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.

Input: Consider Input:   The goal of compressed sensing is to learn a structured signal $x$
  from a limited number of noisy linear measurements $y \approx Ax$.  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
  $G: \R^k \to \R^n$.  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 $G: \R^{2k} \to \R^n$ with $O(1)$ layers
  and $O(kn)$ activations per layer, such that the range of $G$
  contains all $k$-sparse vectors.


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


Input: Consider Input: Creating a knowledge base that is accurate, up-to-date and complete remains a significant challenge despite substantial efforts in automated knowledge base construction.   In this paper, we present Alexandria -- a system for unsupervised, high-precision knowledge base construction. Alexandria uses a probabilistic program to define a process of converting knowledge base facts into unstructured text.   Using probabilistic inference, we can invert this program and so retrieve facts, schemas and entities from web text. The use of a probabilistic program allows uncertainty in the text to be propagated through to the retrieved facts, which increases accuracy and helps merge facts from multiple sources. Because Alexandria does not require labelled training data, knowledge bases can be constructed with the minimum of manual input. We demonstrate this by constructing a high precision (typically 97\%+) knowledge base for people from a single seed fact.

Output: This paper presents a system for unsupervised, high-precision knowledge base construction using a probabilistic program to define a process of converting knowledge base facts into unstructured text.


Input: Consider Input: Graph Convolution Network (GCN) has been recognized as one of the most effective graph models for semi-supervised learning, but it extracts merely the first-order or few-order neighborhood information through information propagation, which suffers performance drop-off for deeper structure. Existing approaches that deal with the higher-order neighbors tend to take advantage of adjacency matrix power. In this paper, we assume a seemly trivial condition that the higher-order neighborhood information may be similar to that of the first-order neighbors. Accordingly, we present an unsupervised approach to describe such similarities and learn the weight matrices of higher-order neighbors automatically through Lasso that minimizes the feature loss between the first-order and higher-order neighbors, based on which we formulate the new convolutional filter for GCN to learn the better node representations. Our model, called higher-order weighted GCN (HWGCN), has achieved the state-of-the-art results on a number of node classification tasks over Cora, Citeseer and Pubmed datasets.


Output: We propose HWGCN to mix the relevant neighborhood information at different orders to better learn node representations.