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]: When considering simultaneously a finite number of tasks, multi-output learning enables one to account for the similarities of the tasks via appropriate regularizers. We propose a generalization of the classical setting to a continuum of tasks by using vector-valued RKHSs.
[A]: We propose an extension of multi-output learning to a continuum of tasks using operator-valued kernels.


[Q]: Deep neural networks have been shown to perform well in many classical machine learning problems, especially in image classification tasks. However, researchers have found that neural networks can be easily fooled, and they are surprisingly sensitive to small perturbations imperceptible to humans.   Carefully crafted input images (adversarial examples) can force a well-trained neural network to provide arbitrary outputs.   Including adversarial examples during training is a popular defense mechanism against adversarial attacks. In this paper we propose a new defensive mechanism under the generative adversarial network~(GAN) framework. We model the adversarial noise using a generative network, trained jointly with a classification discriminative network as a minimax game. We show empirically that our adversarial network approach works well against black box attacks, with performance on par with state-of-art methods such as ensemble adversarial training and adversarial training with projected gradient descent.

[A]: Jointly train an adversarial noise generating network with a classification network to provide better robustness to adversarial attacks.


[Q]: In this paper, we describe the "implicit autoencoder" (IAE), a generative autoencoder in which both the generative path and the recognition path are parametrized by implicit distributions. We use two generative adversarial networks to define the reconstruction and the regularization cost functions of the implicit autoencoder, and derive the learning rules based on maximum-likelihood learning. Using implicit distributions allows us to learn more expressive posterior and conditional likelihood distributions for the autoencoder. Learning an expressive conditional likelihood distribution enables the latent code to only capture the abstract and high-level information of the data, while the remaining information is captured by the implicit conditional likelihood distribution. For example, we show that implicit autoencoders can disentangle the global and local information, and perform deterministic or stochastic reconstructions of the images. We further show that implicit autoencoders can disentangle discrete underlying factors of variation from the continuous factors in an unsupervised fashion, and perform clustering and semi-supervised learning.
[A]:
We propose a generative autoencoder that can learn expressive posterior and conditional likelihood distributions using implicit distributions, and train the model using a new formulation of the ELBO.