# Knot So Simple: A Minimalistic Environment for Spatial Reasoning

arXiv: https://arxiv.org/abs/2505.18028 · HTML: https://mlsanity.com/paper/2505.18028/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 38 references that are in the map.
- First posted on arXiv 23 May 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 23 of 23)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [ALFRED: A Benchmark for Interpreting Grounded Instructions for Everyday Tasks](https://mlsanity.com/paper/1912.01734/) (2019)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [A Corpus for Reasoning About Natural Language Grounded in Photographs](https://mlsanity.com/paper/1811.00491/) (2018)
- [VILA-U: a Unified Foundation Model Integrating Visual Understanding and Generation](https://mlsanity.com/paper/2409.04429/) (2024)
- [Visual Spatial Reasoning](https://mlsanity.com/paper/2205.00363/) (2022)
- [Compositionality decomposed: how do neural networks generalise?](https://mlsanity.com/paper/1908.08351/) (2019)
- [EmbodiedBench: Comprehensive Benchmarking Multi-modal Large Language Models for Vision-Driven Embodied Agents](https://mlsanity.com/paper/2502.09560/) (2025)
- [Exploring Length Generalization in Large Language Models](https://mlsanity.com/paper/2207.04901/) (2022)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [SoftGym: Benchmarking Deep Reinforcement Learning for Deformable Object Manipulation](https://mlsanity.com/paper/2011.07215/) (2020)
- [RoboCraft: Learning to See, Simulate, and Shape Elasto-Plastic Objects with Graph Networks](https://mlsanity.com/paper/2205.02909/) (2022)
- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Self-Improving Transformers Overcome Easy-to-Hard and Length Generalization Challenges](https://mlsanity.com/paper/2502.01612/) (2025)
- [Symbolic Brittleness in Sequence Models: on Systematic Generalization in Symbolic Mathematics](https://mlsanity.com/paper/2109.13986/) (2021)
- [Untangling Dense Non-Planar Knots by Learning Manipulation Features and Recovery Policies](https://mlsanity.com/paper/2107.08942/) (2021)
- [Learning Topological Motion Primitives for Knot Planning](https://mlsanity.com/paper/2009.02615/) (2020)
- [lilGym: Natural Language Visual Reasoning with Reinforcement Learning](https://mlsanity.com/paper/2211.01994/) (2022)

## Built on by (most cited first, 2 of 2)

- [TraversalBench: Challenging Paths to Follow for Vision Language Models](https://mlsanity.com/paper/2604.10999/) (2026)
- [MindTopo: Can Foundation Models Reason in Topological Space?](https://mlsanity.com/paper/2609.11900/) (2026)

## Abstract (arXiv)

We propose KnotGym, an interactive environment for complex, spatial reasoning and manipulation. KnotGym includes goal-oriented rope manipulation tasks with varying levels of complexity, all requiring acting from pure image observations. Tasks are defined along a clear and quantifiable axis of complexity based on the number of knot crossings, creating a natural generalization test. KnotGym has a simple observation space, allowing for scalable development, yet it highlights core challenges in integrating acute perception, spatial reasoning, and grounded manipulation. We evaluate methods of different classes, including model-based RL, model-predictive control, and chain-of-thought reasoning, and illustrate the challenges KnotGym presents. KnotGym is available at https://github.com/lil-lab/knotgym.