TASK DEFINITION: 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.
PROBLEM: 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.

SOLUTION: Learned energy based model with score matching

PROBLEM: We propose a rejection sampling scheme using the discriminator of a GAN to
approximately correct errors in the GAN generator distribution. We show that
under quite strict assumptions, this will allow us to recover the data distribution
exactly. We then examine where those strict assumptions break down and design a
practical algorithmcalled Discriminator Rejection Sampling (DRS)that can be
used on real data-sets. Finally, we demonstrate the efficacy of DRS on a mixture of
Gaussians and on the state of the art SAGAN model. On ImageNet, we train an
improved baseline that increases the best published Inception Score from 52.52 to
62.36 and reduces the Frechet Inception Distance from 18.65 to 14.79. We then use
DRS to further improve on this baseline, improving the Inception Score to 76.08
and the FID to 13.75.

SOLUTION: We use a GAN discriminator to perform an approximate rejection sampling scheme on the output of the GAN generator.

PROBLEM: We propose a novel architecture for k-shot classification on the Omniglot dataset. Building on prototypical networks, we extend their architecture to what we call Gaussian prototypical networks. Prototypical networks learn a map between images and embedding vectors, and use their clustering for classification. In our model, a part of the encoder output is interpreted as a confidence region estimate about the embedding point, and expressed as a Gaussian covariance matrix. Our network then constructs a direction and class dependent distance metric on the embedding space, using uncertainties of individual data points as weights. We show that Gaussian prototypical networks are a preferred architecture over vanilla prototypical networks with an equivalent number of parameters. We report results consistent with state-of-the-art performance in 1-shot and 5-shot classification both in 5-way and 20-way regime on the Omniglot dataset. We explore artificially down-sampling a fraction of images in the training set, which improves our performance. Our experiments therefore lead us to hypothesize that Gaussian prototypical networks might perform better in less homogeneous, noisier datasets, which are commonplace in real world applications.

SOLUTION:
A novel architecture for few-shot classification capable of dealing with uncertainty.