Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has resulted in opening doors to solving a variety of real-world problems ranging from mathematical finance to stochastic control for industrial applications. Although feasible, these deep learning methods are still constrained by training time and memory. Tackling these shortcomings, Tensor Neural Networks (TNN) demonstrate that they can provide significant parameter savings while attaining the same accuracy as compared to the classical Dense Neural Network (DNN). In addition, we also show how TNN can be trained faster than DNN for the same accuracy. Besides TNN, we also introduce Tensor Network Initializer (TNN Init), a weight initialization scheme that leads to faster convergence with smaller variance for an equivalent parameter count as compared to a DNN. We benchmark TNN and TNN Init by applying them to solve the parabolic PDE associated with the Heston model, which is widely used in financial pricing theory.

时间序列观察可以看作是对我们通常不知道的规则控制的基本动力系统的实现。对于时间序列学习任务，我们需要了解我们将模型符合可用数据，这是一个独特的实现历史记录。对单个实现的培训通常会导致严重的过度适应缺乏概括。为了解决这个问题，我们引入了一个通用的递归框架，用于时间序列扩展，我们称之为递归插值方法，称为边缘。使用所有先前值的递归插值函数生成新样本，以使增强样品保留原始固有的时间序列动力学。我们执行理论分析以表征所提出的边缘并保证其测试性能。我们将RIM应用于不同的现实世界时间序列案例，以在有关回归，分类和强化学习任务的非官能数据上实现强大的性能。

Since early in the coronavirus disease 2019 (COVID-19) pandemic, there has been interest in using artificial intelligence methods to predict COVID-19 infection status based on vocal audio signals, for example cough recordings. However, existing studies have limitations in terms of data collection and of the assessment of the performances of the proposed predictive models. This paper rigorously assesses state-of-the-art machine learning techniques used to predict COVID-19 infection status based on vocal audio signals, using a dataset collected by the UK Health Security Agency. This dataset includes acoustic recordings and extensive study participant meta-data. We provide guidelines on testing the performance of methods to classify COVID-19 infection status based on acoustic features and we discuss how these can be extended more generally to the development and assessment of predictive methods based on public health datasets.

部分微分方程（PDE）用于对科学和工程中的各种动力系统进行建模。深度学习的最新进展使我们能够以新的方式解决维度的诅咒，从而在更高的维度中解决它们。但是，深度学习方法受到训练时间和记忆的约束。为了解决这些缺点，我们实施了张量神经网络（TNN），这是一种量子启发的神经网络体系结构，利用张量网络的想法来改进深度学习方法。我们证明，与经典密集神经网络（DNN）相比，TNN提供了明显的参数节省，同时获得了与经典密集的神经网络相同的准确性。此外，我们还展示了如何以相同的精度来比DNN更快地训练TNN。我们通过将它们应用于求解抛物线PDE，特别是Black-Scholes-Barenblatt方程，该方程广泛用于金融定价理论，基于基准测试。还讨论了进一步的例子，例如汉密尔顿 - 雅各比 - 贝尔曼方程。

生物视觉系统的神经基础在实验上研究很具有挑战性，特别是因为相对于视觉输入，神经元活性变得越来越非线性。人工神经网络（ANN）可以为改善我们对这一复杂系统的理解提供各种目标，不仅充当硅中新假设产生的感觉皮层的预测数字双胞胎，而且还融合了生物启发的建筑主题，以逐步桥接桥梁生物和机器视觉之间的差距。该鼠标最近已成为研究视觉信息处理的流行模型系统，但是尚未确定识别鼠标视觉系统最新模型的标准化大规模基准。为了填补这一空白，我们提出了感官基准竞赛。我们从小鼠初级视觉皮层中收集了一个大规模数据集，其中包含七个小鼠的28,000多个神经元的反应，并通过数千个自然图像刺激，以及同时的行为测量，包括跑步速度，瞳孔扩张和眼动。基准挑战将基于固定测试集​​中神经元响应的预测性能对模型进行对模型，其中包括两个模型输入的轨道，仅限于刺激（感觉到）或刺激加行为（感觉符号+）。我们提供一个起始套件，以降低进入障碍的障碍，包括教程，预训练的基线模型以及带有一条线命令以进行数据加载和提交的API。我们希望将其视为定期挑战和数据发布的起点，也是衡量鼠标视觉系统及其他大规模神经系统识别模型中进度的标准工具。

