Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions. Recent work has shown that such models can separate generic pairs of non-equivalent geometric graphs, though they may fail to separate some rare and complicated instances. However, these results assume a fully connected graph, where each node possesses complete knowledge of all other nodes. In contrast, often, in application, every node only possesses knowledge of a small number of nearest neighbors. This paper shows that generic pairs of non-equivalent geometric graphs can be separated by message-passing networks with rotation equivariant features as long as the underlying graph is connected. When only invariant intermediate features are allowed, generic separation is guaranteed for generically globally rigid graphs. We introduce a simple architecture, EGENNET, which achieves our theoretical guarantees and compares favorably with alternative architecture on synthetic and chemical benchmarks.

翻译：受化学及其他科学领域应用的启发，本文研究了几何图消息传递神经网络的表达能力，其中节点特征对应于三维空间位置。近期研究表明，此类模型能够区分大多数非等价几何图对，尽管在某些罕见复杂实例上可能失效。然而，这些结论建立在全连接图的假设之上，即每个节点都掌握所有其他节点的完整信息。在实际应用中，节点通常仅能获取少量最近邻节点的信息。本文证明：只要底层图保持连通性，具有旋转等变特征的稀疏连接消息传递网络即可区分大多数非等价几何图对。若仅允许使用不变中间特征，则对于一般性全局刚性图可保证实现普适性区分。我们提出了一种简洁的架构EGENNET，该架构不仅实现了理论保证，在合成与化学基准测试中的表现也优于其他替代架构。