Latent L-systems: Transformer-based Tree Generator

Abstract

We show how a Transformer can encode hierarchical tree-like string structures by introducing a new deep learning-based framework for generating 3D biological tree models represented as Lindenmayer system (L-system) strings. L-systems are string-rewriting procedural systems that encode tree topology and geometry. L-systems are efficient, but creating the production rules is one of the most critical problems precluding their usage in practice. We substitute the procedural rules creation with a deep neural model. Instead of writing the rules, we train a deep neural model that produces the output strings. We train our model on 155k tree geometries that are encoded as L-strings, de-parameterized, and converted to a hierarchy of linear sequences corresponding to branches. An end-to-end deep learning model with an attention mechanism then learns the distributions of geometric operations and branches from the input, effectively replacing the L-system rewriting rule generation. The trained deep model generates new L-strings representing 3D tree models in the same way L-systems do by providing the starting string. Our model allows for the generation of a wide variety of new trees, and the deep model agrees with the input by 93.7% in branching angles, 97.2% in branch lengths, and 92.3% in an extracted list of geometric features. We also validate the generated trees using perceptual metrics showing 97% agreement with input geometric models.