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。

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。

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。

Text classifiers have promising applications in high-stake tasks such as resume screening and content moderation. These classifiers must be fair and avoid discriminatory decisions by being invariant to perturbations of sensitive attributes such as gender or ethnicity. However, there is a gap between human intuition about these perturbations and the formal similarity specifications capturing them. While existing research has started to address this gap, current methods are based on hardcoded word replacements, resulting in specifications with limited expressivity or ones that fail to fully align with human intuition (e.g., in cases of asymmetric counterfactuals). This work proposes novel methods for bridging this gap by discovering expressive and intuitive individual fairness specifications. We show how to leverage unsupervised style transfer and GPT-3's zero-shot capabilities to automatically generate expressive candidate pairs of semantically similar sentences that differ along sensitive attributes. We then validate the generated pairs via an extensive crowdsourcing study, which confirms that a lot of these pairs align with human intuition about fairness in the context of toxicity classification. Finally, we show how limited amounts of human feedback can be leveraged to learn a similarity specification that can be used to train downstream fairness-aware models.

Accurate speed estimation of road vehicles is important for several reasons. One is speed limit enforcement, which represents a crucial tool in decreasing traffic accidents and fatalities. Compared with other research areas and domains, the number of available datasets for vehicle speed estimation is still very limited. We present a dataset of on-road audio-video recordings of single vehicles passing by a camera at known speeds, maintained stable by the on-board cruise control. The dataset contains thirteen vehicles, selected to be as diverse as possible in terms of manufacturer, production year, engine type, power and transmission, resulting in a total of $ 400 $ annotated audio-video recordings. The dataset is fully available and intended as a public benchmark to facilitate research in audio-video vehicle speed estimation. In addition to the dataset, we propose a cross-validation strategy which can be used in a machine learning model for vehicle speed estimation. Two approaches to training-validation split of the dataset are proposed.

Novel view synthesis and 3D modeling using implicit neural field representation are shown to be very effective for calibrated multi-view cameras. Such representations are known to benefit from additional geometric and semantic supervision. Most existing methods that exploit additional supervision require dense pixel-wise labels or localized scene priors. These methods cannot benefit from high-level vague scene priors provided in terms of scenes' descriptions. In this work, we aim to leverage the geometric prior of Manhattan scenes to improve the implicit neural radiance field representations. More precisely, we assume that only the knowledge of the scene (under investigation) being Manhattan is known - with no additional information whatsoever - with an unknown Manhattan coordinate frame. Such high-level prior is then used to self-supervise the surface normals derived explicitly in the implicit neural fields. Our modeling allows us to group the derived normals, followed by exploiting their orthogonality constraints for self-supervision. Our exhaustive experiments on datasets of diverse indoor scenes demonstrate the significant benefit of the proposed method over the established baselines.

Tabular biomedical data is often high-dimensional but with a very small number of samples. Although recent work showed that well-regularised simple neural networks could outperform more sophisticated architectures on tabular data, they are still prone to overfitting on tiny datasets with many potentially irrelevant features. To combat these issues, we propose Weight Predictor Network with Feature Selection (WPFS) for learning neural networks from high-dimensional and small sample data by reducing the number of learnable parameters and simultaneously performing feature selection. In addition to the classification network, WPFS uses two small auxiliary networks that together output the weights of the first layer of the classification model. We evaluate on nine real-world biomedical datasets and demonstrate that WPFS outperforms other standard as well as more recent methods typically applied to tabular data. Furthermore, we investigate the proposed feature selection mechanism and show that it improves performance while providing useful insights into the learning task.

Genome-wide studies leveraging recent high-throughput sequencing technologies collect high-dimensional data. However, they usually include small cohorts of patients, and the resulting tabular datasets suffer from the "curse of dimensionality". Training neural networks on such datasets is typically unstable, and the models overfit. One problem is that modern weight initialisation strategies make simplistic assumptions unsuitable for small-size datasets. We propose Graph-Conditioned MLP, a novel method to introduce priors on the parameters of an MLP. Instead of randomly initialising the first layer, we condition it directly on the training data. More specifically, we create a graph for each feature in the dataset (e.g., a gene), where each node represents a sample from the same dataset (e.g., a patient). We then use Graph Neural Networks (GNNs) to learn embeddings from these graphs and use the embeddings to initialise the MLP's parameters. Our approach opens the prospect of introducing additional biological knowledge when constructing the graphs. We present early results on 7 classification tasks from gene expression data and show that GC-MLP outperforms an MLP.

在我们不断变化的气候中，使用模型来评估天气和气候对社会和企业的后续后果的风险及其后续后果至关重要。这种模型的操作在历史上是定制的，并限制在特定的计算基础架构，驱动数据集和预定义的配置上。这些约束通过缩放模型运行并将模型掌握在感兴趣的用户手中。在这里，我们提出了一个基于云的模块化框架，用于部署和操作地理空间模型，最初应用于气候影响。气候冲击建模框架（CIMF）可以以动态和灵活的方式部署模块化工作流程。用户可以以简化的方式指定工作流程组件，然后可以轻松地将这些组件组织成不同的配置，以以不同的方式和不同的尺度评估风险。这还可以使不同的模型（物理模拟或机器学习模型）和工作流程连接以产生合并的风险评估。洪水建模被用作端到端的示例，以证明CIMF的操作。