# SGA: Plug&Play Geometric Verification for Educational Video Synthesis

arXiv: https://arxiv.org/abs/2607.18116 · HTML: https://mlsanity.com/paper/2607.18116/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 18 of 18)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Text2Video-Zero: Text-to-Image Diffusion Models are Zero-Shot Video Generators](https://mlsanity.com/paper/2303.13439/) (2023)
- [MLLM-as-a-Judge: Assessing Multimodal LLM-as-a-Judge with Vision-Language Benchmark](https://mlsanity.com/paper/2402.04788/) (2024)
- [Photorealistic Video Generation with Diffusion Models](https://mlsanity.com/paper/2312.06662/) (2023)
- [Autoregressive Video Generation without Vector Quantization](https://mlsanity.com/paper/2412.14169/) (2024)
- [Prometheus-Vision: Vision-Language Model as a Judge for Fine-Grained Evaluation](https://mlsanity.com/paper/2401.06591/) (2024)
- [AST-T5: Structure-Aware Pretraining for Code Generation and Understanding](https://mlsanity.com/paper/2401.03003/) (2024)
- [Code2Video: A Code-centric Paradigm for Educational Video Generation](https://mlsanity.com/paper/2510.01174/) (2025)
- [TheoremExplainAgent: Towards Video-based Multimodal Explanations for LLM Theorem Understanding](https://mlsanity.com/paper/2502.19400/) (2025)
- [Creativity in LLM-based Multi-Agent Systems: A Survey](https://mlsanity.com/paper/2505.21116/) (2025)
- [Is Your Video Language Model a Reliable Judge?](https://mlsanity.com/paper/2503.05977/) (2025)
- [Prototyping the use of Large Language Models (LLMs) for adult learning content creation at scale](https://mlsanity.com/paper/2306.01815/) (2023)
- [A Closer Look into Recent Video-based Learning Research: A Comprehensive Review of Video Characteristics, Tools, Technologies, and Learning Effectiveness](https://mlsanity.com/paper/2301.13617/) (2023)
- [Multimodal Safety Evaluation in Generative Agent Social Simulations](https://mlsanity.com/paper/2510.07709/) (2025)
- [A Challenge to Build Neuro-Symbolic Video Agents](https://mlsanity.com/paper/2505.13851/) (2025)
- [SAVeS: Steering Safety Judgments in Vision-Language Models via Semantic Cues](https://mlsanity.com/paper/2603.19092/) (2026)

## Abstract (arXiv)

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. Additionally, we conduct a human evaluation showing that these improvements translate into human preference, with raters preferring SGA over the raw baseline in 84.4% of comparisons and over a VLM-based critic in 65.0%.