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。

在自然界中，动物的集体行为（例如飞鸟）由同一物种的个体之间的相互作用主导。但是，对鸟类物种中这种行为的研究是一个复杂的过程，即人类无法使用常规的视觉观察技术（例如自然界的焦点采样）进行。对于鸟类等社会动物，群体形成的机制可以帮助生态学家了解社交线索及其视觉特征随着时间的流逝（例如姿势和形状）之间的关系。但是，恢复飞行鸟类的不同姿势和形状是一个极具挑战性的问题。解决此瓶颈的一种广泛的解决方案是将姿势和形状从2D图像提取到3D对应关系。 3D视觉的最新进展导致了关于3D形状和姿势估计的许多令人印象深刻的作品，每项作品都有不同的利弊。据我们所知，这项工作是首次尝试概述基于单眼视觉的3D鸟重建的最新进展，使计算机视觉和生物学研究人员概述了现有方法，并比较其特征。

我们考虑经典的1中心问题：给定度量空间中的n个点P，找到p中的点，最小化到P的其他要点的最大距离。我们研究了D维$ \中这个问题的复杂性。 ell_p $ -metrics和编辑和ulam度量串的长度d。我们的1中心问题的结果可以根据D分类如下。 $ \ bullet $ small d：我们提供固定维度$ \ ell_1 $指标中的1中心问题的第一线性时间算法。另一方面，假设击中集猜测（HSC），我们显示，当$ d =ω（\ log n）$时，没有子种式算法可以在任何$ \ ell_p $ -metrics中解决1中心问题，或者在编辑或ulam指标中。 $ \ bullet $大d。当$ d =ω（n）$时，我们将条件下限扩展到编辑度量标准中的1中心问题的子四分之一算法（假设量化SETH）。另一方面，我们给出了一个$（1+ \ epsilon）$ - ulam度量标准中的1美元逼近，运行时间$ \ tilde {o _ {\ epsilon}}（nd + n ^ 2 \ sqrt {d}） $。我们还通过允许近似或通过减小维度D来加强一些上述下限，而是仅针对列出所有必要解决方案的较弱的算法类别。此外，我们扩展了我们的硬度结果，以便在编辑度量标准中排除次级学习的1中位问题的亚级算法，其中给出了一组长度n的n个字符串，目标是在集合中找到一个字符串这最小化了集合中的其余字符串的编辑距离之和。

近年来，可解释的人工智能（XAI）已成为一个非常适合的框架，可以生成人类对“黑盒”模型的可理解解释。在本文中，一种新颖的XAI视觉解释算法称为相似性差异和唯一性（SIDU）方法，该方法可以有效地定位负责预测的整个对象区域。通过各种计算和人类主题实验分析了SIDU算法的鲁棒性和有效性。特别是，使用三种不同类型的评估（应用，人类和功能地面）评估SIDU算法以证明其出色的性能。在对“黑匣子”模型的对抗性攻击的情况下，进一步研究了Sidu的鲁棒性，以更好地了解其性能。我们的代码可在：https：//github.com/satyamahesh84/sidu_xai_code上找到。

Designing experiments often requires balancing between learning about the true treatment effects and earning from allocating more samples to the superior treatment. While optimal algorithms for the Multi-Armed Bandit Problem (MABP) provide allocation policies that optimally balance learning and earning, they tend to be computationally expensive. The Gittins Index (GI) is a solution to the MABP that can simultaneously attain optimality and computationally efficiency goals, and it has been recently used in experiments with Bernoulli and Gaussian rewards. For the first time, we present a modification of the GI rule that can be used in experiments with exponentially-distributed rewards. We report its performance in simulated 2- armed and 3-armed experiments. Compared to traditional non-adaptive designs, our novel GI modified design shows operating characteristics comparable in learning (e.g. statistical power) but substantially better in earning (e.g. direct benefits). This illustrates the potential that designs using a GI approach to allocate participants have to improve participant benefits, increase efficiencies, and reduce experimental costs in adaptive multi-armed experiments with exponential rewards.

