本文研究了无限二维希尔伯特空间之间线性算子的学习。训练数据包括希尔伯特空间中的一对随机输入向量以及在未知的自我接合线性运算符下的嘈杂图像。假设操作员在已知的基础上是对角线化的，则该工作解决了给定数据估算操作员特征值的等效反问题。采用贝叶斯方法，理论分析在无限的数据限制中建立了后部收缩率，而高斯先验者与反向问题的正向图没有直接相关。主要结果还包括学习理论的概括错误保证了广泛的分配变化。这些收敛速率分别量化了数据平滑度和真实特征值衰减或生长的影响，分别是紧凑或无界操作员对样品复杂性的影响。数值证据支持对角线和非对角性环境中的理论。

Geographic features are commonly used to improve the performance of pretrained language models (PLMs) on NLP tasks where they are intuitively beneficial (e.g., geolocation prediction, dialect feature prediction). Existing methods, however, leverage geographic information in task-specific fine-tuning and fail to integrate it into the geo-linguistic knowledge encoded by PLMs, which would make it transferable across different tasks. In this paper, we introduce an approach to task-agnostic geoadaptation of PLMs that forces them to learn associations between linguistic phenomena and geographic locations. Geoadaptation is an intermediate training step that couples language modeling and geolocation prediction in a multi-task learning setup. In our main set of experiments, we geoadapt BERTi\'{c}, a PLM for Bosnian-Croatian-Montenegrin-Serbian (BCMS), using a corpus of geotagged BCMS tweets. Evaluation on three tasks, namely fine-tuned as well as zero-shot geolocation prediction and zero-shot prediction of dialect features, shows that geoadaptation is very effective: e.g., we obtain state-of-the-art performance in supervised geolocation prediction and report massive gains over geographically uninformed PLMs on zero-shot geolocation prediction. Moreover, in follow-up experiments we successfully geoadapt two other PLMs, specifically ScandiBERT on Norwegian, Swedish, and Danish tweets and GermanBERT on Jodel posts in German from Austria, Germany, and Switzerland, proving that the benefits of geoadaptation are not limited to a particular language area and PLM.

机器学习方法最近在求解部分微分方程（PDE）中的承诺。它们可以分为两种广泛类别：近似解决方案功能并学习解决方案操作员。物理知识的神经网络（PINN）是前者的示例，而傅里叶神经操作员（FNO）是后者的示例。这两种方法都有缺点。 Pinn的优化是具有挑战性，易于发生故障，尤其是在多尺度动态系统上。 FNO不会遭受这种优化问题，因为它在给定的数据集上执行了监督学习，但获取此类数据可能太昂贵或无法使用。在这项工作中，我们提出了物理知识的神经运营商（Pino），在那里我们结合了操作学习和功能优化框架。这种综合方法可以提高PINN和FNO模型的收敛速度和准确性。在操作员学习阶段，Pino在参数PDE系列的多个实例上学习解决方案操作员。在测试时间优化阶段，Pino优化预先训练的操作员ANSATZ，用于PDE的查询实例。实验显示Pino优于许多流行的PDE家族的先前ML方法，同时保留与求解器相比FNO的非凡速度。特别是，Pino准确地解决了挑战的长时间瞬态流量，而其他基线ML方法无法收敛的Kolmogorov流程。

神经网络的经典发展主要集中在有限维欧基德空间或有限组之间的学习映射。我们提出了神经网络的概括，以学习映射无限尺寸函数空间之间的运算符。我们通过一类线性积分运算符和非线性激活函数的组成制定运营商的近似，使得组合的操作员可以近似复杂的非线性运算符。我们证明了我们建筑的普遍近似定理。此外，我们介绍了四类运算符参数化：基于图形的运算符，低秩运算符，基于多极图形的运算符和傅里叶运算符，并描述了每个用于用每个计算的高效算法。所提出的神经运营商是决议不变的：它们在底层函数空间的不同离散化之间共享相同的网络参数，并且可以用于零击超分辨率。在数值上，与现有的基于机器学习的方法，达西流程和Navier-Stokes方程相比，所提出的模型显示出卓越的性能，而与传统的PDE求解器相比，与现有的基于机器学习的方法有关的基于机器学习的方法。

众所周知，混乱的系统对预测的挑战是挑战，因为它们对时间的敏感性和由于阶梯时间而引起的错误和错误。尽管这种不可预测的行为，但对于许多耗散系统，长期轨迹的统计数据仍受到一套被称为全球吸引子的不变措施的管辖。对于许多问题，即使状态空间是无限的维度，该集合是有限维度的。对于马尔可夫系统，长期轨迹的统计特性由解决方案操作员唯一确定，该解决方案操作员将系统的演变映射到任意正时间增量上。在这项工作中，我们提出了一个机器学习框架，以学习耗散混沌系统的基础解决方案操作员，这表明所得的学习操作员准确地捕获了短期轨迹和长期统计行为。使用此框架，我们能够预测湍流Kolmogorov流动动力学的各种统计数据，雷诺数为5000。

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.

