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]: Neural networks exhibit good generalization behavior in the
 over-parameterized regime, where the number of network parameters
 exceeds the number of observations. Nonetheless,
 current generalization bounds for neural networks fail to explain this
 phenomenon. In an attempt to bridge this gap, we study the problem of
 learning a two-layer over-parameterized neural network, when the data is generated by a linearly separable function. In the case where the network has Leaky
 ReLU activations, we provide both optimization and generalization guarantees for over-parameterized networks.
 Specifically, we prove convergence rates of SGD to a global
 minimum and provide generalization guarantees for this global minimum
 that are independent of the network size. 
 Therefore, our result clearly shows that the use of SGD for optimization both finds a global minimum, and avoids overfitting despite the high capacity of the model. This is the first theoretical demonstration that SGD can avoid overfitting, when learning over-specified neural network classifiers.
[A]: We show that SGD learns two-layer over-parameterized neural networks with Leaky ReLU activations that provably generalize on linearly separable data.


[Q]: In this paper we use the geometric properties of the optimal transport (OT) problem and the Wasserstein distances to define a prior distribution for the latent space of an auto-encoder. We introduce Sliced-Wasserstein Auto-Encoders (SWAE), that enable one to shape the distribution of the latent space into any samplable probability distribution without the need for training an adversarial network or having a likelihood function specified. In short, we regularize the auto-encoder loss with the sliced-Wasserstein distance between the distribution of the encoded training samples and a samplable prior distribution. We show that the proposed formulation has an efficient numerical solution that provides similar capabilities to Wasserstein Auto-Encoders (WAE) and Variational Auto-Encoders (VAE), while benefiting from an embarrassingly simple implementation. We provide extensive error analysis for our algorithm, and show its merits on three benchmark datasets.
[A]: In this paper we use the sliced-Wasserstein distance to shape the latent distribution of an auto-encoder into any samplable prior distribution. 


[Q]: Multi-relational graph embedding which aims at achieving effective representations with reduced low-dimensional parameters, has been widely used in knowledge base completion. Although knowledge base data usually contains tree-like or cyclic structure, none of existing approaches can embed these data into a compatible space that in line with the structure. To overcome this problem, a novel framework, called Riemannian TransE, is proposed in this paper to embed the entities in a Riemannian manifold. Riemannian TransE models each relation as a move to a point and defines specific novel distance dissimilarity for each relation, so that all the relations are naturally embedded in correspondence to the structure of data. Experiments on several knowledge base completion tasks have shown that, based on an appropriate choice of manifold, Riemannian TransE achieves good performance even with a significantly reduced parameters.
[A]:
Multi-relational graph embedding with Riemannian manifolds and TransE-like loss function.