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.
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Question: Building on the success of deep learning, two modern approaches to learn a probability model of the observed data are Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs). VAEs consider an explicit probability model for the data and compute a generative distribution by maximizing a variational lower-bound on the log-likelihood function. GANs, however, compute a generative model by minimizing a distance between observed and generated probability distributions without considering an explicit model for the observed data. The lack of having explicit probability models in GANs prohibits computation of sample likelihoods in their frameworks and limits their use in statistical inference problems. In this work, we show that an optimal transport GAN with the entropy regularization can be viewed as a generative model that maximizes a lower-bound on average sample likelihoods, an approach that VAEs are based on. In particular, our proof constructs an explicit probability model for GANs that can be used to compute likelihood statistics within GAN's framework. Our numerical results on several datasets demonstrate consistent trends with the proposed theory.

Answer: A statistical approach to compute sample likelihoods in Generative Adversarial Networks

Question: We consider a simple and overarching representation for permutation-invariant functions of sequences (or set functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with k-order interactions, and stochastic optimization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.

Answer: We propose Janossy pooling, a method for learning deep permutation invariant functions designed to exploit relationships within the input sequence and tractable inference strategies such as a stochastic optimization procedure we call piSGD

Question: For understanding generic documents, information like font sizes, column layout, and generally the positioning of words may carry semantic information that is crucial for solving a downstream document intelligence task. Our novel BERTgrid, which is based on Chargrid by Katti et al. (2018), represents a document as a grid of contextualized word piece embedding vectors, thereby making its spatial structure and semantics accessible to the processing neural network. The contextualized embedding vectors are retrieved from a BERT language model. We use BERTgrid in combination with a fully convolutional network on a semantic instance segmentation task for extracting fields from invoices. We demonstrate its performance on tabulated line item and document header field extraction.

Answer:
Grid-based document representation with contextualized embedding vectors for documents with 2D layouts