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.

[EX Q]: Understanding the behavior of  stochastic gradient descent (SGD) in the context of deep neural networks has raised lots of concerns recently. Along this line, we theoretically study a general form of gradient based optimization dynamics with unbiased noise, which unifies SGD and standard Langevin dynamics. Through investigating this general optimization dynamics, we analyze the behavior of SGD on escaping from minima and its regularization effects. A novel indicator is derived to characterize the efficiency of escaping from minima through measuring the alignment of noise covariance and the curvature of loss function. Based on this indicator, two conditions are established to show which type of noise structure is superior to isotropic noise in term of escaping efficiency. We further show that the anisotropic noise in SGD satisfies the two conditions, and thus helps to  escape from sharp and poor minima effectively, towards more stable and flat minima that typically generalize well. We verify our understanding through comparing
 this anisotropic diffusion with full gradient descent plus isotropic diffusion (i.e. Langevin dynamics) and other types of position-dependent noise.
[EX A]: We provide theoretical and empirical analysis on the role of anisotropic noise introduced by stochastic gradient on escaping from minima.

[EX Q]: Learning representations of data is an important issue in machine learning. Though GAN has led to significant improvements in the data representations, it still has several problems such as unstable training, hidden manifold of data, and huge computational overhead. GAN tends to produce the data simply without any information about the manifold of the data, which hinders from controlling desired features to generate. Moreover, most of GAN’s have a large size of manifold, resulting in poor scalability. In this paper, we propose a novel GAN to control the latent semantic representation, called LSC-GAN, which allows us to produce desired data to generate and learns a representation of the data efficiently. Unlike the conventional GAN models with hidden distribution of latent space, we define the distributions explicitly in advance that are trained to generate the data based on the corresponding features by inputting the latent variables that follow the distribution. As the larger scale of latent space caused by deploying various distributions in one latent space makes training unstable while maintaining the dimension of latent space, we need to separate the process of defining the distributions explicitly and operation of generation. We prove that a VAE is proper for the former and modify a loss function of VAE to map the data into the pre-defined latent space so as to locate the reconstructed data as close to the input data according to its characteristics. Moreover, we add the KL divergence to the loss function of LSC-GAN to include this process. The decoder of VAE, which generates the data with the corresponding features from the pre-defined latent space, is used as the generator of the LSC-GAN. Several experiments on the CelebA dataset are conducted to verify the usefulness of the proposed method to generate desired data stably and efficiently, achieving a high compression ratio that can hold about 24 pixels of information in each dimension of latent space. Besides, our model learns the reverse of features such as not laughing (rather frowning) only with data of ordinary and smiling facial expression.
[EX A]: We propose a generative model that not only produces data with desired features from the pre-defined latent space but also fully understands the features of the data to create characteristics that are not in the dataset.

[EX Q]: The concepts of unitary evolution matrices and associative memory have boosted the field of Recurrent Neural Networks (RNN) to state-of-the-art performance in a variety of sequential tasks.   However, RNN still has a limited capacity to manipulate long-term memory.   To bypass this weakness the most successful applications of RNN use external techniques such as attention mechanisms. In this paper we propose a novel RNN model that unifies the state-of-the-art approaches: Rotational Unit of Memory (RUM). The core of RUM is its rotational operation, which is,  naturally,  a unitary matrix, providing architectures with the power to learn long-term dependencies by overcoming the vanishing and exploding gradients problem.   Moreover,  the rotational unit also serves as associative memory. We evaluate our model on synthetic memorization, question answering and language modeling tasks.    RUM learns the Copying Memory task completely and improves the state-of-the-art result in the Recall task.   RUM’s performance in the bAbI Question Answering task is comparable to that of models with attention mechanism. We also improve the state-of-the-art result to 1.189 bits-per-character (BPC) loss in the Character Level Penn Treebank (PTB) task, which is to signify the applications of RUM to real-world sequential data. The universality of our construction, at the core of RNN, establishes RUM as a promising approach to language modeling, speech recognition and machine translation.
[EX A]:
A novel RNN model which outperforms significantly the current frontier of models in a variety of sequential tasks.