Möbius RoPE

Möbius RoPE: Anti-periodic positional encoding improves in-context retrieval reliability

A new arXiv preprint introduces Möbius RoPE, a rotary positional encoding variant using an anti-periodic frequency ladder (θ_i = π(2i+1)/N) that couples sequence endpoints via a closed-form Dirichlet 'dipole' — claimed as the first anti-periodic boundary condition in positional encoding. The authors pretrain 48 models (160M and 410M parameter classes) on 2B FineWeb-Edu tokens and find that a hybrid Möbius arm raises needle-in-a-haystack retrieval from 63.3% to 90.3% at context length 512 with no perplexity cost (29.66 vs. 29.72). The effect is isolated to the anti-periodic structure specifically, as aperiodic and periodic ladder controls do not reproduce it, and swapping the frequency table back to standard RoPE collapses retrieval performance.