自回归前沿扩展：利用图机器学习生成树结构
Autoregressive Frontier Expansion: Growing Trees with Graph Machine Learning
- ETH Zurich（苏黎世联邦理工学院）
- Leipzig University（莱比锡大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出自回归前沿扩展框架，利用SO(2)等变图神经网络和流匹配模型迭代扩展树结构，在神经元和树木生成中实现高保真形态。
AI中文摘要：
树状分支结构在自然界中普遍存在，从植物树木到神经元、血管和呼吸树。其分支形态往往反映功能，因此结构建模对于理解这些系统如何运作至关重要。由于获取真实世界的三维数据通常昂贵或不可行，逼真的生成模型对于模拟和数据增强具有重要价值。现有的形态特异性模型要么限制拓扑生成方式，要么依赖手工调整的机械程序。相比之下，通用三维图生成器不利用或强制树的结构。我们提出自回归前沿扩展，一种通过迭代扩展过程构建树的生成框架，模拟真实树木的生物学生长。在每一步，由SO(2)等变图神经网络参数化的流匹配模型通过预测每个活动分支是否分叉或终止来扩展前沿。我们在皮层神经元和植物树木上评估了我们的方法，包括无条件生成、类别条件生成和形态引导生成。在两个领域中，生成的形态与参考分布高度一致，在条件实验中与指定目标高度一致。
英文摘要：
Tree-like branching structures are common in nature, from botanical trees to neurons, blood vessels and respiratory trees. Their branching shape often reflects function, making structural modelling central to understanding how these systems work. Because acquiring real-world 3D data is often expensive or infeasible, realistic generative models are valuable for simulation and data augmentation. Existing morphology-specific models either constrain how topology is generated or rely on hand-tuned, mechanistic procedures. Generic 3D graph generators, by contrast, do not exploit or enforce the structure of trees. We propose Autoregressive Frontier Expansion, a generative framework that constructs trees through an iterative expansion process, simulating the biological growth of real trees. At each step, a flow-matching model parameterised by an SO(2)-equivariant GNN expands the frontier by predicting whether each active branch bifurcates or terminates. We evaluate our method on cortical neurons and botanical trees in unconditional, class-conditioned, and morphology-guided generation. Across both domains, the generated morphologies agree closely with the reference distributions and, in conditional experiments, with the specified targets.
