Graph neural networks (GNN) have become the default machine learning model for relational datasets, including protein interaction networks, biological neural networks, and scientific collaboration graphs. We use tools from statistical physics and random matrix theory to precisely characterize generalization in simple graph convolution networks on the contextual stochastic block model. The derived curves are phenomenologically rich: they explain the distinction between learning on homophilic and heterophilic graphs and they predict double descent whose existence in GNNs has been questioned by recent work. Our results are the first to accurately explain the behavior not only of a stylized graph learning model but also of complex GNNs on messy real-world datasets. To wit, we use our analytic insights about homophily and heterophily to improve performance of state-of-the-art graph neural networks on several heterophilic benchmarks by a simple addition of negative self-loop filters.

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and noise can make this single estimate inaccurate or misleading. While deep networks such as conditional normalizing flows can be used to sample posteriors in inverse problems, they often yield low-quality samples and uncertainty estimates. In this paper, we propose U-Flow, a Bayesian U-Net based on conditional normalizing flows, which generates high-quality posterior samples and estimates physically-meaningful uncertainty. We show that the proposed model significantly outperforms the recent normalizing flows in terms of posterior sample quality while having comparable performance with the U-Net in point estimation.

我们使用运输公制（Delon和Desolneux 2020）中的单变量高斯混合物中的任意度量空间$ \ MATHCAL {X} $研究数据表示。我们得出了由称为\ emph {Probabilistic Transfersers}的小神经网络实现的特征图的保证。我们的保证是记忆类型：我们证明了深度约为$ n \ log（n）$的概率变压器和大约$ n^2 $ can bi-h \'{o} lder嵌入任何$ n $ - 点数据集从低度量失真的$ \ Mathcal {x} $，从而避免了维数的诅咒。我们进一步得出了概率的bi-lipschitz保证，可以兑换失真量和随机选择的点与该失真的随机选择点的可能性。如果$ \ MATHCAL {X} $的几何形状足够规律，那么我们可以为数据集中的所有点获得更强的Bi-Lipschitz保证。作为应用程序，我们从Riemannian歧管，指标和某些类型的数据集中获得了神经嵌入保证金组合图。

未知视图断层扫描（UVT）从其2D投影以未知的随机取向重建了3D密度图。从Kam（Kam（1980））开始的工作线采用了具有旋转不变的傅立叶特征的矩（MOM）方法，可以在频域中求解UVT，假设方向是均匀分布的。这项工作系列包括基于矩阵分解的最新正交矩阵检索（OMR）方法，虽然优雅地需要有关无法可用的密度的侧面信息，或者无法充分强大。为了使OMR摆脱这些限制，我们建议通过要求它们相互一致来共同恢复密度图和正交矩阵。我们通过deno的参考投影和非负约束来使所得的非凸优化问题正常。这是通过空间自相关功能的新闭合表达式启用的。此外，我们设计了一个易于计算的初始密度图，可有效地降低重建问题的非凸性。实验结果表明，在典型的3D UVT的典型低SNR场景中，具有空间共识的拟议的OMR比以前最新的OMR方法更好。

Implicit representation of shapes as level sets of multilayer perceptrons has recently flourished in different shape analysis, compression, and reconstruction tasks. In this paper, we introduce an implicit neural representation-based framework for solving the inverse obstacle scattering problem in a mesh-free fashion. We express the obstacle shape as the zero-level set of a signed distance function which is implicitly determined by network parameters. To solve the direct scattering problem, we implement the implicit boundary integral method. It uses projections of the grid points in the tubular neighborhood onto the boundary to compute the PDE solution directly in the level-set framework. The proposed implicit representation conveniently handles the shape perturbation in the optimization process. To update the shape, we use PyTorch's automatic differentiation to backpropagate the loss function w.r.t. the network parameters, allowing us to avoid complex and error-prone manual derivation of the shape derivative. Additionally, we propose a deep generative model of implicit neural shape representations that can fit into the framework. The deep generative model effectively regularizes the inverse obstacle scattering problem, making it more tractable and robust, while yielding high-quality reconstruction results even in noise-corrupted setups.

