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 work provides theoretical and empirical evidence that invariance-inducing regularizers can increase predictive accuracy for worst-case spatial transformations (spatial robustness).   Evaluated on these adversarially transformed examples, we demonstrate that adding regularization on top of standard or adversarial training reduces the relative error by 20% for CIFAR10 without increasing the computational cost.   This outperforms handcrafted networks that were explicitly designed to be spatial-equivariant. Furthermore, we observe for SVHN, known to have inherent variance in orientation, that robust training also improves standard accuracy on the test set.

Ex Output:
for spatial transformations robust minimizer also minimizes standard accuracy; invariance-inducing regularization leads to better robustness than specialized architectures


Ex Input:
Understanding the groundbreaking performance of Deep Neural Networks is one
 of the greatest challenges to the scientific community today. In this work, we
 introduce an information theoretic viewpoint on the behavior of deep networks
 optimization processes and their generalization abilities. By studying the Information
 Plane, the plane of the mutual information between the input variable and
 the desired label, for each hidden layer. Specifically, we show that the training of
 the network is characterized by a rapid increase in the mutual information (MI)
 between the layers and the target label, followed by a longer decrease in the MI
 between the layers and the input variable. Further, we explicitly show that these
 two fundamental information-theoretic quantities correspond to the generalization
 error of the network, as a result of introducing a new generalization bound that is
 exponential in the representation compression. The analysis focuses on typical
 patterns of large-scale problems. For this purpose, we introduce a novel analytic
 bound on the mutual information between consecutive layers in the network.
 An important consequence of our analysis is a super-linear boost in training time
 with the number of non-degenerate hidden layers, demonstrating the computational
 benefit of the hidden layers.

Ex Output:
Introduce an information theoretic viewpoint on the behavior of deep networks optimization processes and their generalization abilities


Ex Input:
One of the challenges in training generative models such as the variational auto encoder (VAE) is avoiding posterior collapse. When the generator has too much capacity, it is prone to ignoring latent code. This problem is exacerbated when the dataset is small, and the latent dimension is high. The root of the problem is the ELBO objective, specifically the Kullback–Leibler (KL) divergence term in objective function. This paper proposes a new  objective function to replace the KL term with one that emulates the maximum mean discrepancy (MMD) objective. It also introduces a new technique, named latent clipping, that is used to control distance between samples in latent space. A probabilistic autoencoder model, named $\mu$-VAE, is designed and trained on MNIST and MNIST Fashion datasets, using the new objective function and is shown to outperform models trained with ELBO and $\beta$-VAE objective. The $\mu$-VAE is less prone to posterior collapse, and can generate reconstructions and new samples in good quality. Latent representations learned by $\mu$-VAE are shown to be good and can be used for downstream tasks such as classification.  

Ex Output:

This paper proposes a new  objective function to replace KL term with one that emulates maximum mean discrepancy (MMD) objective.