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: 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.
Example Output: An add-on method for deep learning to detect outliers during prediction-time

Example Input: We present a deep generative model, named Monge-Amp\`ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\`ere equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution. Training of the model amounts to solving an optimal control problem. The Monge-Amp\`ere flow has tractable likelihoods and supports efficient sampling and inference. One can easily impose symmetry constraints in the generative model by designing suitable scalar potential functions. We apply the approach to unsupervised density estimation of the MNIST dataset and variational calculation of the two-dimensional Ising model at the critical point. This approach brings insights and techniques from Monge-Amp\`ere equation, optimal transport, and fluid dynamics into reversible flow-based generative models.
Example Output: A gradient flow based dynamical system for invertible generative modeling

Example Input: We investigate the difficulties of training sparse neural networks and make new observations about optimization dynamics and the energy landscape within the sparse regime. Recent work of \citep{Gale2019, Liu2018} has shown that sparse ResNet-50 architectures trained on ImageNet-2012 dataset converge to solutions that are significantly worse than those found by pruning. We show that, despite the failure of optimizers, there is a linear path with a monotonically decreasing objective from the initialization to the ``good'' solution. Additionally, our attempts to find a decreasing objective path from ``bad'' solutions to the ``good'' ones in the sparse subspace fail. However, if we allow the path to traverse the dense subspace, then we consistently find a path between two solutions. These findings suggest traversing extra dimensions may be needed to escape stationary points found in the sparse subspace.
Example Output:
In this paper we highlight  the difficulty of training sparse neural networks by doing interpolation experiments in the energy landscape