Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries (equivariance) respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.
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诸如合并性和自动分化之类的属性使人工神经网络成为应用中普遍存在的工具。解决更具挑战性的问题导致神经网络逐渐变得更加复杂，因此很难从数学角度定义。我们提出了基于集成理论和参数跨度的概念的分类框架产生的线性层的一般定义。该定义概括并涵盖经典层（例如，密集，卷积），同时保证了层的衍生物对反向传播的存在和计算性。
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Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how simple machines can be combined into more complex ones. We explore finite- and infinite-depth machines, which generalize neural networks and neural ordinary differential equations. Borrowing ideas from functional analysis and kernel methods, we build complete, normed, infinite-dimensional spaces of machines, and we discuss how to find optimal architectures and parameters -- within those spaces -- to solve a given computational problem. In our numerical experiments, these kernel-inspired networks can outperform classical neural networks when the training dataset is small.
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柔性章鱼臂具有卓越的能力，可以协调大量自由度并执行复杂的操纵任务。结果，这些系统继续吸引生物学家和机器人的注意力。在本文中，我们开发了一个三维模型的软章鱼臂，配备了生物力学上逼真的肌肉致动。考虑了所有主要肌肉群施加的内力和夫妇。描述了一种能量塑形控制方法来协调肌肉活动，以便在3D空间中掌握和触及。本文的主要贡献是：（i）主要肌肉群建模以引起三维运动； （ii）基于存储的能量功能的肌肉激活的数学公式； （iii）通过在特殊欧几里得组SE中解决优化问题获得的设计特定于任务的平衡配置的计算有效过程（3）。然后，根据优化问题解决方案引起的共同状态变量，对肌肉控制进行迭代计算。该方法在物理准确的软件环境弹性中得到了数值的证明。报告了模拟观察到的章鱼行为的数值实验的结果。
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在自动操纵，远程操作或物理人类机器人相互作用期间，四足动物的操纵器在与外部力量打交道时必须合规。本文提出了一个全身控制器，该控制器允许实施笛卡尔阻抗控制，以协调跟踪性能以及对机器人基础和操纵器组的理想合规性。控制器是通过使用二次编程（QP）的优化问题制定的，以对系统施加所需的行为，同时满足摩擦锥限制，单方面力量约束，关节和扭矩限制。提出的策略将平台的手臂和底座取代，从而实施了线性双质量弹簧阻尼器系统的行为，并允许独立调整其惯性，刚度和阻尼特性。使用配备了7-DOF操纵器组的90kg HYQ机器人通过广泛的模拟研究来验证控制架构。仿真结果表明，当在手臂的最终效用器上应用外力时，阻抗渲染性能。该论文介绍了完整姿势条件（地面上的所有腿）的结果，并且首次显示阻抗渲染如何受动态步态过程中接触条件的影响。
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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.
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Attention mechanisms form a core component of several successful deep learning architectures, and are based on one key idea: ''The output depends only on a small (but unknown) segment of the input.'' In several practical applications like image captioning and language translation, this is mostly true. In trained models with an attention mechanism, the outputs of an intermediate module that encodes the segment of input responsible for the output is often used as a way to peek into the `reasoning` of the network. We make such a notion more precise for a variant of the classification problem that we term selective dependence classification (SDC) when used with attention model architectures. Under such a setting, we demonstrate various error modes where an attention model can be accurate but fail to be interpretable, and show that such models do occur as a result of training. We illustrate various situations that can accentuate and mitigate this behaviour. Finally, we use our objective definition of interpretability for SDC tasks to evaluate a few attention model learning algorithms designed to encourage sparsity and demonstrate that these algorithms help improve interpretability.
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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.
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KL-regularized reinforcement learning from expert demonstrations has proved successful in improving the sample efficiency of deep reinforcement learning algorithms, allowing them to be applied to challenging physical real-world tasks. However, we show that KL-regularized reinforcement learning with behavioral reference policies derived from expert demonstrations can suffer from pathological training dynamics that can lead to slow, unstable, and suboptimal online learning. We show empirically that the pathology occurs for commonly chosen behavioral policy classes and demonstrate its impact on sample efficiency and online policy performance. Finally, we show that the pathology can be remedied by non-parametric behavioral reference policies and that this allows KL-regularized reinforcement learning to significantly outperform state-of-the-art approaches on a variety of challenging locomotion and dexterous hand manipulation tasks.
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Three main points: 1. Data Science (DS) will be increasingly important to heliophysics; 2. Methods of heliophysics science discovery will continually evolve, requiring the use of learning technologies [e.g., machine learning (ML)] that are applied rigorously and that are capable of supporting discovery; and 3. To grow with the pace of data, technology, and workforce changes, heliophysics requires a new approach to the representation of knowledge.
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