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.

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.
Equip MMD GANs with a new random-forest kernel.

The quality of the features used in visual recognition is of fundamental importance for the overall system. For a long time, low-level hand-designed feature algorithms as SIFT and HOG have obtained the best results on image recognition. Visual features have recently been extracted from trained convolutional neural networks. Despite the high-quality results, one of the main drawbacks of this approach, when compared with hand-designed features, is the training time required during the learning process. In this paper, we propose a simple and fast way to train supervised convolutional models to feature extraction while still maintaining its high-quality. This methodology is evaluated on different datasets and compared with state-of-the-art approaches.
A simple fast method for extracting visual features from convolutional neural networks

We analyze the joint probability distribution on the lengths of the
vectors of hidden variables in different layers of a fully connected
deep network, when the weights and biases are chosen randomly according to
Gaussian distributions, and the input is binary-valued. We show
that, if the activation function satisfies a minimal set of
assumptions, satisfied by all activation functions that we know that
are used in practice, then, as the width of the network gets large,
the ''length process'' converges in probability to a length map
that is determined as a simple function of the variances of the
random weights and biases, and the activation function.

We also show that this convergence may fail for activation functions
that violate our assumptions.
We prove that, for activation functions satisfying some conditions, as a deep network gets wide, the lengths of the vectors of hidden variables converge to a length map.