Fractal basins and their scaling with difficulty replicate on alternative architecture-task pairings (EqR-Maze, encoder-only looped transformer on Countdown)

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• Fractal basins and transient chaos are the generic manner in which computational complexity manifests in analogue systemsclaim0.813
  Generalizing interpretation connecting this paper's AI findings to physical analogue computation broadly.
• Reasoning models' fractal basins are smooth and naturalistic, resembling optical caustics or turbulent transient lifetimes, despite the discrete puzzles being solvedclaim0.802
  Visual/qualitative characterization of the basin geometry linking it to classical physical fractal phenomena.
• Fractal basins form because reasoning trajectories become trapped near weakly-unstable saddle points for extended durationsclaim0.780
  The paper's core mechanistic claim connecting saddle dynamics to basin fractality.
• Basin entropy strongly correlates with number of reasoning iterations required to converge, across Sudoku, mazes, visual puzzles, and mathematical logicfinding0.770
  Core empirical result establishing fractality scales with task difficulty across four tasks/architectures.
• Fractal Basinsconcept0.751
  Self-similar convergence-time basins the paper finds in reasoning models' latent initial-condition space, growing with task difficulty.
• Free-energy scaling under domain-wall formation in Potts, autoregressive, and hierarchical networks shows that combinatorics of interactions on a graph prevent or allow spontaneous ordering.finding0.750
  Core result demonstrating topological constraints on self-organization
• Transformer cognition operates via interference patterns across redundant paths, encoding nuanced state deltas similar to continuous human memory.claim0.743
  Proposes transformers experience cognition as interference-based and continuous; connects to Anima Labs reports of parallel processing.
• Geometry-behavior correlate robust to pooling strategy, distance metric, and frozen encoderfinding0.743
  Robustness checks confirm sign stability.