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 Input:
This paper proposes a dual variational autoencoder (DualVAE), a framework for generating images corresponding to multiclass labels. Recent research on conditional generative models, such as the Conditional VAE, exhibit image transfer by changing labels. However, when the dimension of multiclass labels is large, these models cannot change images corresponding to labels, because learning multiple distributions of the corresponding class is necessary to transfer an image. This leads to the lack of training data. Therefore, instead of conditioning with labels, we condition with latent vectors that include label information. DualVAE divides one distribution of the latent space by linear decision boundaries using labels. Consequently, DualVAE can easily transfer an image by moving a latent vector toward a decision boundary and is robust to the missing values of multiclass labels. To evaluate our proposed method, we introduce a conditional inception score (CIS) for measuring how much an image changes to the target class. We evaluate the images transferred by DualVAE using the CIS in CelebA datasets and demonstrate state-of-the-art performance in a multiclass setting.

Ex Output:
a new framework using dual space for generating images corresponding to multiclass labels when the number of class is large

Ex Input:
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.

Ex Output:
We show that SGD learns two-layer over-parameterized neural networks with Leaky ReLU activations that provably generalize on linearly separable data.

Ex Input:
Variational Auto-Encoders (VAEs) are designed to capture compressible information about a dataset. As a consequence the information stored in the latent space is seldom sufficient to reconstruct a particular image. To help understand the type of information stored in the latent space we train a GAN-style decoder constrained to produce images that the VAE encoder will map to the same region of latent space. This allows us to ''imagine'' the information captured in the latent space. We argue that this is necessary to make a VAE into a truly generative model. We use our GAN to visualise the latent space of a standard VAE and of a $eta$-VAE.

Ex Output:
To understand the information stored in the latent space, we train a GAN-style decoder constrained to produce images that the VAE encoder will map to the same region of latent space.