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finding:basin-entropy-strongly-correlates-with-number-of-reasoning-iterations-required-to-converge-across-sudoku-mazes-visual-puzzles-and-mathematical-logic

Basin entropy strongly correlates with number of reasoning iterations required to converge, across Sudoku, mazes, visual puzzles, and mathematical logic

Core empirical result establishing fractality scales with task difficulty across four tasks/architectures.

Source paper

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Fractal basins trap latent reasoning

(2026) · Jeffrey Lai · Anthony Bao · J. Quinn · William Gilpin

Neighborhood — ranked by edge-count

Papers (1)

paper

Fractal basins trap latent reasoning
mentions

Claims (1)

claim

Reasoning slowdowns are an inevitable consequence of problem hardness in modern AI models
supports
The paper's central interpretive claim, closing statement of the abstract.

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Basin Entropymethod0.780
Metric distinguishing fractal from smooth/random basins, computed by partitioning slices into boxes and taking mean Shannon entropy of settling times.
Hardness-induced fractal basins are ubiquitous in modern reasoning models, emerging even without hand-designed task-specific solvers, across highly distinct architectures and tasksclaim0.778
The paper's generalizing claim distinguishing its contribution from prior narrow demonstrations (e.g., Ercsey-Ravasz & Toroczkai's SAT solver).
Reasoning models' fractal basins are smooth and naturalistic, resembling optical caustics or turbulent transient lifetimes, despite the discrete puzzles being solvedclaim0.776
Visual/qualitative characterization of the basin geometry linking it to classical physical fractal phenomena.
Fractal basins and their scaling with difficulty replicate on alternative architecture-task pairings (EqR-Maze, encoder-only looped transformer on Countdown)finding0.770
Replication check ruling out that fractal basins arise only from one model-task pairing.
After the bifurcation, unstable FTLE directions appear and basin entropy abruptly increasesfinding0.767
Directly ties emergence of solvability to emergence of transient chaos and fractality.
Fractal basins form because reasoning trajectories become trapped near weakly-unstable saddle points for extended durationsclaim0.763
The paper's core mechanistic claim connecting saddle dynamics to basin fractality.
Boundary Basin Entropymethod0.759
Variant of basin entropy averaged only over boxes straddling multiple basin values.
Fractal basins and transient chaos are the generic manner in which computational complexity manifests in analogue systemsclaim0.758
Generalizing interpretation connecting this paper's AI findings to physical analogue computation broadly.