本文介绍了J2扰动兰伯特问题的新颖和快速求解器。求解器由智能初始猜测发生器组成，与差分校正过程组合。智能初始猜测生成器是一个深度神经网络，受过训练，以校正来自未受干扰的Lambert问题的解决方案的初始速度矢量。差分校正模块采用初始猜测并使用正向拍摄过程来进一步更新初始速度并准确地满足终端条件。分析了八种样本形式，并比较了解最佳形式，以培训在J2扰动的兰伯特问题上的神经网络。在代表性测试案例上证明了这种新方法的准确性和性能：Jupiter系统中的多转J2扰动兰伯特问题的解决方案。我们将对所提出的方法对经典标准拍摄方法和基于同型扰动Lambert算法的性能进行比较。结果表明，为了相当的精度水平，所提出的方法明显比其他两个更快。

Artificial Intelligence (AI) and Machine Learning (ML) are weaving their way into the fabric of society, where they are playing a crucial role in numerous facets of our lives. As we witness the increased deployment of AI and ML in various types of devices, we benefit from their use into energy-efficient algorithms for low powered devices. In this paper, we investigate a scale and medium that is far smaller than conventional devices as we move towards molecular systems that can be utilized to perform machine learning functions, i.e., Molecular Machine Learning (MML). Fundamental to the operation of MML is the transport, processing, and interpretation of information propagated by molecules through chemical reactions. We begin by reviewing the current approaches that have been developed for MML, before we move towards potential new directions that rely on gene regulatory networks inside biological organisms as well as their population interactions to create neural networks. We then investigate mechanisms for training machine learning structures in biological cells based on calcium signaling and demonstrate their application to build an Analog to Digital Converter (ADC). Lastly, we look at potential future directions as well as challenges that this area could solve.

Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to the fact that the composition of an arbitrary number of quantum gates, consisting of a series of sequential unitary transformations, is intrinsically linear. This problem has been variously approached in the literature, principally via the introduction of measurements between layers of unitary transformations. In this paper, we introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning typically associated with superior generalization performance in the classical domain, specifically, hierarchical feature learning. Our approach generalizes the notion of Quantum Neural Tangent Kernel, which has been used to study the dynamics of classical and quantum machine learning models. The Quantum Path Kernel exploits the parameter trajectory, i.e. the curve delineated by model parameters as they evolve during training, enabling the representation of differential layer-wise convergence behaviors, or the formation of hierarchical parametric dependencies, in terms of their manifestation in the gradient space of the predictor function. We evaluate our approach with respect to variants of the classification of Gaussian XOR mixtures - an artificial but emblematic problem that intrinsically requires multilevel learning in order to achieve optimal class separation.

Few-shot learning (FSL) is a central problem in meta-learning, where learners must efficiently learn from few labeled examples. Within FSL, feature pre-training has recently become an increasingly popular strategy to significantly improve generalization performance. However, the contribution of pre-training is often overlooked and understudied, with limited theoretical understanding of its impact on meta-learning performance. Further, pre-training requires a consistent set of global labels shared across training tasks, which may be unavailable in practice. In this work, we address the above issues by first showing the connection between pre-training and meta-learning. We discuss why pre-training yields more robust meta-representation and connect the theoretical analysis to existing works and empirical results. Secondly, we introduce Meta Label Learning (MeLa), a novel meta-learning algorithm that learns task relations by inferring global labels across tasks. This allows us to exploit pre-training for FSL even when global labels are unavailable or ill-defined. Lastly, we introduce an augmented pre-training procedure that further improves the learned meta-representation. Empirically, MeLa outperforms existing methods across a diverse range of benchmarks, in particular under a more challenging setting where the number of training tasks is limited and labels are task-specific. We also provide extensive ablation study to highlight its key properties.

Tree-based machine learning algorithms provide the most precise assessment of the feasibility for a country to export a target product given its export basket. However, the high number of parameters involved prevents a straightforward interpretation of the results and, in turn, the explainability of policy indications. In this paper, we propose a procedure to statistically validate the importance of the products used in the feasibility assessment. In this way, we are able to identify which products, called explainers, significantly increase the probability to export a target product in the near future. The explainers naturally identify a low dimensional representation, the Feature Importance Product Space, that enhances the interpretability of the recommendations and provides out-of-sample forecasts of the export baskets of countries. Interestingly, we detect a positive correlation between the complexity of a product and the complexity of its explainers.

