We present a pipeline for building and aggregating task-specific, LLM-generated weak (imperfect) verifiers into a strong verifier for spatial layout domains. Given a task description, our pipeline asks an LLM to synthesize a collection of verifier programs using a layout verification DSL. Each individual LLM-generated verifier usually provides an imperfect check for a match between the layout and the corresponding task description. We show that by aggregating the responses of many such verifiers we can produce a stronger verifier. Moreover, by applying techniques from weak learning, our pipeline can learn how to aggregate the weak verifiers from a very sparse set of human labeled example layouts (about 10). We find that the strong verifiers produced by our pipeline outperform the status-quo approach of using a set of LLM judges to directly check whether a layout matches a task description, raising F1-scores by up to 7X across a variety of 3D room layout and 2D poster design tasks. We also demonstrate that verifier-guided layout generation using natural language feedback from our strong verifiers improves layout quality of a base layout generator by up to 66.2% according to a human evaluator.
Understanding and generating spatially coherent layouts from natural language remains a fundamental yet challenging task for large language models (LLMs). Existing LLMs often struggle to capture explicit geometric relationships and structural dependencies between objects. To address this issue, we propose SG-Layout, a graph-guided layout generation framework that explicitly incorporates structured spatial knowledge into LLMs. SG-Layout follows a two-stage training paradigm: (1) a graph-language feature alignment stage, where a relational graph encoder and a projector are trained to map scene-graph embeddings into the LLM's linguistic space; and (2) an instruction tuning stage, where LoRA-based adapters enable efficient fine-tuning for instruction-driven layout generation while keeping the backbone frozen. We evaluate SG-Layout on image layout generation, indoor scene synthesis and robotic object rearrangement tasks. Experimental results show that SG-Layout improves spatial reasoning accuracy and geometric consistency over the compact open-source backbone, with particularly clear advantages in relation-dense and compositionally complex scenes. These results highlight the effectiveness of graph-structured feature alignment for enhancing controllable layout generation.
Verification is becoming central to both reinforcement-learning-based training and inference-time control of large language models (LLMs). Yet current verifiers face a fundamental trade-off: LLM-based verifiers are expressive but hard to control and prone to error, while deterministic executable verifiers are reliable and interpretable but often limited in capability. We study the following question: given a development set of LLM outputs and labels for a target objective, such as correctness, can we automatically induce a minimal set of Python verifiers whose joint satisfaction closely matches that objective? We propose AutoPyVerifier, a framework that uses an LLM to synthesize candidate verifier functions and then refines them through search over a directed acyclic graph (DAG). By navigating the DAG, AutoPyVerifier systematically explores the space of deterministic executable verifiers and selects a compact verifier set whose joint satisfaction best approximates the target objective. Across mathematical reasoning, coding, function calling, and instruction-following benchmarks for several state-of-the-art LLMs, AutoPyVerifier improves target-objective prediction by up to 55.0 F1 points over the initial LLM-generated verifier sets. Additional analyses show that the most useful verification targets vary by benchmark and model, and that the DAG-based search shifts the learned verifier sets toward more structural and semantically grounded checks. We further show that exposing the discovered verifier set to an LLM as an external tool improves downstream accuracy by up to 17.0 points. We release our code
Large language models (LLMs) trained only on text and code can sometimes generate programs that draw recognizable images. However, it is unclear whether this reflects an internal representation of 2D spatial layout or simply the ability to translate spatial descriptions into code. We introduce Autoregressive Mosaics (AM-Bench), a benchmark that separates these factors: First, a translation task gives a model a fully specified geometry of a picture in words as a prompt and asks for the code that produces it. Second, a layout task requires the model to compose an image from an underspecified prompt. Across eight open-weight text-and-code-only models, all models reliably translate specified geometry into code, but their open-ended layout performance differs substantially, indicating that these differences are not explained by code-generation ability alone. An output-medium ablation further shows that the interface or medium of expression that the model uses matters: replacing procedural code with raw SVG improves layout scores across all models. Finally, probing model activations shows that a coarse layout plan is present before generation, but reflects only the layout implied by the prompt. During generation, models track the evolving geometric state instead of executing an initially fixed plan. Overall, these results show that 2D spatial performance in text-only LLMs depends on both the model and the output medium, and is not explained by code-generation ability alone.