深度操作员的学习已成为减少订购建模和PDE模型发现的有前途的工具。利用深层神经网络的表达能力，尤其是在高维度中，这种方法了解功能状态变量之间的映射。虽然提出的方法仅在因变量中才假设噪声，但用于操作员学习的实验和数值数据也通常在自变量中显示出噪声，因为两个变量都代表了符合测量误差的信号。在标量数据的回归中，未能解释嘈杂的自变量会导致偏差参数估计值。使用嘈杂的自变量，通过普通最小二乘（OLS）拟合的线性模型将显示衰减偏置，其中斜率将被低估。在这项工作中，我们得出了在独立变量和因变量中都具有白噪声的线性操作器回归的衰减偏差的类似物。在非线性环境中，我们在计算上证明了在自变量中存在噪声的情况下，汉堡操作员的作用不足。我们提出了两种操作员回归方法，mor-physics和deponet的变异错误模型（EIV）模型，并证明这些新模型在存在各种操作员学习问题的嘈杂自变量的情况下减少了偏见。考虑到1D和2D的汉堡操作员，我们证明了EIV操作员的学习能够在击败OLS操作员学习的高噪声政权中恢复运营商。我们还引入了一个EIV模型，以进行时间不断发展的PDE发现，并表明OLS和EIV在学习库拉莫托 - 西瓦辛斯基进化运算符中从损坏的数据中进行了类似的表现，这表明偏见在OLS操作员学习中的影响取决于目标操作员的规律性。

卷积神经网络（CNNS）在监督环境中的影响提供了巨大的性能。从CNN中学到的表示，在高度球形歧管上运作，导致了面部识别，面部识别和其他受监督任务的富有魅力结果。具有广泛的激活功能，具有间直觉，在欧几里德空间中执行优于Softmax。这项研究的主要动力是提供见解。首先，暗示立体图投影以将数据从欧几里德空间（$ \ mathbb {r} ^ {n} $）转换为高度球形歧管（$ \ mathbb {s} ^ {n} $）来分析角度边缘损失的性能。其次，从理论上证明了使用立体投影在极度上构建的决策边界义务授权了神经网络的学习。实验已经证明，在现有的最先进的角度边缘目标功能上应用立体摄影改善了标准图像分类数据集的性能（CIFAR-10,100）。此外，我们在疟疾薄血涂片图像上运行了我们的实验，导致有效的结果。该代码可公开可用：https：//github.com/barulalithb/stereo -angular-margin。

Our paper aims to analyze political polarization in US political system using Language Models, and thereby help candidates make an informed decision. The availability of this information will help voters understand their candidates views on the economy, healthcare, education and other social issues. Our main contributions are a dataset extracted from Wikipedia that spans the past 120 years and a Language model based method that helps analyze how polarized a candidate is. Our data is divided into 2 parts, background information and political information about a candidate, since our hypothesis is that the political views of a candidate should be based on reason and be independent of factors such as birthplace, alma mater, etc. We further split this data into 4 phases chronologically, to help understand if and how the polarization amongst candidates changes. This data has been cleaned to remove biases. To understand the polarization we begin by showing results from some classical language models in Word2Vec and Doc2Vec. And then use more powerful techniques like the Longformer, a transformer based encoder, to assimilate more information and find the nearest neighbors of each candidate based on their political view and their background.

While the capabilities of autonomous systems have been steadily improving in recent years, these systems still struggle to rapidly explore previously unknown environments without the aid of GPS-assisted navigation. The DARPA Subterranean (SubT) Challenge aimed to fast track the development of autonomous exploration systems by evaluating their performance in real-world underground search-and-rescue scenarios. Subterranean environments present a plethora of challenges for robotic systems, such as limited communications, complex topology, visually-degraded sensing, and harsh terrain. The presented solution enables long-term autonomy with minimal human supervision by combining a powerful and independent single-agent autonomy stack, with higher level mission management operating over a flexible mesh network. The autonomy suite deployed on quadruped and wheeled robots was fully independent, freeing the human supervision to loosely supervise the mission and make high-impact strategic decisions. We also discuss lessons learned from fielding our system at the SubT Final Event, relating to vehicle versatility, system adaptability, and re-configurable communications.

Object movement identification is one of the most researched problems in the field of computer vision. In this task, we try to classify a pixel as foreground or background. Even though numerous traditional machine learning and deep learning methods already exist for this problem, the two major issues with most of them are the need for large amounts of ground truth data and their inferior performance on unseen videos. Since every pixel of every frame has to be labeled, acquiring large amounts of data for these techniques gets rather expensive. Recently, Zhao et al. [1] proposed one of a kind Arithmetic Distribution Neural Network (ADNN) for universal background subtraction which utilizes probability information from the histogram of temporal pixels and achieves promising results. Building onto this work, we developed an intelligent video surveillance system that uses ADNN architecture for motion detection, trims the video with parts only containing motion, and performs anomaly detection on the trimmed video.