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: We consider the problem of unsupervised learning of a low dimensional, interpretable, latent state of a video containing a moving object. The problem of distilling dynamics from pixels has been extensively considered through the lens of graphical/state space models that exploit Markov structure for cheap computation and structured graphical model priors for enforcing interpretability on latent representations. We take a step towards extending these approaches by discarding the Markov structure; instead, repurposing the recently proposed Gaussian Process Prior Variational Autoencoder for learning sophisticated latent trajectories. We describe the model and perform experiments on a synthetic dataset and see that the model reliably reconstructs smooth dynamics exhibiting U-turns and loops. We also observe that this model may be trained without any beta-annealing or freeze-thaw of training parameters. Training is performed purely end-to-end on the unmodified evidence lower bound objective. This is in contrast to previous works, albeit for slightly different use cases, where application specific training tricks are often required.
Example Output: We learn sohpisticated trajectories of an object purely from pixels with a toy video dataset by using a VAE structure with a Gaussian process prior.

Example Input: As deep learning-based classifiers are increasingly adopted in real-world applications, the importance of understanding how a particular label is chosen grows. Single decision trees are an example of a simple, interpretable classifier, but are unsuitable for use with complex, high-dimensional data. On the other hand, the variational autoencoder (VAE) is designed to learn a factored, low-dimensional representation of data, but typically encodes high-likelihood data in an intrinsically non-separable way.   We introduce the differentiable decision tree (DDT) as a modular component of deep networks and a simple, differentiable loss function that allows for end-to-end optimization of a deep network to compress high-dimensional data for classification by a single decision tree.   We also explore the power of labeled data in a  supervised VAE (SVAE) with a Gaussian mixture prior, which leverages label information to produce a high-quality generative model with improved bounds on log-likelihood.   We combine the SVAE with the DDT to get our classifier+VAE (C+VAE), which is competitive in both classification error and log-likelihood, despite optimizing both simultaneously and using a very simple encoder/decoder architecture.
Example Output: We combine differentiable decision trees with supervised variational autoencoders to enhance interpretability of classification. 

Example Input: The fast generation and refinement of protein backbones would constitute a major advancement to current methodology for the design and development of de novo proteins. In this study, we train Generative Adversarial Networks (GANs) to generate fixed-length full-atom protein backbones, with the goal of sampling from the distribution of realistic 3-D backbone fragments. We represent protein structures by pairwise distances between all backbone atoms, and present a method for directly recovering and refining the corresponding backbone coordinates in a differentiable manner. We show that interpolations in the latent space of the generator correspond to smooth deformations of the output backbones, and that test set structures not seen by the generator during training exist in its image. Finally, we perform sequence design, relaxation, and ab initio folding of a subset of generated structures, and show that in some cases we can recover the generated folds after forward-folding. Together, these results suggest a mechanism for fast protein structure refinement and folding using external energy functions.
Example Output:
We train a GAN to generate and recover full-atom protein backbones , and we show that in select cases we can recover the generated proteins after sequence design and ab initio forward-folding.