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SGA: Plug&Play Geometric Verification for Education... | AI Research

Key Takeaways

  • SGA: Plug&Play Geometric Verification for Educational Video Synthesis Creating educational videos using AI often involves using Large Language Models (LLMs)...
  • Recent work leverages Large Language Models (LLMs) to generate executable code for pedagogical animations using libraries such as Manim.
  • However, ensuring spatial correctness and visual legibility remains challenging, as existing frameworks emphasize pedagogical content while overlooking geometric occlusions.
  • We further introduce the Manim Visual Quality Score (MVQS), a deterministic rendering-free proxy for spatial integrity.
  • SGA: Plug&Play Geometric Verification for Educational Video Synthesis Creating educational videos using AI often involves using Large Language Models (LLMs) to write code for animation libraries like Manim.
Paper AbstractExpand

Recent work leverages Large Language Models (LLMs) to generate executable code for pedagogical animations using libraries such as Manim. However, ensuring spatial correctness and visual legibility remains challenging, as existing frameworks emphasize pedagogical content while overlooking geometric occlusions. We propose the Symbolic Geometric Agent (SGA), a plug-and-play module for code-centric animation pipelines that intercepts LLM-generated code, performs partial execution to extract symbolic scene graphs, and applies targeted refinement when spatial conflicts are detected. We further introduce the Manim Visual Quality Score (MVQS), a deterministic rendering-free proxy for spatial integrity. Experiments on the MMMC-Code benchmark across four LLM backbones and two agentic pipelines show that SGA achieves a peak MVQS of 73.11 (Code2Video + GPT-5.1), corresponding to a 16.1% relative improvement over the raw baseline, and improves MVQS in 7 of 8 backbone x pipeline configurations.

SGA: Plug&Play Geometric Verification for Educational Video Synthesis
Creating educational videos using AI often involves using Large Language Models (LLMs) to write code for animation libraries like Manim. While these models are good at generating the logic for a lesson, they often struggle with the "spatial" side of things—resulting in videos where text overlaps with equations, objects are poorly placed, or visual elements block each other. The Symbolic Geometric Agent (SGA) is a new tool designed to fix these layout issues by acting as a "quality control" layer that checks the code for geometric errors before the video is ever rendered.

How the Symbolic Geometric Agent Works

Instead of waiting for a video to be fully rendered and then asking an AI to critique the final frames—which is slow and often inaccurate—SGA works directly with the code. It performs a "partial execution" of the animation script to build a symbolic map of where every object is located. By analyzing these coordinates, the agent can mathematically detect if two objects are colliding or if text is falling off the screen. If it finds a conflict, it provides specific, actionable feedback to the LLM, which then makes precise, line-level edits to the code to resolve the issue.

A New Way to Measure Quality

To track how well these animations are laid out, the researchers introduced the Manim Visual Quality Score (MVQS). This is a deterministic metric that evaluates the "spatial integrity" of an animation without needing to watch the video. It looks at three main factors: how well objects are separated to avoid overlaps, how effectively they fill the screen, and whether the educational content remains clear and readable. Because it is based on the underlying geometry of the code rather than a subjective visual guess, it provides a reliable, repeatable way to measure if an animation is visually sound.

Performance and Results

The researchers tested SGA across several different LLM models and existing animation pipelines. The results showed that SGA consistently improved the spatial quality of the animations. For example, when paired with the Code2Video pipeline and GPT-5.1, the system achieved a peak MVQS of 73.11, representing a 16.1% improvement over the baseline. Across eight different testing configurations, SGA improved the spatial layout in seven of them, proving that it is an effective "plug-and-play" guardrail for automated educational content creation.

Why This Matters for Education

In an educational context, poor visual layout is more than just an aesthetic problem; it increases the cognitive load on the student, making it harder to learn the material. By ensuring that equations, labels, and geometric shapes are always placed correctly, SGA helps maintain the clarity required for effective teaching. Because it operates as a modular layer, it can be added to existing animation frameworks without requiring the underlying AI models to be retrained or fundamentally changed.

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