FORGE: Fault-Oriented Rework Code Generation for Executable Interlocking Assembly

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.

A GUI command can be correct at the interface level yet still produce an incorrect assembly. An agent must identify the relevant components, respect their structural relationships, and determine which parts should move during recovery. We introduce MAGAR-Bench, a benchmark of 4,000 multimodal samples from 26 assembly families that separates Assembly Decision, Atomic Action, and Minimal Rework. For rework, the objective counts distinct moved parts within the validated recovery candidate set for each state, rather than the number of actions. We also introduce MAGAR, a selective correction framework built on a frozen policy obtained by supervised fine-tuning. Its key design matches correction granularity to output dependencies. Structured candidates revise assembly fields and rework scope, while complete action candidates keep native GUI primitives coupled with their parameters. A learned selector retains the original prediction unless a candidate passes a task-specific intervention threshold. On recorded states from held-out assembly families, MAGAR improves Overall, the task-balanced aggregate, from 37.50 to 41.39, with gains on all three tasks. Across 209 interventions, 70 correct an error and 22 introduce one. These results support task-specific correction while highlighting the remaining tradeoff between fixing errors and preserving reliable predictions.

Large language models (LLMs) can translate natural-language problem descriptions into optimization code, but the code is prone to silent failures: it executes and returns a solver-feasible solution while encoding a semantically incorrect formulation. On compositional problems, the resulting feasibility-correctness gap reaches 90 percentage points. We introduce ReLoop, which combines two mechanisms. Structured generation decomposes code production into a four-stage reasoning chain (understand, formalize, synthesize, verify) to reduce formulation errors during generation. Behavioral verification detects the errors that remain by testing whether the formulation responds correctly to solver-based parameter perturbation, a signal that comes from the solver rather than from LLM self-review and requires no ground truth. The two mechanisms address different error structures: structured generation gives the largest gain on compositional problems (+8.5pp accuracy on RetailOpt-190 with Claude Opus 4.6), and behavioral verification gives its largest gain on localized defects (+4.4pp on MAMO-ComplexLP). With diagnostic execution recovery, ReLoop reaches 100% executable code on Claude Opus 4.6, and relative to direct generation it raises or preserves every reported metric of the three chat-tuned foundation models on all three benchmarks. For the narrowly fine-tuned SFT model we test, the chain-of-thought prompt conflicts with its learned output format and lowers its accuracy on MAMO-ComplexLP; we document and analyze this interaction. We release RetailOpt-190, 190 compositional retail optimization scenarios in which several constraints interact.