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.

[Q]: Adoption of deep learning in safety-critical systems raise the need for understanding what deep neural networks do not understand. Several methodologies to estimate model uncertainty have been proposed, but these methodologies constrain either how the neural network is trained or constructed. We present Outlier Detection In Neural networks (ODIN), an assumption-free method for detecting outlier observations during prediction, based on principles widely used in manufacturing process monitoring. By using a linear approximation of the hidden layer manifold, we add prediction-time outlier detection to models after training without altering architecture or training. We demonstrate that ODIN efficiently detect outliers during prediction on Fashion-MNIST, ImageNet-synsets and speech command recognition.
[A]: An add-on method for deep learning to detect outliers during prediction-time


[Q]: Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. 
 Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models.
[A]: Improved training of current flow-based generative models (Glow and RealNVP) on density estimation benchmarks


[Q]: The tremendous success of deep neural networks has motivated the need to better understand the fundamental properties of these networks, but many of the theoretical results proposed have only been for shallow networks. In this paper, we study an important primitive for understanding the meaningful input space of a deep network: span recovery. For $k<n$, let $\mathbf{A} \in \mathbb{R}^{k \times n}$ be the innermost weight matrix of an arbitrary feed forward neural network $M: \mathbb{R}^n \to  \mathbb{R}$, so $M(x)$ can be written as $M(x) = \sigma(\mathbf{A} x)$, for some network $\sigma: \mathbb{R}^k \to  \mathbb{R}$. The goal is then to recover the row span of $\mathbf{A}$ given only oracle access to the value of $M(x)$. We show that if $M$ is a multi-layered network with ReLU activation functions, then partial recovery is possible: namely, we can provably recover $k/2$ linearly independent vectors in the row span of $\mathbf{A}$ using poly$(n)$ non-adaptive queries to $M(x)$.  Furthermore, if $M$ has differentiable activation functions, we demonstrate that \textit{full} span recovery is possible even when the output is first passed through a sign or $0/1$ thresholding function; in this case our algorithm is adaptive. Empirically, we confirm that full span recovery is not always possible, but only for unrealistically thin layers. For reasonably wide networks, we obtain full span recovery on both random networks and networks trained on MNIST data. Furthermore, we demonstrate the utility of span recovery as an attack by inducing neural networks to misclassify data obfuscated by controlled random noise as sensical inputs. 

[A]:
We provably recover the span of a deep multi-layered neural network with latent structure and empirically apply efficient span recovery algorithms to attack networks by obfuscating inputs.