VIGOR: Verifiable Industrial Geometry Optimization and Repair in Scene Programs

Fuqiang Wang; Zheng Guo; Xiaoming Wu; Hanlin Kong; Nayu Liu; Chuanting Zhang; Daojun Liang; Jingxuan Wei

cs.AIOct 9, 2026

VIGOR: Verifiable Industrial Geometry Optimization and Repair in Scene Programs

Authors: Fuqiang Wang, Zheng Guo, Xiaoming Wu, Hanlin Kong, Nayu Liu, Chuanting Zhang, Daojun Liang, Jingxuan Wei

Organizations: Qilu University of Technology, Jinan, China · Tianjin University, Tianjin, China · Shandong University, Jinan, China · Qilu University of Technology (Shandong Academy of Sciences), Jinan, China ·

Abstract

Large language models (LLMs) increasingly generate structured layouts and executable scene programs from natural-language instructions. However, executability does not imply engineering feasibility: an industrial scene program may execute successfully while its final state still violates coupled boundary, collision, clearance, aisle, or structural constraints. We identify this mismatch as the executability-engineering-feasibility gap, where locally plausible placements can remain globally infeasible because corrections to one device may introduce violations elsewhere. To make this gap measurable in a controlled setting, we construct an execution-grounded industrial scene-program dataset with 1,749 constructible scenarios, complete executable programs, and 94 final-state geometric checks per scenario. We further propose VIGOR, which combines supervised scene-program generation with execution-grounded verification and staged geometric refinement. Supervised fine-tuning establishes complete program generation, local projection resolves independently correctable violations, and joint conflict-graph repair coordinates residual multi-object conflicts while preserving structural relations. Experiments show that VIGOR achieves 96.86% Complete Feasibility and an Overall score of 91.20, outperforming the strongest evaluated baseline by 10.42 points in Overall. These results show that, under controlled industrial layout conditions, reliable scene-program generation requires not only executable programs, but also explicit verification and coordinated resolution of coupled engineering constraints.

Figures & tables

Figure 1: Industrial scene-program generation exposes an engineering-feasibility gap hidden by successful execution. A valid industrial layout must simultaneously satisfy boundary, aisle, clearance, and attachment constraints, while executable programs may still contain coupled multi-object conflicts or broken structural relations that invalidate the final scene.

Figure 2: Overview of VIGOR. SFT generates the initial scene program, verification detects residual violations, and local–joint repair produces a feasible layout.

Figure 3: Construction pipeline of the VIGOR dataset. Public assets and engineering constraints are expanded into candidate conditions, filtered for constructibility, converted into executable scene programs, and finally executed and validated.

Figure 4: Constraint-profile composition of the VIGOR dataset.

Dataset statistics		Generation statistics
Statistic	Count	Statistic	Count
Candidate conditions	2,754	Scene instances	19,239
Final scenarios	1,749	Scene programs	1,749
Train / I / C	1,399 / 175 / 175	Program operations	43,725
Reference layouts	1,749	Geometric checks	164,406
Validated scenarios	1,749	Verified programs	1,749

Table 1: Key statistics of the industrial scene program dataset.

Method	GVB $\downarrow$	BG $\uparrow$	Feas. $\uparrow$	Func. $\uparrow$	BQ-FQ $\uparrow$	Interp-FQ $\uparrow$	Comp-FQ $\uparrow$	Tight-FQ $\uparrow$	Overall $\uparrow$	LLMJudge $\uparrow$
Open-weight Models
GLM-4-9B-0414 ( Z.ai, 2025 )	11.30	34.96	0.00	53.28	24.53	54.56	52.00	49.72	27.07	1.975
Qwen3-14B ( Yang et al., 2025 )	15.47	44.48	0.00	40.78	24.15	42.81	38.75	42.74	25.46	3.225
Gemma-3-12B-IT ( Gemma Team et al., 2025 )	38.21	0.65	0.00	29.87	6.25	29.71	30.03	19.45	13.27	0.325
DeepSeek-Coder-V2-Lite-Instruct ( DeepSeek-AI, 2024 )	80.84	0.00	0.00	2.65	0.00	3.06	2.23	3.46	2.32	0.300
Granite-3.3-8B-Instruct ( IBM Granite Team, 2025 )	44.25	11.01	0.00	11.58	0.00	11.68	11.47	15.61	10.51	1.225

Table 2: Main results on industrial scene-program generation. Models are grouped into open-weight models, closed-source/API models, published methods, and our method. Best and second-best results are highlighted in blue and pink.

Method	Geometry $\uparrow$	Functional $\uparrow$	Feasibility $\uparrow$	Overall $\uparrow$	LLMJudge $\uparrow$
Base	24.78	11.02	0.00	8.95	1.23
Base + $\mathcal{L}\rightarrow\mathcal{J}$	68.42	22.11	0.00	24.03	1.98
VIGOR-SFT	92.79	70.31	14.57	69.34	4.15
VIGOR-SFT + $\mathcal{L}$	97.76	70.37	56.86	81.18	4.10
VIGOR-SFT + $\mathcal{J}$	98.88	68.40	81.43	87.11	4.13
VIGOR	99.59	68.62	96.86	91.20	4.05

Table 3: Ablation study of different VIGOR variants. Best results are highlighted in blue.

Figure 5: Qualitative comparison. VIGOR better preserves spatial constraints and structural relations, avoiding aisle, clearance, and overlap violations.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Process–result capability profiles across industrial scene-program generation methods. Program Process Score measures structured program construction, Final Scene Score measures executed-scene quality, and Unified Capability Score summarizes both perspectives.

Figure 8: Fine-grained task capability analysis across ten industrial scene-generation conditions. Higher values indicate stronger unified structural, geometric, and functional capability.

Parameter	Values	Count
Main-aisle width $w$	$1.00$ – $1.80$ m	17
Equipment clearance $c$	$0.20$ – $0.60$ m	9
Boundary clearance $b$	$0.30$ – $0.70$ m	9
Aisle orientation $o$	$X$ , $Z$	2

Appendix

Table 4: Parameter grid used for task construction.

3D Scene Layout Generation

3D scene layout generation arranges objects and structures into coherent, controllable scenes from text, images, plans, or functional goals.

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Automatically generating interactive 3D indoor scenes from natural language is crucial for virtual reality, gaming, and embodied AI. However, existing LLM-based approaches often suffer from spatial errors and collisions, in part because common scene representations-raw coordinates or verbose code-are difficult for models to reason about 3D spatial relationships and physical constraints. We propose SpatialGrammar, a domain-specific language that represents gravity-aligned indoor layouts as BEV grid placements with deterministic compilation to valid 3D geometry, enabling verifiable constraint checking. Building on this representation, we develop (1) SG-Agent, a closed-loop system that uses compiler feedback to iteratively refine scenes and enforce collision constraints, and (2) SG-Mini, a 104M-parameter model trained entirely on compiler-validated synthetic data. Across 159 test scenes spanning five scenarios of different complexity, SG-Agent improves spatial fidelity and physical plausibility over prior methods, while SG-Mini performs competitively against larger LLM-based baselines on single-shot generation scenarios.

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