change the likelihood function instead and attain the same log likelihood, and thus rate-distortion theory is of relevance to both optimizing priors as well as optimizing likelihood functions. We will experimentally argue for the usefulness of quantities derived from rate-distortion theory in latent variable modeling by applying them to a problem in image modeling.
Use rate-distortion theory to bound how much a latent variable model can be improved

In the past few years, various advancements have been made in generative models owing to the formulation of Generative Adversarial Networks (GANs). GANs have been shown to perform exceedingly well on a wide variety of tasks pertaining to image generation and style transfer. In the field of Natural Language Processing, word embeddings such as word2vec and GLoVe are state-of-the-art methods for applying neural network models on textual data. Attempts have been made for utilizing GANs with word embeddings for text generation. This work presents an approach to text generation using Skip-Thought sentence embeddings in conjunction with GANs based on gradient penalty functions and f-measures. The results of using sentence embeddings with GANs for generating text conditioned on input information are comparable to the approaches where word embeddings are used.
Generating text using sentence embeddings from Skip-Thought Vectors with the help of Generative Adversarial Networks.

We relate the minimax game of generative adversarial networks (GANs) to finding the saddle points of the Lagrangian function for a convex optimization problem, where the discriminator outputs and the distribution of generator outputs play the roles of primal variables and dual variables, respectively. This formulation shows the connection between the standard GAN training process and the primal-dual subgradient methods for convex optimization. The inherent connection does not only provide a theoretical convergence proof for training GANs in the function space, but also inspires a novel objective function for training. The modified objective function forces the distribution of generator outputs to be updated along the direction according to the primal-dual subgradient methods. A toy example shows that the proposed method is able to resolve mode collapse, which in this case cannot be avoided by the standard GAN or Wasserstein GAN. Experiments on both Gaussian mixture synthetic data and real-world image datasets demonstrate the performance of the proposed method on generating diverse samples.

We propose a primal-dual subgradient method for training GANs and this method effectively alleviates mode collapse.