[Lane 1 · numerics] SDPA backward — derivation note for the attention adjoint #1385

Sub-issue of #1384 ([Feature]: scaledDotProductAttention backward — gradients currently stop at attention).

Lane: 1 · Numerics/Research
Skill needed: Linear algebra / autodiff on paper, PyTorch to check. No Kotlin needed.
Size: s (a few hours)
Blocked by: nothing

What to do

1. Read the forward in DefaultCpuOps.scaledDotProductAttention (only to list its options: scale, causal, mask, key-padding lengths).
2. Write the backward: with S = scale·QKᵀ (+mask), P = softmax(S), O = PV: dV = Pᵀ dO, dP = dO Vᵀ, dS = P ⊙ (dP − rowsum(dP ⊙ P)), dQ = scale·dS K, dK = scale·dSᵀ Q. Explain how masks and causal masking affect it.
3. Verify numerically with PyTorch autograd on a tiny case and post the note (Markdown is fine) here.

Acceptance

• Note covers every forward option
• Numerical check against autograd included
• Result reported back on the parent issue

Notes

FlashAttention-2 (Dao, 2023) Algorithm 2 is a good reference for the recomputation trick.

Coverage matrix: docs/modules/ROOT/pages/reference/ops-status-matrix.adoc · How lanes work: Issue taxonomy