Fractal basins trap latent reasoning: chaos explains why LLMs overthink hard problems
wgilpin0 · x · 2026-09-09
William Gilpin's group posted an arXiv paper, Fractal basins trap latent reasoning, using nonlinear dynamics to explain why reasoning models slow down on hard tasks.
Key findings
- Leading reasoning models behave as dynamical systems with fractal basins, showing transient chaos on Sudoku, mazes, visual puzzles, math logic and even ARC-AGI; fractality increases with task difficulty.
- Reasoning slowdowns come from trajectories getting trapped near saddle points, which correspond to nearly-correct attempted solutions — the model wanders among plausible answers.
- This explains 'overthinking': similar prompts can produce reasoning traces differing 10x in length and token cost.
- The authors argue transient chaos is an inevitable tradeoff: sensitivity is needed for hard computations, but inference cost becomes unpredictable.
- A loop transformer trained on integer linear regression shows a mid-training bifurcation where fractal basins appear; the fast Lyapunov indicator correlates with how many candidate solutions the model visits before converging.
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