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 study the problem of training sequential generative models for capturing coordinated multi-agent trajectory behavior, such as  offensive basketball gameplay.   When modeling such settings, it is often beneficial to design hierarchical models that can capture long-term coordination using intermediate variables.   Furthermore, these intermediate variables should capture interesting high-level behavioral semantics in an interpretable and manipulable way. We present a hierarchical framework that can effectively learn such sequential generative models.   Our approach is inspired by recent work on leveraging programmatically produced weak labels, which we extend to the spatiotemporal regime. In addition to synthetic settings, we show how to instantiate our framework to effectively model complex interactions between basketball players and generate realistic multi-agent trajectories of basketball gameplay over long time periods. We validate our approach using both quantitative and qualitative evaluations, including a user study comparison conducted with professional sports analysts.

Output: We blend deep generative models with programmatic weak supervision to generate coordinated multi-agent trajectories of significantly higher quality than previous baselines.


Input: Consider Input: We show that information about whether a neural network's output will be correct or incorrect is present in the outputs of the network's intermediate layers. To demonstrate this effect, we train a new "meta" network to predict from either the final output of the underlying "base" network or the output of one of the base network's intermediate layers whether the base network will be correct or incorrect for a particular input. We find that, over a wide range of tasks and base networks, the meta network can achieve accuracies ranging from 65% - 85% in making this determination.


Output: Information about whether a neural network's output will be correct or incorrect is somewhat present in the outputs of the network's intermediate layers.


Input: Consider Input: Generative Adversarial Networks (GANs) are a very powerful framework for generative modeling. However, they are often hard to train, and learning of GANs often becomes unstable. Wasserstein GAN (WGAN) is a promising framework to deal with the instability problem as it has a good convergence property. One drawback of the WGAN is that it evaluates the Wasserstein distance in the dual domain, which requires some approximation, so that it may fail to optimize the true Wasserstein distance. In this paper, we propose evaluating the exact empirical optimal transport cost efficiently in the primal domain and performing gradient descent with respect to its derivative to train the generator network. Experiments on the MNIST dataset show that our method is significantly stable to converge, and achieves the lowest Wasserstein distance among the WGAN variants at the cost of some sharpness of generated images. Experiments on the 8-Gaussian toy dataset show that better gradients for the generator are obtained in our method. In addition, the proposed method enables more flexible generative modeling than WGAN.


Output: We have proposed a flexible generative model that learns stably by directly minimizing exact empirical Wasserstein distance.