\section{Fused Grouped-Query Attention}
\label{sec:gqa}

Attention is the 1H focus, and it is where the two preceding optimizations
have to come together. Grouped-Query Attention (GQA) shrinks the KV cache
by sharing each KV head across a group of query heads (here $h_q=8$ query
heads to $h_{kv}=1$ KV head, a group factor $G=8$), which makes decoding
feasible at long context but also makes it acutely memory-bound: a decode
step processes a single query position ($T_q=1$) against the entire KV
history, so its arithmetic intensity is low and its time is dominated by
streaming the KV cache out of HBM. FlashAttention-style tiling with an
online-softmax merge avoids ever materializing the full score matrix, but
realizing it as a fast \emph{fused} kernel needs both building blocks from
this report: efficient GEMM issue (\S\ref{sec:gemm}) for the
$Q\!\cdot\!K^{\top}$ and $P\!\cdot\!V$ products, and an efficient on-device
reduction (\S\ref{sec:allreduce}) for the multi-user and
sequence-parallel KV reductions. \emph{Fused} here is meant in the
FlashAttention sense---$Q\!\cdot\!K^{\top}$, the online softmax, and
$P\!\cdot\!V$ collapse into a single kernel that never materializes the
score matrix---and, beyond that, the cross-device KV reduction is absorbed
into the same kernel (on PE\_IPCQ) rather than issued as a separate
all-reduce. This section is the capstone: the fused
kernel that uses the composite command and PE\_IPCQ at the same time.
Multi-head attention (MHA) was studied in prior work and serves here as
the established baseline rather than being re-derived.

