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.

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, and understanding the dynamics of (stochastic) gradient algorithms for solving such formulations has been a grand challenge. As a first step, we restrict to bilinear zero-sum games and give a systematic analysis of popular gradient updates, for both simultaneous and alternating versions. We provide exact conditions for their convergence and find the optimal parameter setup and convergence rates. In particular, our results offer formal evidence that alternating updates converge "better" than simultaneous ones.
We systematically analyze the convergence behaviour of popular gradient algorithms for solving bilinear games, with both simultaneous and alternating updates.

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 scalable in sample size and dimensions mutual information estimator.

Many models based on the Variational Autoencoder are proposed to achieve disentangled latent variables in inference. However, most current work is focusing on designing powerful disentangling regularizers, while the given number of dimensions for the latent representation at initialization could severely inﬂuence the disentanglement. Thus, a pruning mechanism is introduced, aiming at automatically seeking for the intrinsic dimension of the data while promoting disentangled representations. The proposed method is validated on MPI3D and MNIST to be advancing state-of-the-art methods in disentanglement, reconstruction, and robustness. The code is provided on the https://github.com/WeyShi/FYP-of-Disentanglement.

The Pruning VAE is proposed to search for disentangled variables with intrinsic dimension.