finding

active

finding:eqr-sudoku-uncertainty-exponent-decreases-with-zoom-0-249-6e-3-1-0-243-9e-3-10-0-216-4e-3-100

EqR-Sudoku uncertainty exponent decreases with zoom: α=0.249±6e-3 (1×), 0.243±9e-3 (10×), 0.216±4e-3 (100×)

Evidence that EqR-Sudoku basins are 'slim fractals' — scale-dependent, decreasing fractal complexity with resolution.

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

Slim fractals (scale-dependent fractal dimension) arise in physical systems with dissipation, where the saddle-like set decays over time
associated_withsupports
Explains why EqR-Sudoku basins show decreasing fractal dimension with zoom.

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×)finding0.789
Third architecture/task pair confirming near-scale-invariant fractal basin structure.
FPRM-Maze uncertainty exponent is stable across scale: α=0.853±3e-2finding0.746
Evidence that FPRM-Maze basins are true (scale-free) fractals, contrasting with EqR-Sudoku's slim fractal.
QwQ-32B on MATH-500: 21.0% reasoning token reduction at intervention strength -0.96 with only 0.34% accuracy lossfinding0.735
Demonstrates reflection redundancy in stronger model on harder math benchmark
On DeepSeek-R1, P12 ASR under AS at alpha=1.0 is 0.512 vs P04 ASR of 0.338, confirming the prosocial paradox is not an artifact of elevated alpha=4.0 steering.finding0.734
Robustness of the reasoning-model prosocial paradox replication
Generated EqR test mazes have wall fraction ≈0.57finding0.727
Methodological detail characterizing the maze task-instance distribution used.
Mean validated introspective fidelity across concept-model pairs: R²=0.12 (1B), 0.37 (3B), 0.61 (8B); pooled LMM β=0.29, p=5.55×10⁻⁹⁹finding0.724
Strong scaling trend for introspective fidelity when excluding invalid steering-sign pairs
In simulations, positive evidence threshold for Bayesian model reduction corresponds to ΔF ≤ −3, equivalent to odds ratio of exp(−3) ≈ 0.05 (reduced model ~20 times more likely than full model).finding0.723
Quantitative threshold used for accepting reduced models; linked to Bayes factor of ~20
Under reward shaping (G=100, H=-100, F=0), Active Inference scored 99.52, Bayesian RL 99.77, Q-learning 95.56, with nearly identical behavior between belief-based agents.finding0.720
Table 2, row 3, showing equivalence when prior preferences match rewards.