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 Q]: 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.
[EX A]: A gradient flow based dynamical system for invertible generative modeling

[EX Q]: We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed---both because of the underlying physics and because we can only get few measurements. This setting is common in geophysical imaging and remote sensing. We show that in this case the common approach to directly learn the mapping from the measured data to the reconstruction becomes unstable. Instead, we propose to first learn an ensemble of simpler mappings from the data to projections of the unknown image into random piecewise-constant subspaces. We then combine the projections to form a final reconstruction by solving a deconvolution-like problem. We show experimentally that the proposed method is more robust to measurement noise and corruptions not seen during training than a directly learned inverse.
[EX A]: We solve ill-posed inverse problems with scarce ground truth examples by estimating an ensemble of random projections of the model instead of the model itself.

[EX Q]: Due to a resource-constrained environment, network compression has become an important part of deep neural networks research. In this paper, we propose a new compression method, Inter-Layer Weight Prediction (ILWP) and quantization method which quantize the predicted residuals between the weights in all convolution layers based on an inter-frame prediction method in conventional video coding schemes. Furthermore, we found a phenomenon Smoothly Varying Weight Hypothesis (SVWH) which is that the weights in adjacent convolution layers share strong similarity in shapes and values, i.e., the weights tend to vary smoothly along with the layers. Based on SVWH, we propose a second ILWP and quantization method which quantize the predicted residuals between the weights in adjacent convolution layers. Since the predicted weight residuals tend to follow Laplace distributions with very low variance, the weight quantization can more effectively be applied, thus producing more zero weights and enhancing the weight compression ratio. In addition, we propose a new inter-layer loss for eliminating non-texture bits, which enabled us to more effectively store only texture bits. That is, the proposed loss regularizes the weights such that the collocated weights between the adjacent two layers have the same values. Finally, we propose an ILWP with an inter-layer loss and quantization method. Our comprehensive experiments show that the proposed method achieves a much higher weight compression rate at the same accuracy level compared with the previous quantization-based compression methods in deep neural networks.
[EX A]:
We propose a new compression method, Inter-Layer Weight Prediction (ILWP) and quantization method which quantize the predicted residuals between the weights in convolution layers.