# How language models extrapolate outside the training data: A case study in Textualized Gridworld

arXiv: https://arxiv.org/abs/2406.15275 · HTML: https://mlsanity.com/paper/2406.15275/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 21 Jun 2024.

## Builds on (most cited first, 30 of 31)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models](https://mlsanity.com/paper/2310.04406/) (2023)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [LLM-Planner: Few-Shot Grounded Planning for Embodied Agents with Large Language Models](https://mlsanity.com/paper/2212.04088/) (2022)
- [TravelPlanner: A Benchmark for Real-World Planning with Language Agents](https://mlsanity.com/paper/2402.01622/) (2024)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [Chain-of-Thought Reasoning Without Prompting](https://mlsanity.com/paper/2402.10200/) (2024)
- [The Parallelism Tradeoff: Limitations of Log-Precision Transformers](https://mlsanity.com/paper/2207.00729/) (2022)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [On the Inductive Bias of Neural Tangent Kernels](https://mlsanity.com/paper/1905.12173/) (2019)
- [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://mlsanity.com/paper/2311.01460/) (2023)
- [The CoT Collection: Improving Zero-shot and Few-shot Learning of Language Models via Chain-of-Thought Fine-Tuning](https://mlsanity.com/paper/2305.14045/) (2023)
- [The Neural Tangent Kernel in High Dimensions: Triple Descent and a Multi-Scale Theory of Generalization](https://mlsanity.com/paper/2008.06786/) (2020)
- [Beyond A*: Better Planning with Transformers via Search Dynamics Bootstrapping](https://mlsanity.com/paper/2402.14083/) (2024)
- [Transformers Can Do Arithmetic with the Right Embeddings](https://mlsanity.com/paper/2405.17399/) (2024)
- [Evaluating Cognitive Maps and Planning in Large Language Models with CogEval](https://mlsanity.com/paper/2309.15129/) (2023)
- [Learning in High Dimension Always Amounts to Extrapolation](https://mlsanity.com/paper/2110.09485/) (2021)
- [Evaluating Spatial Understanding of Large Language Models](https://mlsanity.com/paper/2310.14540/) (2023)
- [On Limitations of the Transformer Architecture](https://mlsanity.com/paper/2402.08164/) (2024)
- [Advancing Spatial Reasoning in Large Language Models: An In-Depth Evaluation and Enhancement Using the StepGame Benchmark](https://mlsanity.com/paper/2401.03991/) (2024)

## Built on by (most cited first, 7 of 7)

- [Generalizing from SIMPLE to HARD Visual Reasoning: Can We Mitigate Modality Imbalance in VLMs?](https://mlsanity.com/paper/2501.02669/) (2025)
- [Dyna-Think: Synergizing Reasoning, Acting, and World Model Simulation in AI Agents](https://mlsanity.com/paper/2506.00320/) (2025)
- [Mind the Gap Between Spatial Reasoning and Acting! Step-by-Step Evaluation of Agents With Spatial-Gym](https://mlsanity.com/paper/2604.09338/) (2026)
- [LLMs for Text-Based Exploration and Navigation Under Partial Observability](https://mlsanity.com/paper/2604.09604/) (2026)
- [TSLM: Tree-Structured Language Modeling for Divergent Thinking](https://mlsanity.com/paper/2601.22688/) (2026)
- [Distributed Zeroth-Order Policy Gradient for Networked Multi-agent Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2605.15697/) (2026)
- [Steered Generation via Gradient-Based Optimization on Sparse Query Features](https://mlsanity.com/paper/2605.23040/) (2026)

## Abstract (arXiv)

Language models' ability to extrapolate learned behaviors to novel, more complex environments beyond their training scope is highly unknown. This study introduces a path planning task in a textualized Gridworld to probe language models' extrapolation capabilities. We show that conventional approaches, including next token prediction and Chain of Thought (CoT) finetuning, fail to extrapolate in larger, unseen environments. Inspired by human cognition and dual process theory, we propose cognitive maps for path planning, a novel CoT framework that simulates humanlike mental representations. Our experiments show that cognitive maps not only enhance extrapolation to unseen environments but also exhibit humanlike characteristics through structured mental simulation and rapid adaptation. Our finding that these cognitive maps require specialized training schemes and cannot be induced through simple prompting opens up important questions about developing general-purpose cognitive maps in language models. Our comparison with exploration-based methods further illuminates the complementary strengths of offline planning and online exploration.