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May 15, 2026Open Access

Yare 3-6-9 Rotary Positional Encoding: A Digital-Root Frequency Schedule for RoPE

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Authors

WWWeslyn Cory Whitehead

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Overview

Proposed digital-root frequency schedules improve encoding in neural networks, suggesting enhanced performance in long-context tasks.

Key Points

  • The aim is to improve Rotary Positional Encoding by introducing structured frequency schedules based on digital-root principles.
  • Proposed two new frequency schedules: vortex_369 and digital_root_doubling.
  • Implemented a non-destructive runtime patch over the HuggingFace RoPE inv_freq buffer.
  • Conducted a benchmark suite (LongBench) to compare new schedules with existing methods.
  • Identified closed-form period structure for both new schedules without empirical validation.
  • Implemented norm preservation and determinism in the reference implementation.
  • Empirical results to be presented in future work (v1.1).

Cite This Study

Weslyn Cory Whitehead (2026) studied this question.

synapsesocial.com/papers/6a06b940e7dec685947abd9fhttps://doi.org/10.5281/zenodo.20150178
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Digital-Root Rotary Position Encoding: The 1-2-4-8-7-5 Cycle as a Basis for Sequence Position Representation2026
  2. 2Digital-Root Rotary Position Encoding: The 1→2→4→8→7→5 Cycle as a Basis for Sequence Position Representation2026
  3. 3Number-Theoretic Scheduling: Golden-Ratio and Digital-Root Bases for Position, Rank, and Noise2026
  4. 4HoPE: Hyperbolic Rotary Positional Encoding for Stable Long-Range Dependency Modeling in Large Language Models2025
  5. 5Context-aware Rotary Position Embedding2025