Fractal basins trap latent reasoning

This paper argues that reasoning slowdowns in AI are not merely software inefficiencies but signatures of transient chaos. Modeling latent-state reasoning as a discrete dynamical system, the researchers vary initial hidden states and map each state to its convergence time, revealing fractal basins whose complexity rises with task difficulty. The effect appears across Equilibrium Reasoners, Fixed-Point Reasoning Models, Parcae, and Tiny Recursive Model on Sudoku-Extreme, Maze-Hard, Countdown arithmetic, and ARC-AGI-1. Hard instances contain weakly unstable saddle points corresponding to nearly correct but invalid solutions—such as Sudoku grids with repeated digits or maze dead ends—which scatter nearby trajectories and produce long, unpredictable reasoning routes. Basin entropy correlates strongly with the number of reasoning loops, while the fast Lyapunov indicator identifies boundaries between divergent solution paths and tracks how often a trace changes candidate answers. A training study on integer linear systems shows that fractal structure emerges at a bifurcation where incorrect fixed points become saddles and the model first acquires multistep reasoning; only the core variables requiring Gaussian elimination exhibit positive finite-time Lyapunov exponents. The analysis uses 200×200 initial-state grids and at least 300 valid slices per model-task setting. The findings also contextualize overthinking: it can nearly double inference cost, while adversarial prompts can consume 10x more compute. Finally, the paper notes that compact recurrent systems with 7M parameters have surpassed language models exceeding 10B parameters on ARC-AGI, and examines Parcae as a 140M-parameter example, suggesting that reasoning capability depends on navigating—and escaping—complex latent landscapes rather than scale alone.