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 Q]: We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed---both because of the underlying physics and because we can only get few measurements. This setting is common in geophysical imaging and remote sensing. We show that in this case the common approach to directly learn the mapping from the measured data to the reconstruction becomes unstable. Instead, we propose to first learn an ensemble of simpler mappings from the data to projections of the unknown image into random piecewise-constant subspaces. We then combine the projections to form a final reconstruction by solving a deconvolution-like problem. We show experimentally that the proposed method is more robust to measurement noise and corruptions not seen during training than a directly learned inverse.
[EX A]: We solve ill-posed inverse problems with scarce ground truth examples by estimating an ensemble of random projections of the model instead of the model itself.

[EX Q]: The Variational Auto Encoder (VAE) is a popular generative 
latent variable model that is often 
applied for representation learning.
 Standard VAEs assume continuous valued 
latent variables and are trained by maximization
of the evidence lower bound (ELBO). Conventional methods obtain a 
differentiable estimate of the ELBO with reparametrized sampling and
optimize it with Stochastic Gradient Descend (SGD). However, this is not possible if 
we want to train VAEs with discrete valued latent variables, 
since reparametrized sampling is not possible. Till now, there
exist no simple solutions to circumvent this problem.
 In this paper, we propose an easy method to train VAEs 
with binary or categorically valued latent representations. Therefore, we use a differentiable
estimator for the ELBO which is based on importance sampling. In experiments, we verify the approach and
train two different VAEs architectures with Bernoulli and 
Categorically distributed latent representations on two different benchmark
datasets.	
[EX A]: We propose an easy method to train Variational Auto Encoders (VAE) with discrete latent representations, using importance sampling

[EX Q]: Vanishing and exploding gradients are two of the main obstacles in training deep neural networks, especially in capturing long range dependencies in recurrent neural networks (RNNs). In this paper, we present an efficient parametrization of the transition matrix of an RNN that allows us to stabilize the gradients that arise in its training. Specifically, we parameterize the transition matrix by its singular value decomposition (SVD), which allows us to explicitly track and control its singular values. We attain efficiency by using tools that are common in numerical linear algebra, namely Householder reflectors for representing the orthogonal matrices that arise in the SVD. By explicitly controlling the singular values, our proposed svdRNN method allows us to easily solve the exploding gradient problem and we observe that it empirically solves the vanishing gradient issue to a large extent. We note that the SVD parameterization can be used for any rectangular weight matrix, hence it can be easily extended to any deep neural network, such as a multi-layer perceptron. Theoretically, we demonstrate that our parameterization does not lose any expressive power, and show how it potentially makes the optimization process easier. Our extensive  experimental results also demonstrate that the proposed framework converges faster, and has good generalization, especially when the depth is large. 

[EX A]:
To solve the gradient vanishing/exploding problems, we proprose an efficient parametrization of the transition matrix of RNN that loses no expressive power, converges faster and has good generalization.