Although deep learning has made remarkable progress in processing various types of data such as images, text and speech, they are known to be susceptible to adversarial perturbations: perturbations specifically designed and added to the input to make the target model produce erroneous output. Most of the existing studies on generating adversarial perturbations attempt to perturb the entire input indiscriminately. In this paper, we propose ExploreADV, a general and flexible adversarial attack system that is capable of modeling regional and imperceptible attacks, allowing users to explore various kinds of adversarial examples as needed. We adapt and combine two existing boundary attack methods, DeepFool and Brendel\&Bethge Attack, and propose a mask-constrained adversarial attack system, which generates minimal adversarial perturbations under the pixel-level constraints, namely ``mask-constraints''. We study different ways of generating such mask-constraints considering the variance and importance of the input features, and show that our adversarial attack system offers users good flexibility to focus on sub-regions of inputs, explore imperceptible perturbations and understand the vulnerability of pixels/regions to adversarial attacks. We demonstrate our system to be effective based on extensive experiments and user study.

We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The method is based on tensor-train and flow-based generative modeling. Our method first efficiently constructs an approximate density in the tensor-train form via solving the tensor cores from a linear system based on the kernel density estimators of low-dimensional marginals. We then train a continuous-time flow model from this tensor-train density to the observed empirical distribution by performing a maximum likelihood estimation. The proposed method combines the optimization-less feature of the tensor-train with the flexibility of the flow-based generative models. Numerical results are included to demonstrate the performance of the proposed method.

在本文中，我们提出了一个基于树张量网状状态的密度估计框架。所提出的方法包括使用Chow-Liu算法确定树拓扑，并获得线性系统通过草图技术定义张量 - 网络组件的线性系统。开发了草图功能的新颖选择，以考虑包含循环的图形模型。提供样品复杂性保证，并通过数值实验进一步证实。

逆波散射旨在使用对象如何散射传入波的数据来确定对象的属性。为了收集信息，传感器被放在不同的位置以彼此发送和接收波。传感器位置和入射波频率的选择决定了散射器特性的重建质量。本文介绍了增强学习，以开发精确成像，以决定传感器位置和波频率以智能方式适应不同的散射器，从而通过有限的成像资源获得重建质量的显着改善。将提供广泛的数值结果，以证明所提出的方法比现有方法的优越性。

在本文中，我们介绍了一种草图算法，用于构建其样品概率密度的张量列车表示。我们的方法偏离了基于标准的递归SVD构建张量列车的程序。取而代之的是，我们为单个张量火车芯制定并求解一系列小型线性系统。这种方法可以避免维数的诅咒，从而威胁恢复问题的算法和样本复杂性。具体而言，对于马尔可夫模型，我们证明可以使用相对于尺寸恒定的样品复杂性回收张量芯。最后，我们通过几个数值实验说明了该方法的性能。

社区检测和正交组同步是科学和工程中各种重要应用的基本问题。在这项工作中，我们考虑了社区检测和正交组同步的联合问题，旨在恢复社区并同时执行同步。为此，我们提出了一种简单的算法，该算法由频谱分解步骤组成，然后是彼此枢转的QR分解（CPQR）。所提出的算法与数据点数线性有效且缩放。我们还利用最近开发的“休闲一淘汰”技术来建立近乎最佳保证，以确切地恢复集群成员资格，并稳定地恢复正交变换。数值实验证明了我们算法的效率和功效，并确认了我们的理论表征。

在设计和使用中推进锂离子电池（LIBS）是推广未来几十年充电的关键，以减轻人类导致的气候变化。对LIB降级的理解不足是一个重要的瓶颈，限制电池耐用性和安全性。在这里，我们提出了基于混合物理学和数据驱动的模型，用于电池劣化的在线诊断和预后。与现有电池建模努力相比，我们的目标是建立一个具有物理学的模型作为其骨干和统计学习技术作为增强功能。这种混合模型具有更好的普遍性和可解释性，以及与其预测相关的良好校准的不确定性，使其更有价值并且与在现实使用情况下的安全关键应用程序更有价值。