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.

Q: 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.

A: We blend deep generative models with programmatic weak supervision to generate coordinated multi-agent trajectories of significantly higher quality than previous baselines.
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Q: Computations for the softmax function in neural network models are expensive when the number of output classes is large. This can become a significant issue in both training and inference for such models. In this paper, we present Doubly Sparse Softmax (DS-Softmax), Sparse Mixture of Sparse of Sparse Experts, to improve the efficiency for softmax inference. During training, our method learns a two-level class hierarchy by dividing entire output class space into several partially overlapping experts. Each expert is responsible for a learned subset of the output class space and each output class only belongs to a small number of those experts. During inference, our method quickly locates the most probable expert to compute small-scale softmax. Our method is learning-based and requires no knowledge of the output class partition space a priori. We empirically evaluate our method on several real-world tasks and demonstrate that we can achieve significant computation reductions without loss of

A: We present doubly sparse softmax, the sparse mixture of sparse of sparse experts, to improve the efficiency for softmax inference through exploiting the two-level overlapping hierarchy.
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Q: {\em Saliency methods} attempt to explain a deep net's decision by assigning a {\em score} to each feature/pixel in the input, often doing this credit-assignment via the gradient of the output with respect to input.
Recently \citet{adebayosan} questioned the validity of many of these methods since they do not pass simple {\em sanity checks}, which test whether the scores shift/vanish when layers of the trained net are randomized, or when the net is retrained using random labels for inputs. % for the inputs. %Surprisingly, the tested methods did not pass these checks: the explanations were relatively unchanged .

We propose a simple fix to existing saliency methods that helps them pass sanity checks, which we call {\em competition for pixels}. This involves computing saliency maps for all possible labels in the classification task, and using a simple competition among them to identify and remove less relevant pixels from the map. Some theoretical justification is provided for it and its performance is empirically demonstrated on several popular methods.

A:
We devise a mechanism called competition among pixels that allows (approximately) complete saliency methods to pass the sanity checks.
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