FPRM-Maze uncertainty exponent is stable across scale: α=0.853±3e-2

Evidence that FPRM-Maze basins are true (scale-free) fractals, contrasting with EqR-Sudoku's slim fractal.

Source paper

extracted_from

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

Hardness-induced fractal basins are ubiquitous in modern reasoning models, emerging even without hand-designed task-specific solvers, across highly distinct architectures and tasks
supports
The paper's generalizing claim distinguishing its contribution from prior narrow demonstrations (e.g., Ercsey-Ravasz & Toroczkai's SAT solver).

Hypotheses (1)

hypothesis

Most reasoning models are expected to exhibit some form of doubly transient chaos, because properties like convergence-to-fixed-answers act as a dissipation-like mechanism
associated_with
Forward-looking predictive claim about reasoning models generally, based on the analogy to damped physical systems.

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.

Parcae-Countdown uncertainty exponent across scales: α=0.912±8e-3 (1×), 0.846±6e-3 (10×), 0.861±3e-2 (100×), 0.887±2e-2 (1000×)finding0.784
Third architecture/task pair confirming near-scale-invariant fractal basin structure.
Mean validated introspective fidelity across concept-model pairs: R²=0.12 (1B), 0.37 (3B), 0.61 (8B); pooled LMM β=0.29, p=5.55×10⁻⁹⁹finding0.748
Strong scaling trend for introspective fidelity when excluding invalid steering-sign pairs
EqR-Sudoku uncertainty exponent decreases with zoom: α=0.249±6e-3 (1×), 0.243±9e-3 (10×), 0.216±4e-3 (100×)finding0.746
Evidence that EqR-Sudoku basins are 'slim fractals' — scale-dependent, decreasing fractal complexity with resolution.
Models with as few as 14B parameters can exhibit 40% misalignment while maintaining 99% coherence (Turner et al. 2025 result)finding0.737
Concurrent work result showing emergent misalignment occurs in small models
After insecure fine-tuning, all four models converge toward MFQ profiles near the scale ceiling (~4-5) across all five foundationsfinding0.736
Supporting signature for persona-model collapse: unconditioned moral profiles saturate near ceiling
The difficulty boundary for truth directions replicates across all four tested models (Llama-3.2-3B, Llama-3.1-8B, Gemma-2-2b, Gemma-2-9b); generalization to F3-F5 remains consistently low regardless of model size or family.finding0.727
Establishes generalizability of the core difficulty-boundary finding across model families.
Generated EqR test mazes have wall fraction ≈0.57finding0.726
Methodological detail characterizing the maze task-instance distribution used.
Impulsivity→interest steering: probe entropy increases (LMM slope=0.024, p=2.30×10⁻⁴) but report entropy does not (p=0.11)finding0.724
Evidence of a bottleneck between richer internal variation and final report distribution in impulsivity→interest condition