Fractal basins trap latent reasoning

A study submitted to arXiv on 4 Sep 2026 by William Gilpin finds that leading AI reasoning models exhibit transient chaos and fractal basins, with fractality increasing with task difficulty across tasks like Sudoku, maze solving, visual puzzles, and mathematical logic. The research shows reasoning slowdowns are an inevitable consequence of problem hardness, as models become trapped near saddle points corresponding to nearly-correct solutions.

Computer Science Machine Learning Submitted on 4 Sep 2026 Title:Fractal basins trap latent reasoning View PDF /pdf/2609.04963 HTML experimental https://arxiv.org/html/2609.04963v1 Abstract: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. Submission history From: William Gilpin view email /show-email/7195b41d/2609.04963 via William Gilpin as proxy v1 Fri, 4 Sep 2026 10:11:36 UTC 17,726 KB References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender IArxiv Recommender What is IArxiv? https://iarxiv.org/about arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .