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.

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。

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。

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.

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.

The pandemic of these very recent years has led to a dramatic increase in people wearing protective masks in public venues. This poses obvious challenges to the pervasive use of face recognition technology that now is suffering a decline in performance. One way to address the problem is to revert to face recovery methods as a preprocessing step. Current approaches to face reconstruction and manipulation leverage the ability to model the face manifold, but tend to be generic. We introduce a method that is specific for the recovery of the face image from an image of the same individual wearing a mask. We do so by designing a specialized GAN inversion method, based on an appropriate set of losses for learning an unmasking encoder. With extensive experiments, we show that the approach is effective at unmasking face images. In addition, we also show that the identity information is preserved sufficiently well to improve face verification performance based on several face recognition benchmark datasets.

As language models have grown in parameters and layers, it has become much harder to train and infer with them on single GPUs. This is severely restricting the availability of large language models such as GPT-3, BERT-Large, and many others. A common technique to solve this problem is pruning the network architecture by removing transformer heads, fully-connected weights, and other modules. The main challenge is to discern the important parameters from the less important ones. Our goal is to find strong metrics for identifying such parameters. We thus propose two strategies: Cam-Cut based on the GradCAM interpretations, and Smooth-Cut based on the SmoothGrad, for calculating the importance scores. Through this work, we show that our scoring functions are able to assign more relevant task-based scores to the network parameters, and thus both our pruning approaches significantly outperform the standard weight and gradient-based strategies, especially at higher compression ratios in BERT-based models. We also analyze our pruning masks and find them to be significantly different from the ones obtained using standard metrics.

We propose the fully differentiable $\nabla$-RANSAC.It predicts the inlier probabilities of the input data points, exploits the predictions in a guided sampler, and estimates the model parameters (e.g., fundamental matrix) and its quality while propagating the gradients through the entire procedure. The random sampler in $\nabla$-RANSAC is based on a clever re-parametrization strategy, i.e.\ the Gumbel Softmax sampler, that allows propagating the gradients directly into the subsequent differentiable minimal solver. The model quality function marginalizes over the scores from all models estimated within $\nabla$-RANSAC to guide the network learning accurate and useful probabilities.$\nabla$-RANSAC is the first to unlock the end-to-end training of geometric estimation pipelines, containing feature detection, matching and RANSAC-like randomized robust estimation. As a proof of its potential, we train $\nabla$-RANSAC together with LoFTR, i.e. a recent detector-free feature matcher, to find reliable correspondences in an end-to-end manner. We test $\nabla$-RANSAC on a number of real-world datasets on fundamental and essential matrix estimation. It is superior to the state-of-the-art in terms of accuracy while being among the fastest methods. The code and trained models will be made public.

We present temporally layered architecture (TLA), a biologically inspired system for temporally adaptive distributed control. TLA layers a fast and a slow controller together to achieve temporal abstraction that allows each layer to focus on a different time-scale. Our design is biologically inspired and draws on the architecture of the human brain which executes actions at different timescales depending on the environment's demands. Such distributed control design is widespread across biological systems because it increases survivability and accuracy in certain and uncertain environments. We demonstrate that TLA can provide many advantages over existing approaches, including persistent exploration, adaptive control, explainable temporal behavior, compute efficiency and distributed control. We present two different algorithms for training TLA: (a) Closed-loop control, where the fast controller is trained over a pre-trained slow controller, allowing better exploration for the fast controller and closed-loop control where the fast controller decides whether to "act-or-not" at each timestep; and (b) Partially open loop control, where the slow controller is trained over a pre-trained fast controller, allowing for open loop-control where the slow controller picks a temporally extended action or defers the next n-actions to the fast controller. We evaluated our method on a suite of continuous control tasks and demonstrate the advantages of TLA over several strong baselines.

Deep neural networks have long training and processing times. Early exits added to neural networks allow the network to make early predictions using intermediate activations in the network in time-sensitive applications. However, early exits increase the training time of the neural networks. We introduce QuickNets: a novel cascaded training algorithm for faster training of neural networks. QuickNets are trained in a layer-wise manner such that each successive layer is only trained on samples that could not be correctly classified by the previous layers. We demonstrate that QuickNets can dynamically distribute learning and have a reduced training cost and inference cost compared to standard Backpropagation. Additionally, we introduce commitment layers that significantly improve the early exits by identifying for over-confident predictions and demonstrate its success.