gqa decode: fix cube_base output-store; measure batch scaling on one SIP

Concurrency fix (completes the cube_base change): the decode kernel's
output store o_base still used the global cube_id while every load used
the user-local cube_local. For a single user (cube_base=0) they coincide,
so it was masked; a second batched user (cube_base>0) overshot its o shard
into an unmapped VA, mis-decoded to a phantom sip0.cube0.pe8 and raised a
RoutingError. Switch o_base to cube_local (one line); single-user results
are byte-identical (decode smoke/correctness pass).

Batch harness (un-skipped): create all users' tensors first, then submit
all launches deferred and drain together, so deploys don't drive an
already-submitted launch and serialize the batch. Concurrent users on
disjoint CUBE groups now overlap to within 3-5% of the single-user
latency. Swept B in {1,2,capacity} at 8K (high-B dense runs are the
expensive ones; throughput is near-linear in B).

Measured result: aggregate throughput at a full SIP rises from 0.86
(1-kv-per-cube, 2 users) to 1.41 requests/us (8-kv-per-cube, 16 users) —
the dense mapping wins throughput, the spread mapping wins latency.
S5.2 batch paragraph updated projected -> measured; add batch_scaling
figure and plot_batch_scaling.py.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

docs/report/1H-codesign-paper/sections/05-gqa.tex

@@ -240,26 +240,43 @@ requires lifting $M$, either by the long-context Q-tile split
 (\S\ref{sec:gqa-composite}) or by batching multiple users---which is also
 the lever that converts a mapping's density into throughput.
 
-\paragraph{Latency versus batched throughput (projected).} The latency
-ladder and the density trade-off pull in opposite directions once a SIP
-serves more than one request. Decode users are independent---each attends
-its own KV cache---and these mappings generate no cross-CUBE traffic, so a
-SIP can run several users at once on disjoint CUBE groups, up to $16/C$
-users: two for \textsf{1-kv-per-cube}, sixteen for \textsf{8-kv-per-cube}.
-Projecting from the measured single-user latencies under perfect overlap
-(an idealization---no concurrent multi-user run has been measured yet; see
-\S\ref{sec:future}), aggregate throughput at a full SIP is
-$\text{users}/\text{latency}$: at $8$K it rises from \SI{0.89}{}
-(\textsf{1-kv-per-cube}, 2 users) to \SI{1.48}{}~requests\,/\,\si{\micro\second}
-(\textsf{8-kv-per-cube}, 16 users), so the \emph{dense} mapping wins on
-throughput even though it is the \emph{slowest} per request; at $64$K the
-projected throughputs converge (\SI{0.17}{}--\SI{0.18}{}) because latency
-there already scales as $1/C$. The design conclusion is therefore
-regime-dependent: \textsf{1-kv-per-cube} is the latency-optimal choice for
-single-stream or low-batch decode, while denser mappings are the
-throughput-optimal choice for high-batch short-context serving. These are
-\emph{projections} assuming zero cross-user interference; validating them
-against a concurrent multi-user run is 2H work (\S\ref{sec:future}).
+\paragraph{Latency versus batched throughput.} The latency ladder and the
+density trade-off pull in opposite directions once a SIP serves more than
+one request. Decode users are independent---each attends its own KV
+cache---and these mappings generate no cross-CUBE traffic, so a SIP runs
+several users at once on disjoint CUBE groups, up to $16/C$ users: two for
+\textsf{1-kv-per-cube}, sixteen for \textsf{8-kv-per-cube}. We measure this
+directly, launching $B$ concurrent users and reading aggregate latency off
+the shared clock (Figure~\ref{fig:gqa-batch}). The overlap is nearly
+perfect: aggregate latency stays within \SI{3}{}--\SI{5}{\percent} of the
+single-user latency all the way to a full SIP (\textsf{8-kv-per-cube} at
+$16$ users is \SI{11.4}{} vs.\ \SI{10.8}{\micro\second}), so that small
+residual is the only cross-user interference the shared fabric adds.
+Aggregate throughput at $8$K therefore rises almost linearly with $B$, from
+\SI{0.86}{}~requests\,/\,\si{\micro\second} (\textsf{1-kv-per-cube}, capped
+at two users) to \SI{1.41}{} (\textsf{8-kv-per-cube}, sixteen users): the
+\emph{dense} mapping wins on throughput even though it is the \emph{slowest}
+per request, because it packs $8\times$ more concurrent users onto the SIP.
+The design conclusion is regime-dependent: \textsf{1-kv-per-cube} is the
+latency-optimal choice for single-stream or low-batch decode, while denser
+mappings are the throughput-optimal choice for high-batch short-context
+serving. At long context the per-request latencies already scale as $1/C$,
+so the same accounting predicts the throughputs converge; a measured
+long-context batch sweep is 2H work (\S\ref{sec:future}).
+
+\begin{figure}[t]
+\centering
+\includegraphics[width=\linewidth]{gqa_short_context/batch_scaling.png}
+\caption{Batch scaling at $S_{kv}{=}8$K: aggregate throughput (requests per
+\si{\micro\second}) versus the number of concurrent decode users on one SIP,
+each user on a disjoint CUBE group. Each mapping scales almost linearly with
+$B$ up to its SIP capacity $16/C$---\textsf{1-kv-per-cube} saturates at two
+users, \textsf{8-kv-per-cube} at sixteen. The dense mapping reaches the
+highest throughput; the spread mapping is latency-optimal but
+capacity-limited. Concurrent users overlap to within
+\SI{3}{}--\SI{5}{\percent} of the single-user latency.}
+\label{fig:gqa-batch}
+\end{figure}
 
