Randomized trial analyzes position, rank, and noise using golden-ratio and digital-root sequences, indicating optimal scheduling methods.
Key Points
This research aims to unify two number-theoretic scheduling methods using the golden ratio and digital root to improve coverage and reduce aliasing effects.
Developed golden-ratio twist and digital-root doubling sequence for position and rank scheduling.
Proved theorems regarding continuous coverage with golden ratio and finite cyclic structure for digital-root.
Provided specific scheduling recipes for position encoding and LoRA rank adjustments.
The golden ratio φ⁻¹ is identified as the lowest-discrepancy Weyl generator for continuous coverage, supporting non-repeating patterns.
For finite structures, the digital-root group is shown to effectively manage anti-period-3 aliasing.