In this letter, we present an extension to TensorNet, a state-of-the-art
equivariant Cartesian tensor neural network potential, allowing it to handle
charged molecules and spin states without architectural changes or increased
costs. By incorporating these attributes, we address input degeneracy issues,
enhancing the model's predictive accuracy across diverse chemical systems. This
advancement significantly broadens TensorNet's applicability, maintaining its
efficiency and accuracy.

我们在这封信中介绍了 TensorNet 的一个扩展，它是一种最先进的等变笛卡尔张量神经网络势能，不需要架构改变或增加成本即可处理带电的分子和自旋态。通过结合这些属性，我们解决了输入退化问题，提高了模型在不同化学系统中的预测准确性。这一进步显著拓宽了 TensorNet 的适用范围，同时保持了效率和准确性。

关于在笛卡尔张量神经网络势函数中包含电荷和自旋状态的问题

On the Inclusion of Charge and Spin States in Cartesian Tensor Neural  Network Potentials

In recent years, countless research papers have addressed the topics of
knowledge graph creation, extension, or completion in order to create knowledge
graphs that are larger, more correct, or more diverse. This research is
typically motivated by the argumentation that using such enhanced knowledge
graphs to solve downstream tasks will improve performance. Nonetheless, this is
hardly ever evaluated. Instead, the predominant evaluation metrics - aiming at
correctness and completeness - are undoubtedly valuable but fail to capture the
complete picture, i.e., how useful the created or enhanced knowledge graph
actually is. Further, the accessibility of such a knowledge graph is rarely
considered (e.g., whether it contains expressive labels, descriptions, and
sufficient context information to link textual mentions to the entities of the
knowledge graph). To better judge how well knowledge graphs perform on actual
tasks, we present KGrEaT - a framework to estimate the quality of knowledge
graphs via actual downstream tasks like classification, clustering, or
recommendation. Instead of comparing different methods of processing knowledge
graphs with respect to a single task, the purpose of KGrEaT is to compare
various knowledge graphs as such by evaluating them on a fixed task setup. The
framework takes a knowledge graph as input, automatically maps it to the
datasets to be evaluated on, and computes performance metrics for the defined
tasks. It is built in a modular way to be easily extendable with additional
tasks and datasets.

通过实际任务检测知识图谱的质量的 KGrEaT 框架，能够评估其对于分类、聚类或推荐等固定任务设置的性能指标。

KGrEaT: 通过下游任务评估知识图谱的框架

KGrEaT: A Framework to Evaluate Knowledge Graphs via Downstream Tasks

This paper presents Point Convolutional Neural Networks (PCNN): a novel
framework for applying convolutional neural networks to point clouds. The
framework consists of two operators: extension and restriction, mapping point
cloud functions to volumetric functions and vise-versa. A point cloud
convolution is defined by pull-back of the Euclidean volumetric convolution via
an extension-restriction mechanism.
The point cloud convolution is computationally efficient, invariant to the
order of points in the point cloud, robust to different samplings and varying
densities, and translation invariant, that is the same convolution kernel is
used at all points. PCNN generalizes image CNNs and allows readily adapting
their architectures to the point cloud setting.
Evaluation of PCNN on three central point cloud learning benchmarks
convincingly outperform competing point cloud learning methods, and the vast
majority of methods working with more informative shape representations such as
surfaces and/or normals.

本文介绍了点卷积神经网络（PCNN）的框架和两个算子：扩展和限制。此外，还定义了点云卷积的概念，其具有高效性，不受各种因素的影响，并可将卷积核用于任何点云中。通过三项常见的点云学习基准测试，证明了 PCNN 方法的有效性。

通过扩展算子的点卷积神经网络

Point Convolutional Neural Networks by Extension Operators

We prove that the non-commutative perspective of an operator convex function
is the unique extension of the corresponding commutative perspective that
preserves homogeneity and convexity.

证明了非交换视角下的算子凸函数是与其对应的交换视角下的算子凸函数唯一延拓，并且保持了同次性和凸性。