In the realm of Graph Neural Networks (GNNs), two exciting research
directions have recently emerged: Subgraph GNNs and Graph Transformers. In this
paper, we propose an architecture that integrates both approaches, dubbed
Subgraphormer, which combines the enhanced expressive power, message-passing
mechanisms, and aggregation schemes from Subgraph GNNs with attention and
positional encodings, arguably the most important components in Graph
Transformers. Our method is based on an intriguing new connection we reveal
between Subgraph GNNs and product graphs, suggesting that Subgraph GNNs can be
formulated as Message Passing Neural Networks (MPNNs) operating on a product of
the graph with itself. We use this formulation to design our architecture:
first, we devise an attention mechanism based on the connectivity of the
product graph. Following this, we propose a novel and efficient positional
encoding scheme for Subgraph GNNs, which we derive as a positional encoding for
the product graph. Our experimental results demonstrate significant performance
improvements over both Subgraph GNNs and Graph Transformers on a wide range of
datasets.

本文提出了一个结合 Subgraph GNNs 和 Graph Transformers 的架构，名为 Subgraphormer，通过将 Subgraph GNNs 的增强表达能力、消息传递机制和聚合方案与 Graph Transformers 中最重要的组件 —— 注意力机制和位置编码相结合。我们的方法基于 Subgraph GNNs 和自身的图像乘积之间的新联系，将 Subgraph GNNs 表述为在图像乘积上操作的 Message Passing Neural Networks (MPNNs)。我们利用这种表述设计了我们的架构：首先，我们设计了一个基于图像乘积的连接性的注意力机制。其次，我们提出了一种新颖高效的 Subgraph GNNs 位置编码方案，将其推导为图像乘积的位置编码。我们的实验结果显示，在广泛的数据集上，相比于 Subgraph GNNs 和 Graph Transformers，我们的方法显著提升了性能。

子图形转化器：通过图产品统一子图图神经网络与图变形器

Subgraphormer: Unifying Subgraph GNNs and Graph Transformers via Graph  Products

Machine-learning potentials provide computationally efficient and accurate
approximations of the Born-Oppenheimer potential energy surface. This potential
determines many materials properties and simulation techniques usually require
its gradients, in particular forces and stress for molecular dynamics, and heat
flux for thermal transport properties. Recently developed potentials feature
high body order and can include equivariant semi-local interactions through
message-passing mechanisms. Due to their complex functional forms, they rely on
automatic differentiation (AD), overcoming the need for manual implementations
or finite-difference schemes to evaluate gradients. This study demonstrates a
unified AD approach to obtain forces, stress, and heat flux for such
potentials, and provides a model-independent implementation. The method is
tested on the Lennard-Jones potential, and then applied to predict cohesive
properties and thermal conductivity of tin selenide using an equivariant
message-passing neural network potential.

该研究使用机器学习潜力提供的 Born-Oppenheimer 势能表面来预测锡硒化物的粘聚性和热导率，其复杂的功能形式依赖于自动微分，并且使用了一种统一的自动微分方法来获得自动微分梯度，包括力，应力和热通量。

应用自动微分求解压力和热通量

Stress and heat flux via automatic differentiation

Graph neural networks (GNNs) emerged recently as a standard toolkit for
learning from data on graphs. Current GNN designing works depend on immense
human expertise to explore different message-passing mechanisms, and require
manual enumeration to determine the proper message-passing depth. Inspired by
the strong searching capability of neural architecture search (NAS) in CNN,
this paper proposes Graph Neural Architecture Search (GNAS) with novel-designed
search space. The GNAS can automatically learn better architecture with the
optimal depth of message passing on the graph. Specifically, we design Graph
Neural Architecture Paradigm (GAP) with tree-topology computation procedure and
two types of fine-grained atomic operations (feature filtering and neighbor
aggregation) from message-passing mechanism to construct powerful graph network
search space. Feature filtering performs adaptive feature selection, and
neighbor aggregation captures structural information and calculates neighbors'
statistics. Experiments show that our GNAS can search for better GNNs with
multiple message-passing mechanisms and optimal message-passing depth. The
searched network achieves remarkable improvement over state-of-the-art manual
designed and search-based GNNs on five large-scale datasets at three classical
graph tasks. Codes can be found at this https URL

本文提出的 Graph Neural Architecture Search 可以自动化搜索图神经网络的最佳深度和最佳的消息传递机制，以达到优越的图任务结果。