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 Input:
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.

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

Ex Input:
We study the role of intrinsic motivation as an exploration bias for reinforcement learning in sparse-reward synergistic tasks, which are tasks where multiple agents must work together to achieve a goal they could not individually. Our key idea is that a good guiding principle for intrinsic motivation in synergistic tasks is to take actions which affect the world in ways that would not be achieved if the agents were acting on their own. Thus, we propose to incentivize agents to take (joint) actions whose effects cannot be predicted via a composition of the predicted effect for each individual agent. We study two instantiations of this idea, one based on the true states encountered, and another based on a dynamics model trained concurrently with the policy. While the former is simpler, the latter has the benefit of being analytically differentiable with respect to the action taken. We validate our approach in robotic bimanual manipulation tasks with sparse rewards; we find that our approach yields more efficient learning than both 1) training with only the sparse reward and 2) using the typical surprise-based formulation of intrinsic motivation, which does not bias toward synergistic behavior. Videos are available on the project webpage: https://sites.google.com/view/iclr2020-synergistic.

Ex Output:
We propose a formulation of intrinsic motivation that is suitable as an exploration bias in multi-agent sparse-reward synergistic tasks, by encouraging agents to affect the world in ways that would not be achieved if they were acting individually.

Ex Input:
Though state-of-the-art sentence representation models can perform tasks requiring significant knowledge of grammar, it is an open question how best to evaluate their grammatical knowledge. We explore five experimental methods inspired by prior work evaluating pretrained sentence representation models. We use a single linguistic phenomenon, negative polarity item (NPI) licensing, as a case study for our experiments. NPIs like 'any' are grammatical only if they appear in a licensing environment like negation ('Sue doesn't have any cats' vs. '*Sue has any cats'). This phenomenon is challenging because of the variety of NPI licensing environments that exist. We introduce an artificially generated dataset that manipulates key features of NPI licensing for the experiments. We find that BERT has significant knowledge of these features, but its success varies widely across different experimental methods. We conclude that a variety of methods is necessary to reveal all relevant aspects of a model's grammatical knowledge in a given domain.

Ex Output:
Different methods for analyzing BERT suggest different (but compatible) conclusions in a case study on NPIs.