# Code as Worlds: Agentic Discovery of Executable World Representations for Physical Reasoning

arXiv: https://arxiv.org/abs/2608.27549 · HTML: https://mlsanity.com/paper/2608.27549/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 90 of its 115 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)
- LLM agents and tool use / [Multimodal and embodied agents](https://mlsanity.com/agents/multimodal-and-embodied-agents/)

## Builds on (most cited first, 30 of 90)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiency](https://mlsanity.com/paper/2508.18265/) (2025)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Kosmos-2: Grounding Multimodal Large Language Models to the World](https://mlsanity.com/paper/2306.14824/) (2023)
- [Modeling Context in Referring Expressions](https://mlsanity.com/paper/1608.00272/) (2016)
- [SAM 3: Segment Anything with Concepts](https://mlsanity.com/paper/2511.16719/) (2025)
- [Generation and Comprehension of Unambiguous Object Descriptions](https://mlsanity.com/paper/1511.02283/) (2015)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [VILA: On Pre-training for Visual Language Models](https://mlsanity.com/paper/2312.07533/) (2023)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Thinking in Space: How Multimodal Large Language Models See, Remember, and Recall Spaces](https://mlsanity.com/paper/2412.14171/) (2024)
- [Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAs](https://mlsanity.com/paper/2503.01743/) (2025)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [VACE: All-in-One Video Creation and Editing](https://mlsanity.com/paper/2503.07598/) (2025)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)

## Built on by (most cited first, 14 of 14)

- [4DCodeBench: Benchmarking Agents on Inverse Graphics of Dynamic Scenes](https://mlsanity.com/paper/2610.03715/) (2026)
- [EMPIRIC: Experiment-Driven Learning of Residual World Models for Robot Planning](https://mlsanity.com/paper/2609.35047/) (2026)
- [Teaching Vision-Language Models to Use the Scale They Are Given: Label-Free Equivariance Training for Metric Physical Reasoning](https://mlsanity.com/paper/2609.00658/) (2026)
- [Predictive Semantic Safety: From Visual Physical Reasoning to Safety-Critical Control](https://mlsanity.com/paper/2609.34356/) (2026)
- [EurekaBench: Measuring Agentic Ability to Discover New Scientific Insights](https://mlsanity.com/paper/2610.00492/) (2026)
- [World Editing: Intervening on Executable Worlds at Increasing Depth](https://mlsanity.com/paper/2610.02331/) (2026)
- [Memento 3: Model-Based Recursive Self-Improvement through Reflective Rulebooks](https://mlsanity.com/paper/2610.11794/) (2026)
- [AgentGarten: Code Worlds for Evolving Agents](https://mlsanity.com/paper/2610.12374/) (2026)
- [VETR: Execution-Grounded Self-Improving Agent for Symbolic Graphics Reasoning](https://mlsanity.com/paper/2610.13098/) (2026)
- [S-Space: Exploring Spatial Workspace in Multimodal Language Models](https://mlsanity.com/paper/2610.13527/) (2026)
- [ExeWorldBench: Benchmarking Code-Based Executable 3D World Modeling](https://mlsanity.com/paper/2610.15166/) (2026)
- [CivWorldBench: Evaluating Language World Models in Structured Multi-Agent Sandbox Worlds](https://mlsanity.com/paper/2610.16450/) (2026)
- [D-World: An Explicit World-Language-Action Model with Recursive Self-Improvement under Dual Control](https://mlsanity.com/paper/2610.17114/) (2026)
- [PhysCodeGym: Benchmarking Coding Agents for Physically Verifiable 4D Reconstruction](https://mlsanity.com/paper/2610.17288/) (2026)

## Abstract (arXiv)

Physical understanding and reasoning depend on forming compact and generalizable representations of the world. While modern vision-language models can recognize and explain diverse physical events, they often lack explicit representations of the underlying mechanisms-such as object states, physical parameters, and governing dynamics-needed for reliably reasoning how the world evolves and responds to interventions. In this work, we introduce Code-as-World, a paradigm that represents physical worlds through executable world representations. By expressing physical composition, dynamic evolution, and visual appearance as executable code, Code-as-World provides a compact, quantitatively grounded, and controllable abstraction of the physical world. To construct such representations from multimodal observations, such as natural-language descriptions or real-world videos, we develop an agentic discovery loop inspired by abductive reasoning, where an agent proposes, executes, renders, verifies, and iteratively refines executable world hypotheses. As a concrete application, we use verified executable worlds to provide scalable physical supervision for training vision-language models on quantitative physical reasoning. Experiments show that Code-as-World-VL achieves state-of-the-art performance on QuantiPhy and surpasses leading proprietary models, highlighting the potential of executable world representations as a scalable foundation for physical intelligence.