储层计算系统是使用驱动的动力系统构建的，在该系统中，外部输入可以改变系统的发展状态。这些范例用于信息处理，机器学习和计算。在此框架中需要解决的一个基本问题是输入与系统状态之间的统计关系。本文提供的条件可以保证驱动系统的渐近措施的存在和唯一性，并表明当输入和输出过程的集合赋予了Wasserstein距离时，它们对输入过程的依赖性是连续的。这些发展中的主要工具是将这些不变的度量表征为在这种情况下出现并在论文中进行了大量研究的自然定义的FOIA算子的固定点。这些固定点是通过在驱动系统中施加新引入的随机状态合同性来获得的，该系统在示例中很容易验证。可以通过非国家缩减的系统来满足随机状态的合同性，这通常是为了保证储层计算中的回声状态属性的需求。结果，即使不存在Echo State属性，也可能会得到满足。

庆祝的Takens嵌入定理界面涉及通过通用延迟观察地图在适当的维度的欧几里德空间中嵌入动态系统的吸引子。嵌入也建立了一种拓扑共轭。在本文中，我们展示了如何将任意序列映射到另一个空间中作为非自治动态系统的吸引力的解决方案。这种映射还需要拓扑缀合物和序列与吸引人的解决方案空间之间的嵌入。这一结果不是嵌入定理的Takens的概括，但有助于我们了解所广泛用于应用程序的离散时间状态模型所需的究竟是什么，以将外部刺激嵌入到其解决方案上。我们的成果解决了关于自主动态系统扰动的另一个基本问题。我们描述了当外源噪声渗透到连续的局部不可缩续的吸引装置（如稳定的固定点）的离散时间自主动态系统的局部不可缩短的局部噪声时究竟发生了什么。

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.

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.

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.

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.

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.

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.

In the Earth's magnetosphere, there are fewer than a dozen dedicated probes beyond low-Earth orbit making in-situ observations at any given time. As a result, we poorly understand its global structure and evolution, the mechanisms of its main activity processes, magnetic storms, and substorms. New Artificial Intelligence (AI) methods, including machine learning, data mining, and data assimilation, as well as new AI-enabled missions will need to be developed to meet this Sparse Data challenge.

Late-life depression (LLD) is a highly prevalent mood disorder occurring in older adults and is frequently accompanied by cognitive impairment (CI). Studies have shown that LLD may increase the risk of Alzheimer's disease (AD). However, the heterogeneity of presentation of geriatric depression suggests that multiple biological mechanisms may underlie it. Current biological research on LLD progression incorporates machine learning that combines neuroimaging data with clinical observations. There are few studies on incident cognitive diagnostic outcomes in LLD based on structural MRI (sMRI). In this paper, we describe the development of a hybrid representation learning (HRL) framework for predicting cognitive diagnosis over 5 years based on T1-weighted sMRI data. Specifically, we first extract prediction-oriented MRI features via a deep neural network, and then integrate them with handcrafted MRI features via a Transformer encoder for cognitive diagnosis prediction. Two tasks are investigated in this work, including (1) identifying cognitively normal subjects with LLD and never-depressed older healthy subjects, and (2) identifying LLD subjects who developed CI (or even AD) and those who stayed cognitively normal over five years. To the best of our knowledge, this is among the first attempts to study the complex heterogeneous progression of LLD based on task-oriented and handcrafted MRI features. We validate the proposed HRL on 294 subjects with T1-weighted MRIs from two clinically harmonized studies. Experimental results suggest that the HRL outperforms several classical machine learning and state-of-the-art deep learning methods in LLD identification and prediction tasks.