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.

  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.

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

In this paper, we explore meta-learning for few-shot text classification. Meta-learning has shown strong performance in computer vision, where low-level patterns are transferable across learning tasks. However, directly applying this approach to text is challenging–lexical features highly informative for one task maybe insignificant for another. Thus, rather than learning solely from words, our model also leverages their distributional signatures, which encode pertinent word occurrence patterns. Our model is trained within a meta-learning framework to map these signatures into attention scores, which are then used to weight the lexical representations of words. We demonstrate that our model consistently outperforms prototypical networks learned on lexical knowledge (Snell et al., 2017) in both few-shot text classification and relation classification by a significant margin across six benchmark datasets (19.96% on average in 1-shot classification).
Meta-learning methods used for vision, directly applied to NLP, perform worse than nearest neighbors on new classes; we can do better with distributional signatures.

Injecting adversarial examples during training, known as adversarial training, can improve robustness against one-step attacks, but not for unknown iterative attacks. To address this challenge, we first show iteratively generated adversarial images easily transfer between networks trained with the same strategy. Inspired by this observation, we propose cascade adversarial training, which transfers the knowledge of the end results of adversarial training. We train a network from scratch by injecting iteratively generated adversarial images crafted from already defended networks in addition to one-step adversarial images from the network being trained. We also propose to utilize embedding space for both classification and low-level (pixel-level) similarity learning to ignore unknown pixel level perturbation. During training, we inject adversarial images without replacing their corresponding clean images and penalize the distance between the two embeddings (clean and adversarial). Experimental results show that cascade adversarial training together with our proposed low-level similarity learning efficiently enhances the robustness against iterative attacks, but at the expense of decreased robustness against one-step attacks. We show that combining those two techniques can also improve robustness under the worst case black box attack scenario.

Cascade adversarial training + low level similarity learning improve robustness against both white box and black box attacks.