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]: Deep networks face challenges of ensuring their robustness against inputs that cannot be effectively represented by information learned from training data. We attribute this vulnerability to the limitations inherent to activation-based representation. To complement the learned information from activation-based representation, we propose utilizing a gradient-based representation that explicitly focuses on missing information. In addition, we propose a directional constraint on the gradients as an objective during training to improve the characterization of missing information. To validate the effectiveness of the proposed approach, we compare the anomaly detection performance of gradient-based and activation-based representations. We show that the gradient-based representation outperforms the activation-based representation by 0.093 in CIFAR-10 and 0.361 in CURE-TSR datasets in terms of AUROC averaged over all classes. Also, we propose an anomaly detection algorithm that uses the gradient-based representation, denoted as GradCon, and validate its performance on three benchmarking datasets. The proposed method outperforms the majority of the state-of-the-art algorithms in CIFAR-10, MNIST, and fMNIST datasets with an average AUROC of 0.664, 0.973, and 0.934, respectively.
[A]: We propose a gradient-based representation for characterizing information that deep networks have not learned.


[Q]: To provide principled ways of designing proper Deep Neural Network (DNN) models, it is essential to understand the loss surface of DNNs under realistic assumptions. We introduce interesting aspects for understanding the local minima and overall structure of the loss surface. The parameter domain of the loss surface can be decomposed into regions in which activation values (zero or one for rectified linear units) are consistent. We found that, in each region, the loss surface have properties similar to that of linear neural networks where every local minimum is a global minimum. This means that every differentiable local minimum is the global minimum of the corresponding region. We prove that for a neural network with one hidden layer using rectified linear units under realistic assumptions. There are poor regions that lead to poor local minima, and we explain why such regions exist even in the overparameterized DNNs.
[A]: The loss surface of neural networks is a disjoint union of regions where every local minimum is a global minimum of the corresponding region.


[Q]: Predicting the future in real-world settings, particularly from raw sensory observations such as images, is exceptionally challenging. Real-world events can be stochastic and unpredictable, and the high dimensionality and complexity of natural images requires the predictive model to build an intricate understanding of the natural world. Many existing methods tackle this problem by making simplifying assumptions about the environment. One common assumption is that the outcome is deterministic and there is only one plausible future. This can lead to low-quality predictions in real-world settings with stochastic dynamics. In this paper, we develop a stochastic variational video prediction (SV2P) method that predicts a different possible future for each sample of its latent variables. To the best of our knowledge, our model is the first to provide effective stochastic multi-frame prediction for real-world video. We demonstrate the capability of the proposed method in predicting detailed future frames of videos on multiple real-world datasets, both action-free and action-conditioned. We find that our proposed method produces substantially improved video predictions when compared to the same model without stochasticity, and to other stochastic video prediction methods. Our SV2P implementation will be open sourced upon publication.
[A]:
Stochastic variational video prediction in real-world settings.