标题： 通过狄拉克扩散的排列不变谱学习 显示英文标题

标题： Permutation-Invariant Spectral Learning via Dyson Diffusion

摘要： 扩散模型在生成建模中起着核心作用，并通过扩散邻接矩阵表示来适应图。 最多有$n!$种这样的表示，对于具有$n$个节点的图来说是一个挑战，仅通过使用排列等变学习架构才能部分缓解。 尽管计算效率高，现有的图扩散模型在区分某些图族时仍然存在困难，除非图数据被加入了特定特征。 这一缺陷源于在学习架构中强制施加归纳偏见。 在本工作中，我们利用随机矩阵理论来分析提取扩散过程的谱特性，使我们能够将归纳偏见从架构转移到动态过程中。 在此基础上，我们引入了迪森扩散模型，该模型使用迪森的布朗运动来捕捉邻接矩阵上奥恩斯坦-乌伦贝克过程的谱动态，同时保留所有非谱信息。 我们证明，迪森扩散模型能够准确学习图谱，并优于现有的图扩散模型。 显示英文摘要

摘要： Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to $n!$ such representations for graphs with $n$ nodes is only partially mitigated by using permutation-equivariant learning architectures. Despite their computational efficiency, existing graph diffusion models struggle to distinguish certain graph families, unless graph data are augmented with ad hoc features. This shortcoming stems from enforcing the inductive bias within the learning architecture. In this work, we leverage random matrix theory to analytically extract the spectral properties of the diffusion process, allowing us to push the inductive bias from the architecture into the dynamics. Building on this, we introduce the Dyson Diffusion Model, which employs Dyson's Brownian Motion to capture the spectral dynamics of an Ornstein-Uhlenbeck process on the adjacency matrix while retaining all non-spectral information. We demonstrate that the Dyson Diffusion Model learns graph spectra accurately and outperforms existing graph diffusion models.