Selective Rotary Position Embedding

arXiv cs.CL / 4/27/2026

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Key Points

The paper proposes Selective RoPE, an input-dependent rotary position embedding that generalizes standard RoPE and allows rotation by arbitrary angles in both softmax and linear transformer settings.
It argues that softmax attention implicitly performs a hidden rotational operation on query-key pairs, revealing an underlying positional structure.
The authors connect positional encoding behavior to state-space and gated linear transformer mechanisms, suggesting the real part relates to forgetting while the imaginary part encodes positions via rotations.
Experiments show that adding Selective RoPE to gated transformers improves language modeling performance and helps on challenging sequence tasks such as copying, state tracking, and retrieval.

Abstract

Position information is essential for language modeling. In softmax transformers, Rotary Position Embeddings (\textit{RoPE}) encode positions through \textit{fixed-angle} rotations, while in linear transformers, order is handled via input-dependent (selective) gating that decays past key-value associations. Selectivity has generally been shown to improve language-related tasks. Inspired by this, we introduce \textit{Selective RoPE}, an \textit{input-dependent} rotary embedding mechanism, that generalizes \textit{RoPE}, and enables rotation in \textit{arbitrary angles} for both linear and softmax transformers. We show that softmax attention already performs a hidden form of these rotations on query-key pairs, uncovering an implicit positional structure. We further show that in state-space models and gated linear transformers, the real part manages forgetting while the imaginary part encodes positions through rotations. We validate our method by equipping gated transformers with \textit{Selective RoPE}, demonstrating that its input-dependent rotations improve performance in language modeling and on difficult sequence tasks like copying, state tracking, and retrieval.