# Transformers Struggle to Use Their Emergent World Models: Revisiting the Tower of Hanoi, and the Illusion of Thinking

arXiv: https://arxiv.org/abs/2608.07077 · HTML: https://mlsanity.com/paper/2608.07077/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in World models for language agents, one of 11 directions in World models.
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Placed in

- World models / [World models for language agents](https://mlsanity.com/wm/world-models-for-language-agents/)
- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 8 of 8)

- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Chain-of-Thought Reasoning In The Wild Is Not Always Faithful](https://mlsanity.com/paper/2503.08679/) (2025)
- [Inspecting and Editing Knowledge Representations in Language Models](https://mlsanity.com/paper/2304.00740/) (2023)
- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)

## Abstract (arXiv)

The Tower of Hanoi is a simple planning puzzle that in prior work has proven challenging for large reasoning models (LRMs). Current models solve the standard formulation of the puzzle, but still struggle with the flat-to-flat variant (where initial and goal states are not restricted to have all rings on a single peg). This paper presents an in-depth study of how both small, in-house Transformers and large, third-party LRMs solve this task. To understand the failures mechanistically, we first train small Transformers from scratch on precomputed solution traces. Using a variety of interpretability techniques, we show that these Transformers develop an emergent world model: a linearly decodable, geometrically faithful representation of the puzzle's state space (the Sierpinski triangle), that is causally involved in solving the puzzles. Second, we return to the large LLMs and apply our techniques to two frontier reasoning models, Qwen3.6-27B and DeepSeek-R1-Distill-Qwen-32B, that attempt to solve the task through extended chain-of-thought. Surprisingly, we find that both models encode the Sierpinski world model near-perfectly at the end of the prompt, and yet fail at the majority of tasks when there are more than 3 rings. We locate the source of this failure in the decaying representation of the world model. We probe for the representation at different stages during planning, and establish causality by showing that performance can be improved by injecting the prompt-time representation at inference. The failure of the models is thus one of maintenance of the required representations, not their absence, and performance is at least partially recoverable. These results thus reframe the reported collapse in performance from prior work: current Large Reasoning Models build a world model, and then lose it.