The problem of graph isomorphism is an important but challenging problem in
the field of graph analysis, for example: analyzing the similarity of two
chemical molecules, or studying the expressive ability of graph neural
networks. WL test is a method to judge whether two graphs are isomorphic, but
it cannot distinguish all non-isomorphic graphs. As an improvement of WL, k-WL
has stronger isomorphism discrimination ability, and as k increases, its
discrimination ability is strictly increasing. However, whether the isomorphic
discrimination power of k-WL is strictly increasing for more complex 3D graphs,
or whether there exists k that can discriminate all 3D graphs, remains
unexplored. This paper attempts to explore this problem from the perspective of
graph generation.

用图生成的角度探讨了 k-WL 在更复杂的三维图形中是否能够严格提高同构判别能力，以及是否存在能够判别所有三维图形的 k 值。

3-(F) WL 是否足够区分所有的三维图形？

Is 3-(F)WL Enough to Distinguish All 3D Graphs?

We study the problem of learning conditional distributions of the form $p(G |
\hat G)$, where $G$ and $\hat G$ are two 3D graphs, using continuous
normalizing flows. We derive a semi-equivariance condition on the flow which
ensures that conditional invariance to rigid motions holds. We demonstrate the
effectiveness of the technique in the molecular setting of receptor-aware
ligand generation.

研究使用连续归一化流学习条件分布的问题，确保对刚体运动的条件不变性，并在受体感知配体生成的分子设置中展示了该技术的有效性。

半等变条件归一化流

Semi-Equivariant Conditional Normalizing Flows

Many real-world data can be modeled as 3D graphs, but learning
representations that incorporates 3D information completely and efficiently is
challenging. Existing methods either use partial 3D information, or suffer from
excessive computational cost. To incorporate 3D information completely and
efficiently, we propose a novel message passing scheme that operates within
1-hop neighborhood. Our method guarantees full completeness of 3D information
on 3D graphs by achieving global and local completeness. Notably, we propose
the important rotation angles to fulfill global completeness. Additionally, we
show that our method is orders of magnitude faster than prior methods. We
provide rigorous proof of completeness and analysis of time complexity for our
methods. As molecules are in essence quantum systems, we build the
\underline{com}plete and \underline{e}fficient graph neural network (ComENet)
by combing quantum inspired basis functions and the proposed message passing
scheme. Experimental results demonstrate the capability and efficiency of
ComENet, especially on real-world datasets that are large in both numbers and
sizes of graphs. Our code is publicly available as part of the DIG library
(https://github.com/divelab/DIG).

本文提出了一种在三维图形中完全且高效地传递信息的新方案，通过使用重要的旋转角度实现了全局完整性，并组合了量子启发式基础函数和该方案提出的消息传递模式，构建了用于分子系统的全面高效图神经网络（ComENet）。