Design for Descent: What Makes a Shape Grammar Easy to Optimize?
Successive steps of a tree grammar designed for descent being optimized to match the SIGGRAPH logo. This work shows how careful consideration of the needs of optimization motivates the design of shape grammars well-suited for descent, turning difficult inverse tasks on structured representations into a straightforward gradient-based iterative optimization on the user's objectives.
Abstract
Shape grammars offer a powerful framework for computational design, but synthesizing shape programs to achieve specific goals remains challenging. Inspired by the success of gradient-based optimization in high-dimensional, nonconvex spaces such as those in machine learning, we ask: what makes a shape grammar amenable to gradient-based optimization? To explore this, we introduce Stochastic Rewrite Descent (SRD), an algorithm that interleaves structural rewrites with continuous parameter updates, taking steps in both to optimize a given objective. We analyze the core challenges which have previously prevented optimizing shape programs via descent, and identify a set of desirable properties for grammars that support effective optimization, along with concrete grammar design recommendations to achieve them. We validate this approach across three shape grammars, demonstrating its effectiveness in diverse domains including image fitting, text-driven generation, and topology optimization. Through ablations and comparisons, we show that grammars satisfying our proposed properties lead to significantly better optimization performance. The goal of this work is to open the door to more general and flexible computational paradigms for inverse design with shape grammars.
Optimization towards Target Images
Optimization towards Text Prompts using SDS Loss
Topology Optimization
Acknowledgements
This work is supported by the National Science Foundation under Grant No. 2212049 and 2219864 and the Sloan Research Fellowship. GPU compute is provided by NVIDIA Academic Grant Program.
Citation
@inproceedings{kodnongbua2025d4descent,
author = {Kodnongbua, Milin and Zhang, Zihan and Sharp, Nicholas and Schulz, Adriana},
title = {Design for Descent: What Makes a Shape Grammar Easy to Optimize?},
year = {2025},
isbn = {9798400721373},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3757377.3764004},
doi = {10.1145/3757377.3764004},
abstract = {Shape grammars offer a powerful framework for computational design, but synthesizing shape programs to achieve specific goals remains challenging. Inspired by the success of gradient-based optimization in high-dimensional, nonconvex spaces such as those in machine learning, we ask: what makes a shape grammar amenable to gradient-based optimization? To explore this, we introduce Stochastic Rewrite Descent (SRD), an algorithm that interleaves structural rewrites with continuous parameter updates, taking steps in both to optimize a given objective. We analyze the core challenges which have previously prevented optimizing shape programs via descent, and identify a set of desirable properties for grammars that support effective optimization, along with concrete grammar design recommendations to achieve them. We validate this approach across three shape grammars, demonstrating its effectiveness in diverse domains including image fitting, text-driven generation, and topology optimization. Through ablations and comparisons, we show that grammars satisfying our proposed properties lead to significantly better optimization performance. The goal of this work is to open the door to more general and flexible computational paradigms for inverse design with shape grammars.},
booktitle = {SIGGRAPH Asia 2025 Conference Papers},
articleno = {210},
numpages = {12},
location = {Hong Kong, Hong Kong},
series = {SA '25},
keywords = {optimization, shape grammar, procedural modeling},
}