HySPE: Positional Encoding via Symplectic Dual Shears
We introduce Hyperbolic Symplectic Positional Encoding (HySPE), grounding positional attention in non-compact symplectic transformations. While canonical Rotary Position Embedding (RoPE) parameterizes the compact, elliptic branch of $\Sp(2,\R)$ via rotations, HySPE operationalizes its hyperbolic branch via a damped symmetric composition of dual shears, yielding a conformally symplectic contraction with two spectral decay rates per channel pair. To eliminate the exponential representation drift inherent to naive absolute factorizations, we diagonalize the operator in its invariant eigenbasis and introduce blockwise coordinate rebasing with adaptive centered execution. This guarantees lengt...
| Authors | Zhongping Ji |
|---|---|
| Primary category | cs.CL |
| Published | 7 October 2026 |
| Last updated at source | 7 October 2026 |
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