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 adversarial training procedure proposed by Madry et al. (2018) is one of the most effective methods to defend against adversarial examples in deep neural net- works (DNNs). In our paper, we shed some lights on the practicality and the hardness of adversarial training by showing that the effectiveness (robustness on test set) of adversarial training has a strong correlation with the distance between a test point and the manifold of training data embedded by the network. Test examples that are relatively far away from this manifold are more likely to be vulnerable to adversarial attacks. Consequentially, an adversarial training based defense is susceptible to a new class of attacks, the “blind-spot attack”, where the input images reside in “blind-spots” (low density regions) of the empirical distri- bution of training data but is still on the ground-truth data manifold. For MNIST, we found that these blind-spots can be easily found by simply scaling and shifting image pixel values. Most importantly, for large datasets with high dimensional and complex data manifold (CIFAR, ImageNet, etc), the existence of blind-spots in adversarial training makes defending on any valid test examples difficult due to the curse of dimensionality and the scarcity of training data. Additionally, we find that blind-spots also exist on provable defenses including (Kolter & Wong, 2018) and (Sinha et al., 2018) because these trainable robustness certificates can only be practically optimized on a limited set of training data.

Ex Output:
We show that even the strongest adversarial training methods cannot defend against adversarial examples crafted on slightly scaled and shifted test images.


Ex 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.


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


Ex Input:
To study how mental object representations are related to behavior, we estimated sparse, non-negative representations of objects using human behavioral judgments on images representative of 1,854 object categories. These representations predicted a latent similarity structure between objects, which captured most of the explainable variance in human behavioral judgments. Individual dimensions in the low-dimensional embedding were found to be highly reproducible and interpretable as conveying degrees of taxonomic membership, functionality, and perceptual attributes. We further demonstrated the predictive power of the embeddings for explaining other forms of human behavior, including categorization, typicality judgments, and feature ratings, suggesting that the dimensions reflect human conceptual representations of objects beyond the specific task.

Ex Output:

Human behavioral judgments are used to obtain sparse and interpretable representations of objects that generalize to other tasks