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: Energy based models outputs unmormalized log-probability values given datasamples. Such a estimation is essential in a variety of application problems suchas sample generation, denoising, sample restoration, outlier detection, Bayesianreasoning, and many more. However, standard maximum likelihood training iscomputationally expensive due to the requirement of sampling model distribution. Score matching potentially alleviates this problem, and denoising score matching(Vincent, 2011) is a particular convenient version. However, previous attemptsfailed to produce models capable of high quality sample synthesis. We believethat it is because they only performed denoising score matching over a singlenoise scale. To overcome this limitation, here we instead learn an energy functionusing all noise scales. When sampled using Annealed Langevin dynamics andsingle step denoising jump, our model produced high-quality samples comparableto state-of-the-art techniques such as GANs, in addition to assigning likelihood totest data comparable to previous likelihood models. Our model set a new sam-ple quality baseline in likelihood-based models. We further demonstrate that our model learns sample distribution and generalize well on an image inpainting tasks.
Example Output: Learned energy based model with score matching

Example Input: In most current formulations of adversarial training, the discriminators can be expressed as single-input operators, that is, the mapping they define is separable over observations. In this work, we argue that this property might help explain the infamous mode collapse phenomenon in adversarially-trained generative models. Inspired by discrepancy measures and two-sample tests between probability distributions, we propose distributional adversaries that operate on samples, i.e., on sets of multiple points drawn from a distribution, rather than on single observations. We show how they can be easily implemented on top of existing models. Various experimental results show that generators trained in combination with our distributional adversaries are much more stable and are remarkably less prone to mode collapse than traditional models trained with observation-wise prediction discriminators. In addition, the application of our framework to domain adaptation results in strong improvement over recent state-of-the-art.
Example Output: We show that the mode collapse problem in GANs may be explained by a lack of information sharing between observations in a training batch, and propose a distribution-based framework for globally sharing information between gradients that leads to more stable and effective adversarial training.

Example Input: While it has not yet been proven, empirical evidence suggests that model generalization is related to local properties of the optima which can be described via the Hessian. We connect model generalization with the local property of a solution under the PAC-Bayes paradigm. In particular, we prove that model generalization ability is related to the Hessian, the higher-order "smoothness" terms characterized by the Lipschitz constant of the Hessian, and the scales of the parameters. Guided by the proof, we propose a metric to score the generalization capability of the model, as well as an algorithm that optimizes the perturbed model accordingly.
Example Output:
a theory connecting Hessian of the solution and the generalization power of the model