Autoregressive Frontier Expansion: Growing Trees with Graph Machine Learning

2026-09-29

AI Summary

This study addresses the high cost of acquiring tree-like 3D data and the difficulty existing models face in balancing topological constraints with generative generalizability. To this end, we propose an autoregressive frontier expansion framework that introduces a flow matching model based on SO(2)-equivariant graph neural networks. By simulating biological growth mechanisms, the method iteratively constructs tree-like structures, employing an autoregressive strategy to dynamically predict branch bifurcation or termination. Experiments demonstrate that the proposed model achieves morphological distributions highly consistent with real data across both unconditional and conditional generation tasks for cortical neurons and plant trees. This work effectively overcomes the limitations of conventional approaches, enabling high-fidelity generation of tree-like 3D structures under strict topological constraints.

Abstract

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.

Problem

• tree-like branching structures
• generative models
• 3D graph generation
• morphological modeling
• data augmentation

Innovation

• Autoregressive Frontier Expansion
• Flow Matching
• SO(2)-equivariant GNN
• Tree Generation
• Graph Machine Learning