Image classification with small datasets has been an active research area in the recent past. However, as research in this scope is still in its infancy, two key ingredients are missing for ensuring reliable and truthful progress: a systematic and extensive overview of the state of the art, and a common benchmark to allow for objective comparisons between published methods. This article addresses both issues. First, we systematically organize and connect past studies to consolidate a community that is currently fragmented and scattered. Second, we propose a common benchmark that allows for an objective comparison of approaches. It consists of five datasets spanning various domains (e.g., natural images, medical imagery, satellite data) and data types (RGB, grayscale, multispectral). We use this benchmark to re-evaluate the standard cross-entropy baseline and ten existing methods published between 2017 and 2021 at renowned venues. Surprisingly, we find that thorough hyper-parameter tuning on held-out validation data results in a highly competitive baseline and highlights a stunted growth of performance over the years. Indeed, only a single specialized method dating back to 2019 clearly wins our benchmark and outperforms the baseline classifier.

Dataset scaling, also known as normalization, is an essential preprocessing step in a machine learning pipeline. It is aimed at adjusting attributes scales in a way that they all vary within the same range. This transformation is known to improve the performance of classification models, but there are several scaling techniques to choose from, and this choice is not generally done carefully. In this paper, we execute a broad experiment comparing the impact of 5 scaling techniques on the performances of 20 classification algorithms among monolithic and ensemble models, applying them to 82 publicly available datasets with varying imbalance ratios. Results show that the choice of scaling technique matters for classification performance, and the performance difference between the best and the worst scaling technique is relevant and statistically significant in most cases. They also indicate that choosing an inadequate technique can be more detrimental to classification performance than not scaling the data at all. We also show how the performance variation of an ensemble model, considering different scaling techniques, tends to be dictated by that of its base model. Finally, we discuss the relationship between a model's sensitivity to the choice of scaling technique and its performance and provide insights into its applicability on different model deployment scenarios. Full results and source code for the experiments in this paper are available in a GitHub repository.\footnote{https://github.com/amorimlb/scaling\_matters}

The devastation caused by the coronavirus pandemic makes it imperative to design automated techniques for a fast and accurate detection. We propose a novel non-invasive tool, using deep learning and imaging, for delineating COVID-19 infection in lungs. The Ensembling Attention-based Multi-scaled Convolution network (EAMC), employing Leave-One-Patient-Out (LOPO) training, exhibits high sensitivity and precision in outlining infected regions along with assessment of severity. The Attention module combines contextual with local information, at multiple scales, for accurate segmentation. Ensemble learning integrates heterogeneity of decision through different base classifiers. The superiority of EAMC, even with severe class imbalance, is established through comparison with existing state-of-the-art learning models over four publicly-available COVID-19 datasets. The results are suggestive of the relevance of deep learning in providing assistive intelligence to medical practitioners, when they are overburdened with patients as in pandemics. Its clinical significance lies in its unprecedented scope in providing low-cost decision-making for patients lacking specialized healthcare at remote locations.

Objective: Imbalances of the electrolyte concentration levels in the body can lead to catastrophic consequences, but accurate and accessible measurements could improve patient outcomes. While blood tests provide accurate measurements, they are invasive and the laboratory analysis can be slow or inaccessible. In contrast, an electrocardiogram (ECG) is a widely adopted tool which is quick and simple to acquire. However, the problem of estimating continuous electrolyte concentrations directly from ECGs is not well-studied. We therefore investigate if regression methods can be used for accurate ECG-based prediction of electrolyte concentrations. Methods: We explore the use of deep neural networks (DNNs) for this task. We analyze the regression performance across four electrolytes, utilizing a novel dataset containing over 290000 ECGs. For improved understanding, we also study the full spectrum from continuous predictions to binary classification of extreme concentration levels. To enhance clinical usefulness, we finally extend to a probabilistic regression approach and evaluate different uncertainty estimates. Results: We find that the performance varies significantly between different electrolytes, which is clinically justified in the interplay of electrolytes and their manifestation in the ECG. We also compare the regression accuracy with that of traditional machine learning models, demonstrating superior performance of DNNs. Conclusion: Discretization can lead to good classification performance, but does not help solve the original problem of predicting continuous concentration levels. While probabilistic regression demonstrates potential practical usefulness, the uncertainty estimates are not particularly well-calibrated. Significance: Our study is a first step towards accurate and reliable ECG-based prediction of electrolyte concentration levels.