# Fractal basins trap latent reasoning

arXiv: https://arxiv.org/abs/2609.04963 · HTML: https://mlsanity.com/paper/2609.04963/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 2 of its 8 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 2 of 2)

- [Parcae: Scaling Laws For Stable Looped Language Models](https://mlsanity.com/paper/2604.12946/) (2026)
- [Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers](https://mlsanity.com/paper/2606.18206/) (2026)

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

- [When Recursive Models Finish Computing](https://mlsanity.com/paper/2609.26487/) (2026)
- [Reasoning with Neural Cellular Automata](https://mlsanity.com/paper/2609.36126/) (2026)

## Abstract (arXiv)

Reasoning allows artificial intelligence models to revisit and correct their mistakes, enabling recent frontier advances in mathematical theorem solving, software engineering, and autonomous task planning. Reasoning models are widely observed to reason for longer on harder tasks, but the general mechanism responsible for these slowdowns is unknown. Here, we show that reasoning models exhibit transient chaos, a physical consequence of the computational complexity of difficult tasks. As a consequence, we show that diverse leading reasoning models are dynamical systems with fractal basins, with fractality increasing with task difficulty across diverse tasks like Sudoku and maze solving, visual puzzles, and mathematical logic. We show that transient chaos emerges due to reasoning becoming trapped for extended durations near saddle points, which we show correspond to nearly-correct attempted solutions of the underlying problem. Our results show that reasoning slowdowns are an inevitable consequence of problem hardness in modern artificial intelligence models, and establish reasoning traces as a rich new class of dynamical system.