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]: In this paper, we propose a novel kind of kernel, random forest kernel, to enhance the empirical performance of MMD GAN. Different from common forests with deterministic routings, a probabilistic routing variant is used in our innovated random-forest kernel, which is possible to merge with the CNN frameworks. Our proposed random-forest kernel has the following advantages: From the perspective of random forest, the output of GAN discriminator can be viewed as feature inputs to the forest, where each tree gets access to merely a fraction of the features, and thus the entire forest benefits from ensemble learning. In the aspect of kernel method, random-forest kernel is proved to be characteristic, and therefore suitable for the MMD structure. Besides, being an asymmetric kernel, our random-forest kernel is much more flexible, in terms of capturing the differences between distributions. Sharing the advantages of CNN, kernel method, and ensemble learning, our random-forest kernel based MMD GAN obtains desirable empirical performances on CIFAR-10, CelebA and LSUN bedroom data sets. Furthermore, for the sake of completeness, we also put forward comprehensive theoretical analysis to support our experimental results.
[A]: Equip MMD GANs with a new random-forest kernel.

[Q]: We propose a new representation, one-pixel signature, that can be used to reveal the characteristics of the convolution neural networks (CNNs). Here, each CNN classifier is associated with a signature that is created by generating, pixel-by-pixel, an adversarial value that is the result of the largest change to the class prediction. The one-pixel signature is agnostic to the design choices of CNN architectures such as type, depth, activation function, and how they were trained. It can be computed efficiently for a black-box classifier without accessing the network parameters. Classic networks such as LetNet, VGG, AlexNet, and ResNet demonstrate different characteristics in their signature images. For application, we focus on the classifier backdoor detection problem where a CNN classifier has been maliciously inserted with an unknown Trojan. We show the effectiveness of the one-pixel signature in detecting backdoored CNN. Our proposed one-pixel signature representation is general and it can be applied in problems where discriminative classifiers, particularly neural network based, are to be characterized.
[A]: Cnvolutional neural networks characterization for backdoored classifier detection and understanding.

[Q]: The lack of crisp mathematical models that capture the structure of real-world
data sets is a major obstacle to the detailed theoretical understanding of deep
neural networks. Here, we first demonstrate the effect of structured data sets
by experimentally comparing the dynamics and the performance of two-layer
networks trained on two different data sets: (i) an unstructured synthetic data
set containing random i.i.d. inputs, and (ii) a simple canonical data set such
as MNIST images. Our analysis reveals two phenomena related to the dynamics of
the networks and their ability to generalise that only appear when training on
structured data sets. Second, we introduce a generative model for data sets,
where high-dimensional inputs lie on a lower-dimensional manifold and have
labels that depend only on their position within this manifold. We call it the
*hidden manifold model* and we experimentally demonstrate that training
networks on data sets drawn from this model reproduces both the phenomena seen
during training on MNIST.
[A]:
We demonstrate how structure in data sets impacts neural networks and introduce a generative model for synthetic data sets that reproduces this impact.