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 Input:
We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of M data points on the nondifferentiability of the ReLU divides the parameter space into at most 2^M regions, which makes analysis difficult. By exploiting polyhedral geometry, we reduce the total computation down to one convex quadratic program (QP) for each hidden node, O(M) (in)equality tests, and one (or a few) nonconvex QP. For the last QP, we show that our specific problem can be solved efficiently, in spite of nonconvexity. In the benign case, we solve one equality constrained QP, and we prove that projected gradient descent solves it exponentially fast. In the bad case, we have to solve a few more inequality constrained QPs, but we prove that the time complexity is exponential only in the number of inequality constraints. Our experiments show that either benign case or bad case with very few inequality constraints occurs, implying that our algorithm is efficient in most cases.

Ex Output:
A theoretical algorithm for testing local optimality and extracting descent directions at nondifferentiable points of empirical risks of one-hidden-layer ReLU networks.


Ex Input:
Data augmentation (DA) is fundamental against overfitting in large convolutional neural networks, especially with a limited training dataset. In images, DA is usually based on heuristic transformations, like geometric or color transformations. Instead of using predefined transformations, our work learns data augmentation directly from the training data by learning to transform images with an encoder-decoder architecture combined with a spatial transformer network. The transformed images still belong to the same class, but are new, more complex samples for the classifier. Our experiments show that our approach is better than previous generative data augmentation methods, and comparable to predefined transformation methods when training an image classifier.

Ex Output:
Automatic Learning of data augmentation using a GAN based architecture to improve an image classifier


Ex 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.

Ex Output:

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