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Creators/Authors contains: "Wang, Zichao"

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  4. Computing or approximating the convex hull of a dataset plays a role in a wide range of applications, including economics, statistics, and physics, to name just a few. However, convex hull computation and approximation is exponentially complex, in terms of both memory and computation, as the ambient space dimension increases. In this paper, we propose DeepHull, a new convex hull approximation algorithm based on convex deep networks (DNs) with continuous piecewise-affine nonlinearities and nonnegative weights. The idea is that binary classification between true data samples and adversarially generated samples with such a DN naturally induces a polytope decision boundary that approximates the true data convex hull. A range of exploratory experiments demonstrates that DeepHull efficiently produces a meaningful convex hull approximation, even in a high-dimensional ambient space.
  5. The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key DNN architecture remains to be kernelized, namely, the recurrent neural network (RNN). In this paper we introduce and study the Recurrent Neural Tangent Kernel (RNTK), which provides new insights into the behavior of overparametrized RNNs. A key property of the RNTK should greatly benefit practitioners is its ability to compare inputs of different length. To this end, we characterize how the RNTK weights different time steps to form its output under different initialization parameters and nonlinearity choices. A synthetic and 56 real-world data experiments demonstrate that the RNTK offers significant performance gains over other kernels, including standard NTKs, across a wide array of data sets.
  6. The ever growing amount of educational content renders it increasingly difficult to manually generate sufficient practice or quiz questions to accompany it. This paper introduces QG-Net, a recurrent neural network-based model specifically designed for automatically generating quiz questions from educational content such as textbooks. QG-Net, when trained on a publicly available, general-purpose question/answer dataset and without further fine-tuning, is capable of generating high quality questions from textbooks, where the content is significantly different from the training data. Indeed, QG-Net outperforms state-of-the-art neural network-based and rules-based systems for question generation, both when evaluated using standard benchmark datasets and when using human evaluators. QG-Net also scales favorably to applications with large amounts of educational content, since its performance improves with the amount of training data.