RoPE attention is an exact forward-pass gradient step with softmax intact
We derive an exact gradient-step representation of the RoPE-softmax forward pass. For every deterministic RoPE-softmax attention head with arbitrary affine projection weights, we construct a query-dependent effective matrix $ΔM_i$ satisfying $y_i = μ_i + u_i^\top ΔM_i$, where $μ_i$ is the uniform mean of the attended values and $u_i$ is the augmented query input. The construction applies the classical exponential divided difference $ρ= φ_1$ to retain the softmax exactly. Its positive coefficients give a unit gradient-step representation on a query-conditioned quadratic objective. The same function connects the RoPE generator to exact positional finite differences. We derive a tokenwise fo...
| Authors | Julie Huang, Maggie Chlon, Leon Chlon |
|---|---|
| Primary category | stat.ML |
| Published | 6 September 2026 |
| Last updated at source | 6 September 2026 |
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