Self-Attention Dynamics with Rotary Position Embeddings: Twisted States and Explicit Consensus Rates on the Sphere
Rotary position embeddings (RoPE) modify attention scores through position-dependent rotations, but their effect on normalized token dynamics is not captured by the vanilla spherical self-attention model. We study the continuous-time dynamics obtained when queries and keys are rotated while values remain on the unit sphere. The resulting attention kernel is reversible and admits a sharp uniform softmax floor, yet the natural RoPE interaction energy has derivatives of both signs within one fixed nontrivial system. Every consensus state remains an equilibrium, and its transverse linearization is a reversible Markov operator whose kernel depends on the consensus point through its energy acro...
| Authors | Hao Ye |
|---|---|
| Primary category | math.DS |
| Published | 27 July 2026 |
| Last updated at source | 27 July 2026 |
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