Natural-Language to Geometry Diagrams: A Constraint-Based Pipeline for Precise Visual Reasoning

From Symbolic Perception to Logical Deduction: A Framework for Guiding Language Models in Geometric Reasoning

Plane geometry remains a significant challenge in AI, requiring the integration of visual perception and mathematical reasoning. While Large Multimodal Models (LMMs) naturally handle visuo-linguistic inputs, they are often computationally intensive and opaque. We demonstrate that a pure Large Language Model (LLM), when equipped with specialized modules, can rival state-of-the-art LMMs on complex geometry problems. Our framework integrates a Geometric Vision Parser, which translates diagrams into symbolic form, with a Symbolic Solver that performs formal deductions, thereby mitigating hallucinations and promoting interpretable reasoning. To enable rigorous evaluation, we curate a benchmark of challenging problems from the 2025 Chinese Zhongkao examinations, ensuring data novelty and testing deeper deductive skills. Experiments demonstrate that our approach achieves performance comparable to Gemini 2.5 Pro while delivering clearer, human-like solutions.

LVR-Draw: A Language-Vision Pipeline for Robotic Drawing with Interactive Scene Verification and Correction

This paper presents LVR-Draw, a fully local language–vision pipeline for robotic drawing that integrates structured scene generation, multimodal verification and correction, and deterministic execution within a unified Human–AI–Robot loop. Given a natural language prompt, a Large Language Model (LLM) generates a structured scene representation in a predefined format, which is rendered into an interpretable image. A Vision–Language Model (VLM) then performs visual inspection to detect inconsistencies in object placement and spatial relationships. These observations are processed by the LLM to produce structured editing operations, enabling iterative refinement of the scene. After validation, the refined scene is converted into executable robot instructions through a deterministic pipeline, supporting predictable and reproducible execution without using generative models for control. Experimental results suggest that the system can generate valid scene representations, support multimodal correction, and preserve drawing order during physical execution.

Beyond Surface Forms: Symbolic Edits as a Test for Logical Reasoning with LLMs

Logical reasoning with large language models (LLMs) is a critical capability, as it reflects a system's ability to correctly deduce hypotheses from a given context using faithful deductive processes. However, LLM reasoning has often been shown to be sensitive to small surface-level variations in problem formulation, raising questions about whether models truly follow the underlying logical structure. Studying this behavior is challenging because the symbolic components of logical problems, such as operators and predicates, are difficult to systematically manipulate in natural language. We introduce a tool-driven framework for generating controlled, label-preserving edits to logical reasoning problems. Our method operates on symbolic representations of first-order logic and constraint satisfaction problem tasks, enabling targeted modifications to logical operators and other structural components before translating them back into natural language. Using this framework, we evaluate various LLMs under cumulative and individual operator edits and analyze their behavior in response to these changes. Our quantitative and qualitative analyses show that LLM reasoning behavior under controlled operator edits is inconsistent, regardless of model size or family: models sometimes adapt correctly to structural changes but often fail to track their logical consequences. The results from this automated stress test enable an evaluation of language models across different dimensions and help measure the reliability of their reasoning.

From Terminology to Diagrams: Visual-Instruction Generation for Scientific Diagram Understanding

Vision-language models (VLMs) have demonstrated strong performance in visual question answering with natural images. However, they continue to struggle with scientific diagrams, which are designed to convey functional or relational meaning rather than literal scenes. We therefore introduce a framework for generating large-scale diagram-grounded instruction data by leveraging terminology derived from scientific curricula. Our approach systematically extracts domain concepts, synthesizes atomic facts, retrieves relevant diagrams from the web, and generates multimodal supervision in the form of diagram captions and multiple-choice questions. Using this pipeline, we construct SciGram, a dataset of over 194K diagrams and 1.4M visual instructions across life, earth, and physical sciences. Despite relying on noisy web data and synthetic annotations, models fine-tuned on SciGram achieve substantial improvements on diagram-centric benchmarks, including TQA, ScienceQA, and AI2D, outperforming or matching state-of-the-art VLMs while using fewer training instances. Furthermore, augmenting existing models such as LLaVA OneVision with SciGram establishes new state-of-the-art performance on diagram question answering. Our results highlight the effectiveness of terminology-grounded instruction generation as a general strategy for improving vision-language reasoning in scientific domains. To support future research in scientific diagram understanding, we release both the SciGram dataset and models.

ExpConCAD: Experience-Guided Text-to-CAD Generation from Shape Descriptions with Implicit Spatial Constraints

Text-to-CAD aims to generate executable CAD programs from natural-language descriptions. However, real-world descriptions are often underspecified and omit critical spatial constraints required for valid CAD construction, a challenge that has been largely overlooked by existing methods. In this paper, we argue that missing spatial constraints should be inferred with respect to the underlying construction structure and informed by reusable design experience. Based on this insight, we propose ExpConCAD, an experience-enhanced framework for implicit spatial constraint completion. ExpConCAD first recovers the intended construction structure and constraint scopes, then retrieves relevant constraint-completion experience for similar scopes to complete the missing spatial constraints, and finally generates executable CadQuery programs. Extensive experiments demonstrate the effectiveness of ExpConCAD and provide insights into the role of construction structure understanding and experience memory in spatial constraint completion. Our code is available at: https://github.com/Hotjiashell/ExpConCAD.

GeoMind: Explicit Spatial Reasoning via Dual-Reference Geometric Modeling