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.

Input: Consider 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.

Output: A gradient flow based dynamical system for invertible generative modeling

Input: Consider Input: This paper introduces a framework for solving combinatorial optimization problems by learning from input-output examples of optimization problems. We introduce a new memory augmented neural model in which the memory is not resettable (i.e the information stored in the memory after processing an input example is kept for the next seen examples). We used deep reinforcement learning to train a memory controller agent to store useful memories. Our model was able to outperform hand-crafted solver on Binary Linear Programming (Binary LP). The proposed model is tested on different Binary LP instances with large number of variables (up to 1000 variables) and constrains (up to 700 constrains).

Output: We propose a memory network model to solve Binary LP instances where the memory information is perseved for long-term use.

Input: Consider Input: Convolutional neural networks (CNNs) are commonly trained using a fixed spatial image size predetermined for a given model. Although trained on images of a specific size, it is well established that CNNs can be used to evaluate a wide range of image sizes at test time, by adjusting the size of intermediate feature maps.
In this work, we describe and evaluate a novel mixed-size training regime that mixes several image sizes at training time. We demonstrate that models trained using our method are more resilient to image size changes and generalize well even on small images. This allows faster inference by using smaller images at test time. For instance, we receive a 76.43% top-1 accuracy using ResNet50 with an image size of 160, which matches the accuracy of the baseline model with 2x fewer computations.
Furthermore, for a given image size used at test time, we show this method can be exploited either to accelerate training or the final test accuracy. For example, we are able to reach a 79.27% accuracy with a model evaluated at a 288 spatial size for a relative improvement of 14% over the baseline.
Output: Training convnets with mixed image size can improve results across multiple sizes at evaluation