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.

Example 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.

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

Example Input: We introduce a new type of deep contextualized word representation that models both (1) complex characteristics of word use (e.g., syntax and semantics), and (2) how these uses vary across linguistic contexts (i.e., to model polysemy).   Our word vectors are learned functions of the internal states of a deep bidirectional language model (biLM), which is pretrained on a large text corpus. We show that these representations can be easily added to existing models and significantly improve the state of the art across six challenging NLP problems, including question answering, textual entailment and sentiment analysis.   We also present an analysis showing that exposing the deep internals of the pretrained network is crucial, allowing downstream models to mix different types of semi-supervision signals.

Example Output: We introduce a new type of deep contextualized word representation that significantly improves the state of the art for a range of challenging NLP tasks.

Example Input: We present Random Partition Relaxation (RPR), a method for strong quantization of the parameters of convolutional neural networks to binary (+1/-1) and ternary (+1/0/-1) values. Starting from a pretrained model, we first quantize the weights and then relax random partitions of them to their continuous values for retraining before quantizing them again and switching to another weight partition for further adaptation.   We empirically evaluate the performance of RPR with ResNet-18, ResNet-50 and GoogLeNet on the ImageNet classification task for binary and ternary weight networks. We show accuracies beyond the state-of-the-art for binary- and ternary-weight GoogLeNet and competitive performance for ResNet-18 and ResNet-50 using a SGD-based training method that can easily be integrated into existing frameworks.
Example Output:
State-of-the-art training method for binary and ternary weight networks based on alternating optimization of randomly relaxed weight partitions