\subsection{Summary}
\label{sec:gqa-analysis}

The section's results line up into one picture of the fused kernel.
Placement is decided by memory first and communication second: only the
64-way splits fit production context, and among them the both-axes
sequence shard (Case~6) minimizes the per-token collective by merging
softmax state rather than partial scores. Command form is decided by
roofline position: the composite command removes the per-tile issue work
in both regimes, but converts to wall-clock only in compute-bound prefill,
while memory-bound decode stays bound by KV streaming regardless of command
form. The thread connecting the two is that, once composite issue makes
GEMM cheap and leaves the MAC array idle, the fused kernel's latency is set
almost entirely by data movement---streaming the KV cache and reducing
partials across PEs---which is exactly the cost the communication-side
work (on-device reduction, lazy load/compute overlap, fast TCM staging and
torus links) is built to attack. Roofline framing
(\S\ref{sec:roofline}) turns this observation into a sizing and sharding
programme in the next two subsections: capacity planning
(\S\ref{sec:capacity-planning}) and parallelism selection
(\S\ref{sec:parallelism-selection}). What this implies for hardware
investment across the report as a whole is taken up in the discussion.