We develop Bayesian neural networks (BNNs) that permit to model generic nonlinearities and time variation for (possibly large sets of) macroeconomic and financial variables. From a methodological point of view, we allow for a general specification of networks that can be applied to either dense or sparse datasets, and combines various activation functions, a possibly very large number of neurons, and stochastic volatility (SV) for the error term. From a computational point of view, we develop fast and efficient estimation algorithms for the general BNNs we introduce. From an empirical point of view, we show both with simulated data and with a set of common macro and financial applications that our BNNs can be of practical use, particularly so for observations in the tails of the cross-sectional or time series distributions of the target variables.

数据的表示对于机器学习方法至关重要。内核方法用于丰富特征表示，从而可以更好地概括。量子内核有效地实施了在量子系统的希尔伯特空间中编码经典数据的有效复杂的转换，甚至导致指数加速。但是，我们需要对数据的先验知识来选择可以用作量子嵌入的适当参数量子电路。我们提出了一种算法，该算法通过组合优化过程自动选择最佳的量子嵌入过程，该过程修改了电路的结构，更改门的发生器，其角度（取决于数据点）以及各种门的QUBIT行为。由于组合优化在计算上是昂贵的，因此我们基于均值周围的核基质系数的指数浓度引入了一个标准，以立即丢弃任意大部分的溶液，这些溶液被认为性能较差。与基于梯度的优化（例如可训练的量子内核）相反，我们的方法不受建筑贫瘠的高原影响。我们已经使用人工和现实数据集来证明相对于随机生成的PQC的方法的提高。我们还比较了不同优化算法的效果，包括贪婪的局部搜索，模拟退火和遗传算法，表明算法选择在很大程度上影响了结果。

这项工作提出了利用对机器人周围环境的逐步改善的象征感知知识的一步，以证明适用于自动驾驶问题的正确反应性控制合成。结合了运动控制和信息收集的抽象模型，我们表明假设保证规范（线性时间逻辑的子类）可用于定义和解决谨慎计划的流量规则。我们提出了一种新颖的表示，称为符号改进树，以捕获有关环境的增量知识，并体现了各种符号感知输入之间的关系。利用增量知识来合成机器人的验证反应性计划。案例研究表明，即使在部分遮挡的环境中，拟议方法在合成控制输入方面的疗效。

在基于学术和行业的研究中，在线评估方法都被视为推荐系统等交互式应用程序的黄金标准。自然，这样做的原因是，我们可以直接测量依赖干预措施的实用程序指标，这是向用户显示的建议。然而，由于多种原因，在线评估方法是昂贵的，并且对于可靠的离线评估程序仍然存在明确的需求。在行业中，离线指标通常被用作一线评估，以生成有前途的候选模型来在线评估。在学术工作中，对在线系统的有限访问使离线指标是验证新方法的事实上的方法。存在两个类别的离线指标：基于代理的方法和反事实方法。头等舱通常与我们关心的在线指标相关，而后一类仅根据在现实世界中无法实现的假设提供理论保证。在这里，我们表明基于模拟的比较为离线指标提供了前进的方向，并认为它们是可取的评估手段。

本文提出了一种转移学习方法，以重新校准我们先前开发的车轮探针神经网络（WHONET），以在全球导航卫星系统（GNSS）不可用的环境中进行车辆定位。已显示WHONET具有学习车轮速度测量中不确定性的能力，以校正和准确的车辆定位。这些不确定性可能表现为轮胎压力从泥泞和不平坦的地形或车轮滑动中的驾驶变化。但是，关注数据驱动方法（例如WHONET模型）的共同原因通常是无法将模型推广到新车。在机器学习模型在特定领域进行培训但部署在另一个领域的情况下，该模型的性能降低了。在现实生活中，从变化到车辆的动力学到传感器噪声的新模式分布，有几个因素对这种降解有影响，偏见会使测试传感器数据的数据因训练数据而异。因此，挑战是探索允许训练有素的机器学习模型自发适应新车辆域的技术。因此，我们提出了重新校准的轮循环神经网络（R-WHONET），该神经网络将WHONET模型从其源域（最初训练该模型的车辆和环境）适应到目标域（一种新车辆，在其上进行了训练）。训练有素的模型将被部署）。通过在几个GNSS中断场景上进行性能评估 - 短期复杂驾驶方案以及长期GNSS中断方案。我们证明，在源域中训练的模型并不能很好地推广到目标域中的新车辆。但是，我们表明，我们的新提议的框架将WHONET模型对目标域中的新车辆的概括提高了32％。