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.

Various gradient compression schemes have been proposed to mitigate the communication cost in distributed training of large scale machine learning models. Sign-based methods, such as signSGD (Bernstein et al., 2018), have recently been gaining popularity because of their simple compression rule and connection to adaptive gradient methods, like ADAM. In this paper, we perform a general analysis of sign-based methods for non-convex optimization. Our analysis is built on intuitive bounds on success probabilities and does not rely on special noise distributions nor on the boundedness of the variance of stochastic gradients. Extending the theory to distributed setting within a parameter server framework, we assure exponentially fast variance reduction with respect to number of nodes, maintaining 1-bit compression in both directions and using small mini-batch sizes. We validate our theoretical findings experimentally.
General analysis of sign-based methods (e.g. signSGD) for non-convex optimization, built on intuitive bounds on success probabilities.

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

Fine-tuning language models, such as BERT, on domain specific corpora has proven to be valuable in domains like scientific papers and biomedical text. In this paper, we show that fine-tuning BERT on legal documents similarly provides valuable improvements on NLP tasks in the legal domain. Demonstrating this outcome is significant for analyzing commercial agreements, because obtaining large legal corpora is challenging due to their confidential nature. As such, we show that having access to large legal corpora is a competitive advantage for commercial applications, and academic research on analyzing contracts.

Fine-tuning BERT on legal corpora provides marginal, but valuable, improvements on NLP tasks in the legal domain.