Exact Finite Attention Responses From RoPE Derivatives

• URL: http://arxiv.org/abs/2609.14127v1
• Date: Sat, 12 Sep 2026 20:15:37 GMT
• Title: Exact Finite Attention Responses From RoPE Derivatives
• Abstract summary: We derive exact local responses for attention interventions, allowing candidate edits to be scored from a cached baseline and one backward pass.<n>The resulting predictions achieve 95.36--96.52% sign accuracy across 92,160 executed positional edits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We derive exact local responses for attention interventions, allowing candidate edits to be scored from a cached baseline and one backward pass. The starting point is the RoPE derivative $\partial_p z(p) = A z(p)$: its integral gives the finite positional displacement, which we carry through the softmax without linearising either rotation or normalisation. The resulting predictions achieve 95.36--96.52% sign accuracy across 92,160 executed positional edits on 768 held-out prompt sets, reducing answer-margin MAE by 73.6--82.5% against the positional Jacobian and by 36.2--50.9% against zero. For simultaneous key and value edits, the same divided-difference calculus isolates the interaction term $C_{KV} = \sum_j (p'_j - p_j)\,\varepsilon_j$, which is omitted by adding separate attributions. Retaining it reduces downstream margin MAE by more than a factor of nine in every setting of a 5,120-intervention sweep across two Qwen sizes, two tasks, and multiple layers; reductions against a quadratic interaction correction are 75.9--98.5%. Exactness concerns the edited attention write; downstream predictions contract that response with a baseline gradient and are evaluated by native execution. The calculus also yields a KL certificate for local approximation error, an exact query-conditioned gradient-step representation whose curvature identifies attention-preserving query directions, and minimum-norm query control. Sparse evaluation supports candidate ranking and cache decisions under explicit local distortion criteria.

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