Internalizing Geometric Law: Learning from Solver Residuals for Precision-Critical Generation
Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints. We study open-ended geometric synthesis from natural language: translating free-form descriptions into precise constructions whose entities must simultaneously satisfy dozens of interacting constraints. To make this tractable, we release PyGeoX, a programmable geometric DSL that compiles declarative constraints into a differentiable loss, and PyGeoX-Bench, a stratified suite of 300 problems with per-constraint verifiable rewards. Using PyGeoX as a verifier, we identify a failure mode we call Outlier Gradien...
| Authors | Rafael Cabral, Pang Zixi, Ziyi Shou et al. |
|---|---|
| Primary category | cs.LG |
| Published | 8 June 2026 |
| Last updated at source | 8 June 2026 |
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