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.
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Question: Driven by the need for parallelizable hyperparameter optimization methods, this paper studies \emph{open loop} search methods: sequences that are predetermined and can be generated before a single configuration is evaluated. Examples include grid search, uniform random search, low discrepancy sequences, and other sampling distributions.
 In particular, we propose the use of $k$-determinantal point processes in  hyperparameter optimization via random search. Compared to conventional uniform random search where hyperparameter settings are sampled independently, a $k$-DPP promotes diversity.   We describe an approach that transforms hyperparameter search spaces for efficient use with a $k$-DPP. In addition, we introduce a novel Metropolis-Hastings algorithm which can sample from $k$-DPPs defined over spaces with a mixture of discrete and continuous dimensions. Our experiments show significant benefits over uniform random search  in realistic scenarios with a limited budget for training supervised learners, whether in serial or parallel.

Answer: Driven by the need for parallelizable, open-loop hyperparameter optimization methods, we propose the use of $k$-determinantal point processes in  hyperparameter optimization via random search.


Question: 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

Answer: 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. 


Question: Many irregular domains such as social networks, financial transactions, neuron connections, and natural language structures are represented as graphs. In recent years, a variety of  graph neural networks (GNNs) have been successfully applied for representation learning and prediction on such graphs. However, in many of the applications, the underlying graph changes over time and existing GNNs are inadequate for handling such dynamic graphs. In this paper we propose a novel technique for learning embeddings of dynamic graphs based on a tensor algebra framework. Our method extends the popular graph convolutional network (GCN) for learning representations of dynamic graphs using the recently proposed tensor M-product technique. Theoretical results that establish the connection between the proposed tensor approach and spectral convolution of tensors are developed. Numerical experiments on real datasets demonstrate the usefulness of the proposed method for an edge classification task on dynamic graphs.

Answer:
We propose a novel tensor based method for graph convolutional networks on dynamic graphs