Transformers Struggle to Use Their Emergent World Models: Revisiting the Tower of Hanoi, and the Illusion of Thinking
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TL;DR - An interpretability study of the Tower of Hanoi shows that both small in-house Transformers and frontier reasoning models build a linearly decodable, geometrically faithful world model of the puzzle (a Sierpinski triangle), but large models lose that representation during extended chain-of-thought — reframing the reported "illusion of thinking" collapse as a maintenance failure rather than an absence of world models.
- Small Transformers trained from scratch on precomputed solution traces develop an emergent, causally involved representation of the puzzle state space matching the Sierpinski triangle structure.
- Qwen3.6-27B and DeepSeek-R1-Distill-Qwen-32B encode this same world model near-perfectly at the end of the prompt, yet fail on the majority of flat-to-flat variants with more than 3 rings.
- Probing across planning stages localizes the failure to decaying world-model representations during generation; injecting the prompt-time representation at inference improves performance, establishing causality and partial recoverability.
- The flat-to-flat variant (arbitrary initial and goal configurations, not all rings on one peg) is the discriminating task where current LRMs still break down.
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Transformers Struggle to Use Their Emergent World Models: Revisiting the Tower of Hanoi, and the Illusion of Thinking
TL;DR - An interpretability study of the Tower of Hanoi shows that both small in-house Transformers and frontier reasoning models build a linearly decodable, geometrically faithful world model of the puzzle (a Sierpinski triangle), but large models lose that representation during extended chain-of-thought — reframing the reported "illusion of thinking" collapse as a maintenance failure rather than an absence of world models.
- Small Transformers trained from scratch on precomputed solution traces develop an emergent, causally involved representation of the puzzle state space matching the Sierpinski triangle structure.
- Qwen3.6-27B and DeepSeek-R1-Distill-Qwen-32B encode this same world model near-perfectly at the end of the prompt, yet fail on the majority of flat-to-flat variants with more than 3 rings.
- Probing across planning stages localizes the failure to decaying world-model representations during generation; injecting the prompt-time representation at inference improves performance, establishing causality and partial recoverability.
- The flat-to-flat variant (arbitrary initial and goal configurations, not all rings on one peg) is the discriminating task where current LRMs still break down.