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.

Input: Consider Input: Despite the fact that generative models are extremely successful in practice, the theory underlying this phenomenon is only starting to catch up with practice. In this work we address the question of the universality of generative models: is it true that neural networks can approximate any data manifold arbitrarily well? We provide a positive answer to this question and show that under mild assumptions on the activation function one can always find a feedforward neural network that maps the latent space onto a set located within the specified Hausdorff distance from the desired data manifold. We also prove similar theorems for the case of multiclass generative models and cycle generative models, trained to map samples from one manifold to another and vice versa.

Output: We shot that a wide class of manifolds can be generated by ReLU and sigmoid networks with arbitrary precision.


Input: Consider Input: Generative Adversarial Networks (GANs) can achieve state-of-the-art sample quality in generative modelling tasks but suffer from the mode collapse problem. Variational Autoencoders (VAE) on the other hand explicitly maximize a reconstruction-based data log-likelihood forcing it to cover all modes, but suffer from poorer sample quality. Recent works have proposed hybrid VAE-GAN frameworks which integrate a GAN-based synthetic likelihood to the VAE objective to address both the mode collapse and sample quality issues, with limited success. This is because the VAE objective forces a trade-off between the data log-likelihood and divergence to the latent prior. The synthetic likelihood ratio term also shows instability during training. We propose a novel objective with a ``"Best-of-Many-Samples" reconstruction cost and a stable direct estimate of the synthetic likelihood. This enables our hybrid VAE-GAN framework to achieve high data log-likelihood and low divergence to the latent prior at the same time and shows significant improvement over both hybrid VAE-GANS and plain GANs in mode coverage and quality.

Output: We propose a new objective for training hybrid VAE-GANs which lead to significant improvement in mode coverage and quality.


Input: Consider Input: We propose an approach for sequence modeling based on autoregressive normalizing flows. Each autoregressive transform, acting across time, serves as a moving reference frame for modeling higher-level dynamics. This technique provides a simple, general-purpose method for improving sequence modeling, with connections to existing and classical techniques. We demonstrate the proposed approach both with standalone models, as well as a part of larger sequential latent variable models. Results are presented on three benchmark video datasets, where flow-based dynamics improve log-likelihood performance over baseline models.


Output: We show how autoregressive flows can be used to improve sequential latent variable models.