 \begin{figure}[t]
 \centering

docs/sweeps/decode_batch_sweep.csv

@@ -0,0 +1,12 @@
+mode,kv_per_cube,C,S_kv,B,capacity,agg_latency_us,mean_user_latency_us,throughput_users_per_us
+A1,1,8,8192,1,2,2.2471645000005376,2.2471645000005376,0.44500524994932983
+A1,1,8,8192,2,2,2.3131845000012543,2.2471645000012357,0.864608940617973
+A2,2,4,8192,1,4,3.3555127500005475,3.3555127500005475,0.2980170467240325
+A2,2,4,8192,2,4,3.3935227500010514,3.355512750001042,0.5893580645656141
+A2,2,4,8192,4,4,3.4695427500010703,3.3555127500011586,1.1528896711241752
+A4,4,2,8192,1,8,5.586135500000557,5.586135500000557,0.17901463364071643
+A4,4,2,8192,2,8,5.602295500000823,5.586135500000673,0.35699652044411195
+A4,4,2,8192,8,8,5.783285499986028,5.586135499984957,1.3832967436968704
+B,8,1,8192,1,16,10.816091000000947,10.816091000000947,0.09245484343649775
+B,8,1,8192,2,16,10.848411000001535,10.816091000001236,0.18435879687815265
+B,8,1,8192,16,16,11.38492099986691,10.816090999974403,1.4053676788962384

docs/sweeps/plot_scripts/plot_batch_scaling.py

@@ -0,0 +1,61 @@
+"""Batch-scaling figure for concurrent decode users on one SIP.
+
+Reads ``docs/sweeps/decode_batch_sweep.csv`` (from
+``tests/attention/test_gqa_decode_batch_sweep.py``) and plots aggregate
+throughput (requests / us) versus batch size B for the four KV mappings,
+one panel per context length. Each mapping's curve runs up to its SIP
+capacity 16/C (A1=2 ... B=16 users).
+"""
+from pathlib import Path
+
+import csv
+
+import matplotlib.pyplot as plt
+
+ROOT = Path(__file__).resolve().parents[3]
+CSV = ROOT / "docs" / "sweeps" / "decode_batch_sweep.csv"
+OUT = (ROOT / "docs" / "report" / "1H-codesign-paper"
+       / "figures" / "gqa_short_context" / "batch_scaling.png")
+
+MODE_LABEL = {"A1": "1-kv-per-cube", "A2": "2-kv-per-cube",
+              "A4": "4-kv-per-cube", "B": "8-kv-per-cube"}
+MODE_COLOR = {"A1": "#1f77b4", "A2": "#2ca02c",
+              "A4": "#ffd000", "B": "#d62728"}
+MODES = ["A1", "A2", "A4", "B"]
+
+
+def main():
+    rows = list(csv.DictReader(CSV.open()))
+    contexts = sorted({int(r["S_kv"]) for r in rows})
+    fig, axes = plt.subplots(1, len(contexts), figsize=(6.5 * len(contexts), 4.5),
+                             squeeze=False)
+    for col, S in enumerate(contexts):
+        ax = axes[0][col]
+        for m in MODES:
+            pts = sorted(
+                ((int(r["B"]), float(r["throughput_users_per_us"]))
+                 for r in rows if r["mode"] == m and int(r["S_kv"]) == S),
+                key=lambda t: t[0],
+            )
+            if not pts:
+                continue
+            xs, ys = zip(*pts)
+            ax.plot(xs, ys, marker="o", color=MODE_COLOR[m],
+                    label=MODE_LABEL[m])
+            ax.annotate(f"{ys[-1]:.2f}", (xs[-1], ys[-1]),
+                        textcoords="offset points", xytext=(4, 4), fontsize=8)
+        ax.set_title(f"S_kv = {S // 1024}K")
+        ax.set_xlabel("batch size B (concurrent users)")
+        ax.set_ylabel("throughput (requests / µs)")
+        ax.grid(True, alpha=0.3)
+        ax.legend(fontsize=9)
+    fig.suptitle("Batch scaling: aggregate throughput vs concurrent users "
+                 "(one SIP)", fontsize=12, fontweight="bold")
+    fig.tight_layout()
+    OUT.parent.mkdir(parents=True, exist_ok=True)
+    fig.savefig(OUT, dpi=140, bbox_inches="tight")
+    print(f"  ✓ {OUT}")
+
+
+if __name__ == "__main__":
+    main()