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]: Generative Adversarial Networks (GANs), when trained on large datasets with diverse modes, are known to produce conflated images which do not distinctly belong to any of the modes. We hypothesize that this problem occurs due to the interaction between two facts: (1) For datasets with large variety, it is likely that the modes lie on separate manifolds. (2) The generator (G) is formulated as a continuous function, and the input noise is derived from a connected set, due to which G's output is a connected set. If G covers all modes, then there must be some portion of G's output which connects them. This corresponds to undesirable, conflated images. We develop theoretical arguments to support these intuitions. We propose a novel method to break the second assumption via learnable discontinuities in the latent noise space. Equivalently, it can be viewed as training several generators, thus creating discontinuities in the G function. We also augment the GAN formulation with a classifier C that predicts which noise partition/generator produced the output images, encouraging diversity between each partition/generator. We experiment on MNIST, celebA, STL-10, and a difficult dataset with clearly distinct modes, and show that the noise partitions correspond to different modes of the data distribution, and produce images of superior quality.
[A]: We introduce theory to explain the failure of GANs on complex datasets and propose a solution to fix it.


[Q]: Domain transfer is a exciting and challenging branch of machine learning because models must learn to smoothly transfer between domains, preserving local variations and capturing many aspects of variation without labels. 
 However, most successful applications to date require the two domains to be closely related (ex. image-to-image, video-video), 
 utilizing similar or shared networks to transform domain specific properties like texture, coloring, and line shapes. 
 Here, we demonstrate that it is possible to transfer across modalities (ex. image-to-audio) by first abstracting the data with latent generative models and then learning transformations between latent spaces. 
 We find that a simple variational autoencoder is able to learn a shared latent space to bridge between two generative models in an unsupervised fashion, and even between different types of models (ex. variational autoencoder and a generative adversarial network). 
 We can further impose desired semantic alignment of attributes with a linear classifier in the shared latent space. 
 The proposed variation autoencoder enables preserving both locality and semantic alignment through the transfer process, as shown in the qualitative and quantitative evaluations.
 Finally, the hierarchical structure decouples the cost of training the base generative models and semantic alignments, enabling computationally efficient and data efficient retraining of personalized mapping functions.
[A]: Conditional VAE on top of latent spaces of pre-trained generative models that enables  transfer between drastically different domains while preserving locality and semantic alignment.


[Q]: RMSProp and ADAM continue to be extremely popular algorithms for training neural nets but their theoretical convergence properties have remained unclear. Further, recent work has seemed to suggest that these algorithms have worse generalization properties when compared to carefully tuned stochastic gradient descent or its momentum variants. In this work, we make progress towards a deeper understanding of ADAM and RMSProp in two ways. First, we provide proofs that these adaptive gradient algorithms are guaranteed to reach criticality for smooth non-convex objectives, and we give bounds on the running time.

 Next we design experiments to empirically study the convergence and generalization properties of RMSProp and ADAM against Nesterov's Accelerated Gradient method on a variety of common autoencoder setups and on VGG-9 with CIFAR-10. Through these experiments we demonstrate the interesting sensitivity that ADAM has to its momentum parameter \beta_1. We show that at very high values of the momentum parameter (\beta_1 = 0.99) ADAM outperforms a carefully tuned NAG on most of our experiments, in terms of getting lower training and test losses. On the other hand, NAG can sometimes do better when ADAM's \beta_1 is set to the most commonly used value: \beta_1 = 0.9, indicating the importance of tuning the hyperparameters of ADAM to get better generalization performance.

 We also report experiments on different autoencoders to demonstrate that NAG has better abilities in terms of reducing the gradient norms, and it also produces iterates which exhibit an increasing trend for the minimum eigenvalue of the Hessian of the loss function at the iterates.
[A]:
In this paper we prove convergence to criticality of (stochastic and deterministic) RMSProp and deterministic ADAM for smooth non-convex objectives and we demonstrate an interesting beta_1 sensitivity for ADAM on autoencoders.