Quadruped robots are currently used in industrial robotics as mechanical aid to automate several routine tasks. However, presently, the usage of such a robot in a domestic setting is still very much a part of the research. This paper discusses the understanding and virtual simulation of such a robot capable of detecting and understanding human emotions, generating its gait, and responding via sounds and expression on a screen. To this end, we use a combination of reinforcement learning and software engineering concepts to simulate a quadruped robot that can understand emotions, navigate through various terrains and detect sound sources, and respond to emotions using audio-visual feedback. This paper aims to establish the framework of simulating a quadruped robot that is emotionally intelligent and can primarily respond to audio-visual stimuli using motor or audio response. The emotion detection from the speech was not as performant as ERANNs or Zeta Policy learning, still managing an accuracy of 63.5%. The video emotion detection system produced results that are almost at par with the state of the art, with an accuracy of 99.66%. Due to its "on-policy" learning process, the PPO algorithm was extremely rapid to learn, allowing the simulated dog to demonstrate a remarkably seamless gait across the different cadences and variations. This enabled the quadruped robot to respond to generated stimuli, allowing us to conclude that it functions as predicted and satisfies the aim of this work.

Real-world robotic grasping can be done robustly if a complete 3D Point Cloud Data (PCD) of an object is available. However, in practice, PCDs are often incomplete when objects are viewed from few and sparse viewpoints before the grasping action, leading to the generation of wrong or inaccurate grasp poses. We propose a novel grasping strategy, named 3DSGrasp, that predicts the missing geometry from the partial PCD to produce reliable grasp poses. Our proposed PCD completion network is a Transformer-based encoder-decoder network with an Offset-Attention layer. Our network is inherently invariant to the object pose and point's permutation, which generates PCDs that are geometrically consistent and completed properly. Experiments on a wide range of partial PCD show that 3DSGrasp outperforms the best state-of-the-art method on PCD completion tasks and largely improves the grasping success rate in real-world scenarios. The code and dataset will be made available upon acceptance.

When robots learn reward functions using high capacity models that take raw state directly as input, they need to both learn a representation for what matters in the task -- the task ``features" -- as well as how to combine these features into a single objective. If they try to do both at once from input designed to teach the full reward function, it is easy to end up with a representation that contains spurious correlations in the data, which fails to generalize to new settings. Instead, our ultimate goal is to enable robots to identify and isolate the causal features that people actually care about and use when they represent states and behavior. Our idea is that we can tune into this representation by asking users what behaviors they consider similar: behaviors will be similar if the features that matter are similar, even if low-level behavior is different; conversely, behaviors will be different if even one of the features that matter differs. This, in turn, is what enables the robot to disambiguate between what needs to go into the representation versus what is spurious, as well as what aspects of behavior can be compressed together versus not. The notion of learning representations based on similarity has a nice parallel in contrastive learning, a self-supervised representation learning technique that maps visually similar data points to similar embeddings, where similarity is defined by a designer through data augmentation heuristics. By contrast, in order to learn the representations that people use, so we can learn their preferences and objectives, we use their definition of similarity. In simulation as well as in a user study, we show that learning through such similarity queries leads to representations that, while far from perfect, are indeed more generalizable than self-supervised and task-input alternatives.

and widely used information measurement metric, particularly popularized for SSVEP- based Brain-Computer (BCI) interfaces. By combining speed and accuracy into a single-valued parameter, this metric aids in the evaluation and comparison of various target identification algorithms across different BCI communities. To accurately depict performance and inspire an end-to-end design for futuristic BCI designs, a more thorough examination and definition of ITR is therefore required. We model the symbiotic communication medium, hosted by the retinogeniculate visual pathway, as a discrete memoryless channel and use the modified capacity expressions to redefine the ITR. We use graph theory to characterize the relationship between the asymmetry of the transition statistics and the ITR gain with the new definition, leading to potential bounds on data rate performance. On two well-known SSVEP datasets, we compared two cutting-edge target identification methods. Results indicate that the induced DM channel asymmetry has a greater impact on the actual perceived ITR than the change in input distribution. Moreover, it is demonstrated that the ITR gain under the new definition is inversely correlated with the asymmetry in the channel transition statistics. Individual input customizations are further shown to yield perceived ITR performance improvements. An algorithm is proposed to find the capacity of binary classification and further discussions are given to extend such results to ensemble techniques.We anticipate that the results of our study will contribute to the characterization of the highly dynamic BCI channel capacities, performance thresholds, and improved BCI stimulus designs for a tighter symbiosis between the human brain and computer systems while enhancing the efficiency of the underlying communication resources.