instruction:
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.
question:
The goal of compressed sensing is to learn a structured signal $x$
from a limited number of noisy linear measurements $y pprox Ax$. In
traditional compressed sensing, ''structure'' is represented by
sparsity in some known basis. Inspired by the success of deep
learning in modeling images, recent work starting with~\cite{BDJP17}
has instead considered structure to come from a generative model
$G: \R^k o \R^n$. We present two results establishing the
difficulty of this latter task, showing that existing bounds are
tight.

First, we provide a lower bound matching the~\cite{BDJP17} upper
bound for compressed sensing from $L$-Lipschitz generative models
$G$. In particular, there exists such a function that requires
roughly $\Omega(k \log L)$ linear measurements for sparse recovery
to be possible. This holds even for the more relaxed goal of
\emph{nonuniform} recovery.

Second, we show that generative models generalize sparsity as a
representation of structure. In particular, we construct a
ReLU-based neural network $G: \R^{2k} o \R^n$ with $O(1)$ layers
and $O(kn)$ activations per layer, such that the range of $G$
contains all $k$-sparse vectors.

answer:
Lower bound for compressed sensing w/ generative models that matches known upper bounds

question:
Deep latent variable models are powerful tools for representation learning. In this paper, we adopt the deep information bottleneck model, identify its shortcomings and propose a model that circumvents them. To this end, we apply a copula transformation which, by restoring the invariance properties of the information bottleneck method, leads to disentanglement of the features in the latent space. Building on that, we show how this transformation translates to sparsity of the latent space in the new model. We evaluate our method on artificial and real data.
answer:
We apply the copula transformation to the Deep Information Bottleneck which leads to restored invariance properties and a disentangled latent space with superior predictive capabilities.

question:
We consider the question of how to assess generative adversarial networks, in particular with respect to whether or not they generalise beyond memorising the training data. We propose a simple procedure for assessing generative adversarial network performance based on a principled consideration of what the actual goal of generalisation is. Our approach involves using a test set to estimate the Wasserstein distance between the generative distribution produced by our procedure, and the underlying data distribution. We use this procedure to assess the performance of several modern generative adversarial network architectures. We find that this procedure is sensitive to the choice of ground metric on the underlying data space, and suggest a choice of ground metric that substantially improves performance. We finally suggest that attending to the ground metric used in Wasserstein generative adversarial network training may be fruitful, and outline a concrete pathway towards doing so.
answer:
Assess whether or not your GAN is actually doing something other than memorizing the training data.