我们研究了由覆盖在R ^ M中的N维歧管支持的概率措施的近似 - 由可逆流和单层注射部件组成的神经网络。当M <= 3N时，我们显示R ^ n和r ^ m之间的注射流量在可扩展的嵌入物图像中支持的普遍近似措施，这是标准嵌入的适当子集。在这个制度拓扑障碍物中，拓扑障碍能够作为可允许的目标。当m> = 3n + 1时，我们使用称为*清洁技巧*的代数拓扑的论点来证明拓扑障碍物消失和注射般的流动普遍近似任何可分辨率的嵌入。沿途，我们表明，可以在Brehmer et Cranmer 2020中的猜想中建立“反向”可以建立铭刻流动网络的最优性。此外，设计的网络可以简单，它们可以配备其他属性，例如一个新的投影结果。

由于下采样层的存在，卷积神经网络缺乏转变标准。在图像分类中，最近提出了自适应多相下采样（APS-D）以使CNN完全换档不变。但是，在用于图像重建任务的网络中，它不能自动恢复转移标准规范。我们通过提出自适应多相上升采样（APS-U），传统上采样的非线性扩展来解决该问题，该传统上采样的非线性扩展，其允许CNNS与对称编码器 - 解码器架构（例如U-Net）进行CNN，以表现出完美的换档设备。利用MRI和CT重建实验，我们表明，网络包含APS-D / U层的网络展示了本领域的状态性能，而不会牺牲图像重建质量。此外，与数据增强和抗锯齿等先前的方法不同，从APS-D / U获得的标准规范中的增益也扩展到训练分布外的图像。

Machine learning models are typically evaluated by computing similarity with reference annotations and trained by maximizing similarity with such. Especially in the bio-medical domain, annotations are subjective and suffer from low inter- and intra-rater reliability. Since annotations only reflect the annotation entity's interpretation of the real world, this can lead to sub-optimal predictions even though the model achieves high similarity scores. Here, the theoretical concept of Peak Ground Truth (PGT) is introduced. PGT marks the point beyond which an increase in similarity with the reference annotation stops translating to better Real World Model Performance (RWMP). Additionally, a quantitative technique to approximate PGT by computing inter- and intra-rater reliability is proposed. Finally, three categories of PGT-aware strategies to evaluate and improve model performance are reviewed.

A "heart attack" or myocardial infarction (MI), occurs when an artery supplying blood to the heart is abruptly occluded. The "gold standard" method for imaging MI is Cardiovascular Magnetic Resonance Imaging (MRI), with intravenously administered gadolinium-based contrast (late gadolinium enhancement). However, no "gold standard" fully automated method for the quantification of MI exists. In this work, we propose an end-to-end fully automatic system (MyI-Net) for the detection and quantification of MI in MRI images. This has the potential to reduce the uncertainty due to the technical variability across labs and inherent problems of the data and labels. Our system consists of four processing stages designed to maintain the flow of information across scales. First, features from raw MRI images are generated using feature extractors built on ResNet and MoblieNet architectures. This is followed by the Atrous Spatial Pyramid Pooling (ASPP) to produce spatial information at different scales to preserve more image context. High-level features from ASPP and initial low-level features are concatenated at the third stage and then passed to the fourth stage where spatial information is recovered via up-sampling to produce final image segmentation output into: i) background, ii) heart muscle, iii) blood and iv) scar areas. New models were compared with state-of-art models and manual quantification. Our models showed favorable performance in global segmentation and scar tissue detection relative to state-of-the-art work, including a four-fold better performance in matching scar pixels to contours produced by clinicians.

In this paper, we propose a new neural network architecture based on the H2 matrix. Even though networks with H2-inspired architecture already exist, and our approach is designed to reduce memory costs and improve performance by taking into account the sparsity template of the H2 matrix. In numerical comparison with alternative neural networks, including the known H2-based ones, our architecture showed itself as beneficial in terms of performance, memory, and scalability.