本文提出了一个理论和计算框架，用于基于非欧几里得收缩理论对隐式神经网络的训练和鲁棒性验证。基本思想是将神经网络的鲁棒性分析作为可及性问题，使用（i）$ \ ell _ {\ infty} $ - norm inort input-utput-optup-utput lipschitz常数和（ii）网络的紧密包含函数到过度陈列在其可达集合中。首先，对于给定的隐式神经网络，我们使用$ \ ell _ {\ infty} $ - 矩阵测量方法来为其适应性良好的条件提出足够的条件，设计一种迭代算法来计算其固定点，并为其$ \提供上限ell_ \ infty $ -Norm输入输出Lipschitz常数。其次，我们介绍了一个相关的嵌入式网络，并表明嵌入式网络可用于提供原始网络的可触及式集合的$ \ ell_ \ infty $ -Norm Box过度交配。此外，我们使用嵌入式网络来设计一种迭代算法，用于计算原始系统紧密包含函数的上限。第三，我们使用Lipschitz常数的上限和紧密包含函数的上限来设计两种算法，以训练和稳健性验证隐式神经网络。最后，我们应用算法在MNIST数据集上训练隐式神经网络，并将模型的鲁棒性与通过文献中现有方法训练的模型进行比较。

在本文中，我们介绍了一个高级控制器合成框架，该框架使异构代理团队能够相互协助解决运行时出现的环境冲突。这种冲突解决方法是基于基于时间逻辑的反应性综合，以确保在特定环境假设下的安全性和任务完成。在异质的多机构系统中，每个代理都有望完成自己的任务，以服务全球团队的目标。但是，在运行时，代理商可能会遇到未建模的障碍物（例如门或墙壁），以阻止其完成自己的任务。为了解决这个问题，我们利用其他异质代理解决障碍的能力。提出了一个控制器框架，以在检测到这种情况时将适当的障碍物解决到所需目标的能力重定向。一组涉及双足机器人数字和四轮驱动器的案例研究用于评估行动中的控制器性能。此外，我们在物理多代理机器人系统上实施了拟议的框架，以证明其对现实世界应用的生存能力。

隐式神经网络是一般的学习模型，可以用隐式代数方程替换传统的馈电模型中的层。与传统学习模型相比，隐式网络提供竞争性能和降低的内存消耗。然而，它们可以对输入对抗性扰动保持脆弱。本文提出了隐式神经网络的稳健性验证的理论和计算框架;我们的框架混合在一起混合单调系统理论和收缩理论。首先，给定隐式神经网络，我们介绍了一个相关的嵌入式网络，并显示，给定$ \ ell_ infty $ -norm框限制对输入，嵌入式网络提供$ \ ell_ \ idty $ -norm box超值给定网络的输出。其次，使用$ \ ell _ {\ infty} $ - 矩阵措施，我们为原始和嵌入式系统的良好提出了足够的条件，并设计了一种迭代算法来计算$ \ e _ {\ infty} $ - norm box鲁棒性利润率和可达性和分类问题。第三，独立价值，我们提出了一种新颖的相对分类器变量，导致认证问题的经过认证的对抗性鲁棒性更严格的界限。最后，我们对在Mnist DataSet上培训的非欧几里德单调运营商网络（Nemon）上进行数值模拟。在这些模拟中，我们比较了我们的混合单调对收缩方法的准确性和运行时间与文献中的现有鲁棒性验证方法，以估算认证的对抗性鲁棒性。

本文表明，在某些情况下，由于使用屏障功能而产生的安全性覆盖不必要地受到限制。特别是，我们检查了固定翼碰撞的情况，并表明当使用屏障功能时，在某些情况下，两架固定翼飞机可能比根本没有屏障功能更接近碰撞。此外，我们构建了屏障功能将系统标记为不安全的情况，即使车辆开始任意分开。换句话说，屏障功能可确保安全，但具有不必要的性能成本。因此，我们引入了无模型的屏障功能，该功能采用数据驱动方法来创建屏障功能。我们证明了在两架固定翼飞机的碰撞避免模拟中，无模型屏障功能的有效性。

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.

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.

