# Language-Augmented Semantic Priors for B-Spline Surface Fitting

arXiv: https://arxiv.org/abs/2609.11708 · HTML: https://mlsanity.com/paper/2609.11708/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 53 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 28 of 28)

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- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [CodeT5: Identifier-aware Unified Pre-trained Encoder-Decoder Models for Code Understanding and Generation](https://mlsanity.com/paper/2109.00859/) (2021)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [A Generalist Agent](https://mlsanity.com/paper/2205.06175/) (2022)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [Large Language Models on Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2312.02783/) (2023)
- [CAD-MLLM: Unifying Multimodality-Conditioned CAD Generation With MLLM](https://mlsanity.com/paper/2411.04954/) (2024)
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- [CAD-GPT: Synthesising CAD Construction Sequence with Spatial Reasoning-Enhanced Multimodal LLMs](https://mlsanity.com/paper/2412.19663/) (2024)
- [A Survey on Text-to-SQL Parsing: Concepts, Methods, and Future Directions](https://mlsanity.com/paper/2208.13629/) (2022)
- [Text-to-CAD Generation Through Infusing Visual Feedback in Large Language Models](https://mlsanity.com/paper/2501.19054/) (2025)
- [SQL-PaLM: Improved Large Language Model Adaptation for Text-to-SQL (extended)](https://mlsanity.com/paper/2306.00739/) (2023)
- [ShapeGPT: 3D Shape Generation with A Unified Multi-modal Language Model](https://mlsanity.com/paper/2311.17618/) (2023)
- [Seek-CAD: A Self-refined Generative Modeling for 3D Parametric CAD Using Local Inference via DeepSeek](https://mlsanity.com/paper/2505.17702/) (2025)
- [ReCAD: Reinforcement Learning Enhanced Parametric CAD Model Generation with Vision-Language Models](https://mlsanity.com/paper/2512.06328/) (2025)
- [ConstraintLLM: A Neuro-Symbolic Framework for Industrial-Level Constraint Programming](https://mlsanity.com/paper/2510.05774/) (2025)

## Abstract (arXiv)

The use of B-splines and Non-Uniform Rational B-Splines surfaces constitutes the mathematical foundation of contemporary computer-aided design (CAD) systems. Despite long-term progress, geometric kernels in traditional CAD still rely heavily on predetermined heuristic initialization for surface fitting and parameterization. Meanwhile, the procedural semantics and design intent encoded in modeling histories are largely ignored during geometry generation. This disconnect creates a gap between high-level design intent and solver-executable geometric configuration, often leading to suboptimal and semantically inconsistent fitting results. To bridge this gap, we introduce LASP, a Language-Augmented Semantic Priors framework that leverages large language models (LLMs) to infer structured, solver-usable B-spline priors from procedural modeling histories. Rather than modifying the geometric kernel itself, LASP operates as a semantic reasoning layer above existing solvers. It first translates modeling histories into rich textual descriptions that capture design intent, geometric context, and functional relationships, and then uses a fine-tuned LLM to predict structured B-spline prior parameters. LASP is trained through a two-stage scheme that combines local geometric regularities with long-range contextual dependencies, producing priors that are both interpretable and semantically coherent. This approach furnishes inductive signals that direct the conventional B-spline fitting process toward solutions that more accurately encapsulate the intended design objectives and demonstrate heightened semantic coherence. Compared to traditional machine learning schemes, the experiments demonstrate that language-driven reasoning can serve as a powerful inductive bias for geometric solving, establishing a new paradigm of language-guided geometric optimization in modern CAD systems.