Phase Space Attention:A Hairer Lift Circumvents the Single-Layer Induction Obstruction
We circumvent the Sanford-Hsu-Telgarsky (SHT) single-layer induction obstruction within a linear, one-step, causal, bilinear, symplectically consistent design class on the post-RoPE substrate, by lifting attention onto a symplectic phase space, mirroring Hairer's lift of Stormer-Verlet. The lift exits the premise of the SHT counting argument rather than the bound itself. The reframing exhibits the obstruction as a filter-order gap: a one-layer bilinear score realises a $z$-transform of joint order $(0,0)$, whereas the induction discriminator requires key-side order $\geq 1$. Applying the symplectic upper shear $M_γ:(q,p)\mapsto(q+γp,p)$ to the post-RoPE query and key streams closes it. We...
| Authors | Kingsuk Maitra, Shagun Sood Morteza Hosseini, Suman Gunnala et al. |
|---|---|
| Primary category | cs.LG |
| Published | 26 September 2026 |
| Last updated at source | 26 September 2026 |
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