Managing novelty in perception-based human activity recognition (HAR) is critical in realistic settings to improve task performance over time and ensure solution generalization outside of prior seen samples. Novelty manifests in HAR as unseen samples, activities, objects, environments, and sensor changes, among other ways. Novelty may be task-relevant, such as a new class or new features, or task-irrelevant resulting in nuisance novelty, such as never before seen noise, blur, or distorted video recordings. To perform HAR optimally, algorithmic solutions must be tolerant to nuisance novelty, and learn over time in the face of novelty. This paper 1) formalizes the definition of novelty in HAR building upon the prior definition of novelty in classification tasks, 2) proposes an incremental open world learning (OWL) protocol and applies it to the Kinetics datasets to generate a new benchmark KOWL-718, 3) analyzes the performance of current state-of-the-art HAR models when novelty is introduced over time, 4) provides a containerized and packaged pipeline for reproducing the OWL protocol and for modifying for any future updates to Kinetics. The experimental analysis includes an ablation study of how the different models perform under various conditions as annotated by Kinetics-AVA. The protocol as an algorithm for reproducing experiments using the KOWL-718 benchmark will be publicly released with code and containers at https://github.com/prijatelj/human-activity-recognition-in-an-open-world. The code may be used to analyze different annotations and subsets of the Kinetics datasets in an incremental open world fashion, as well as be extended as further updates to Kinetics are released.

Quantum computing (QC) promises significant advantages on certain hard computational tasks over classical computers. However, current quantum hardware, also known as noisy intermediate-scale quantum computers (NISQ), are still unable to carry out computations faithfully mainly because of the lack of quantum error correction (QEC) capability. A significant amount of theoretical studies have provided various types of QEC codes; one of the notable topological codes is the surface code, and its features, such as the requirement of only nearest-neighboring two-qubit control gates and a large error threshold, make it a leading candidate for scalable quantum computation. Recent developments of machine learning (ML)-based techniques especially the reinforcement learning (RL) methods have been applied to the decoding problem and have already made certain progress. Nevertheless, the device noise pattern may change over time, making trained decoder models ineffective. In this paper, we propose a continual reinforcement learning method to address these decoding challenges. Specifically, we implement double deep Q-learning with probabilistic policy reuse (DDQN-PPR) model to learn surface code decoding strategies for quantum environments with varying noise patterns. Through numerical simulations, we show that the proposed DDQN-PPR model can significantly reduce the computational complexity. Moreover, increasing the number of trained policies can further improve the agent's performance. Our results open a way to build more capable RL agents which can leverage previously gained knowledge to tackle QEC challenges.

Naturally-occurring information-seeking questions often contain questionable assumptions -- assumptions that are false or unverifiable. Questions containing questionable assumptions are challenging because they require a distinct answer strategy that deviates from typical answers to information-seeking questions. For instance, the question "When did Marie Curie discover Uranium?" cannot be answered as a typical when question without addressing the false assumption "Marie Curie discovered Uranium". In this work, we propose (QA)$^2$ (Question Answering with Questionable Assumptions), an open-domain evaluation dataset consisting of naturally-occurring search engine queries that may or may not contain questionable assumptions. To be successful on (QA)$^2$, systems must be able to detect questionable assumptions and also be able to produce adequate responses for both typical information-seeking questions and ones with questionable assumptions. We find that current models do struggle with handling questionable assumptions -- the best performing model achieves 59% human rater acceptability on abstractive QA with (QA)$^2$ questions, leaving substantial headroom for progress.

We propose Panoptic Lifting, a novel approach for learning panoptic 3D volumetric representations from images of in-the-wild scenes. Once trained, our model can render color images together with 3D-consistent panoptic segmentation from novel viewpoints. Unlike existing approaches which use 3D input directly or indirectly, our method requires only machine-generated 2D panoptic segmentation masks inferred from a pre-trained network. Our core contribution is a panoptic lifting scheme based on a neural field representation that generates a unified and multi-view consistent, 3D panoptic representation of the scene. To account for inconsistencies of 2D instance identifiers across views, we solve a linear assignment with a cost based on the model's current predictions and the machine-generated segmentation masks, thus enabling us to lift 2D instances to 3D in a consistent way. We further propose and ablate contributions that make our method more robust to noisy, machine-generated labels, including test-time augmentations for confidence estimates, segment consistency loss, bounded segmentation fields, and gradient stopping. Experimental results validate our approach on the challenging Hypersim, Replica, and ScanNet datasets, improving by 8.4, 13.8, and 10.6% in scene-level PQ over state of the art.