Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distanc...
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We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy st...
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Evaluating the performance of machine learning models under distribution shifts is challenging, especially when we only have unlabeled data from the shifted (target) domain, along with labeled data from the original (...
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Feature learning is thought to be one of the fundamental reasons for the success of deep neural networks. It is rigorously known that in two-layer fully-connected neural networks under certain conditions, one step of ...
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Feature learning is thought to be one of the fundamental reasons for the success of deep neural networks. It is rigorously known that in two-layer fully-connected neural networks under certain conditions, one step of gradient descent on the first layer can lead to feature learning;characterized by the appearance of a separated rank-one component-spike-in the spectrum of the feature matrix. However, with a constant gradient descent step size, this spike only carries information from the linear component of the target function and therefore learning non-linear components is impossible. We show that with a learning rate that grows with the sample size, such training in fact introduces multiple rank-one components, each corresponding to a specific polynomial feature. We further prove that the limiting large-dimensional and large sample training and test errors of the updated neural networks are fully characterized by these spikes. By precisely analyzing the improvement in the training and test errors, we demonstrate that these non-linear features can enhance learning. Copyright 2024 by the author(s)
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy st...
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We propose a multiple-splitting projection test (MPT) for one-sample mean vectors in high-dimensional settings. The idea of projection test is to project high-dimensional samples to a 1-dimensional space using an opti...
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We propose a multiple-splitting projection test (MPT) for one-sample mean vectors in high-dimensional settings. The idea of projection test is to project high-dimensional samples to a 1-dimensional space using an optimal projection direction such that traditional tests can be carried out with projected samples. However, estimation of the optimal projection direction has not been systematically studied in the literature. In this work, we bridge the gap by proposing a consistent estimation via regularized quadratic optimization. To retain type I error rate, we adopt a data-splitting strategy when constructing test statistics. To mitigate the power loss due to data-splitting, we further propose a test via multiple splits to enhance the testing power. We show that the p-values resulted from multiple splits are exchangeable. Unlike existing methods which tend to conservatively combine dependent p- values, we develop an exact level α test that explicitly utilizes the exchangeability structure to achieve better power. Numerical studies show that the proposed test well retains the type I error rate and is more powerful than state-of-the-art tests.
The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull *** achieved the proposed sampling plan by applying the conc...
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The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull *** achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans.A warning sign for acceptance number was proposed to increase the probability of current lot *** optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk.A simulation study was presented to support the proposed sampling plan.A comparison between the proposed and existing sampling plans,namely multiple dependent state(MDS)sampling plans and a modified multiple dependent state(MMDS)sampling plan,was considered under the average sampling number and operating characteristic curve *** addition,the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling *** results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.
This paper proposes and analyzes a Robin-type multiphysics domain decomposition method (DDM) for the steady-state Navier-Stokes-Darcy model with three interface conditions. In addition to the two regular interface con...
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RCGAu is a hybrid real-coded genetic algorithm with "uniform random direction" search mechanism. The uniform random direction search mechanism enhances the local search capability of RCGA. In this paper, RCG...
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