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.

Q: This paper presents a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size. MINE is  back-propable and we prove that it is strongly consistent. We illustrate a handful of applications in which MINE is succesfully applied  to enhance the property of generative models in both unsupervised and supervised settings. We apply our framework to estimate the information bottleneck, and apply it in tasks related to supervised classification problems. Our results  demonstrate substantial added flexibility and improvement in these settings.


A: A scalable in sample size and dimensions mutual information estimator.
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Q: We present a deep generative model, named Monge-Amp\`ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\`ere equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution. Training of the model amounts to solving an optimal control problem. The Monge-Amp\`ere flow has tractable likelihoods and supports efficient sampling and inference. One can easily impose symmetry constraints in the generative model by designing suitable scalar potential functions. We apply the approach to unsupervised density estimation of the MNIST dataset and variational calculation of the two-dimensional Ising model at the critical point. This approach brings insights and techniques from Monge-Amp\`ere equation, optimal transport, and fluid dynamics into reversible flow-based generative models.

A: A gradient flow based dynamical system for invertible generative modeling
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Q: Asynchronous distributed gradient descent algorithms for training of deep neural
 networks are usually considered as inefficient, mainly because of the Gradient delay
 problem. In this paper, we propose a novel asynchronous distributed algorithm
 that tackles this limitation by well-thought-out averaging of model updates, computed
 by workers. The algorithm allows computing gradients along the process
 of gradient merge, thus, reducing or even completely eliminating worker idle time
 due to communication overhead, which is a pitfall of existing asynchronous methods.
 We provide theoretical analysis of the proposed asynchronous algorithm,
 and show its regret bounds. According to our analysis, the crucial parameter for
 keeping high convergence rate is the maximal discrepancy between local parameter
 vectors of any pair of workers. As long as it is kept relatively small, the
 convergence rate of the algorithm is shown to be the same as the one of a sequential
 online learning. Furthermore, in our algorithm, this discrepancy is bounded
 by an expression that involves the staleness parameter of the algorithm, and is
 independent on the number of workers. This is the main differentiator between
 our approach and other solutions, such as Elastic Asynchronous SGD or Downpour
 SGD, in which that maximal discrepancy is bounded by an expression that
 depends on the number of workers, due to gradient delay problem. To demonstrate
 effectiveness of our approach, we conduct a series of experiments on image
 classification task on a cluster with 4 machines, equipped with a commodity communication
 switch and with a single GPU card per machine. Our experiments
 show a linear scaling on 4-machine cluster without sacrificing the test accuracy,
 while eliminating almost completely worker idle time. Since our method allows
 using commodity communication switch, it paves a way for large scale distributed
 training performed on commodity clusters.

A:
A method for an efficient asynchronous distributed training of deep learning models along with theoretical regret bounds.
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