\section{Supporting Agentic Workloads}
\label{sec:agentic}

The fused GQA kernel of \S\ref{sec:gqa} solved the efficient execution of a
\emph{single} logical attention stream: one query stream against one KV
cache, tiled and merged with an online softmax. Agentic inference
introduces a different execution model, in which one request dynamically
\emph{forks} into several cooperating reasoning branches and later
\emph{joins} them. The purpose of this section is to show that this
multi-stream model needs no new attention algorithm---the expensive
hardware machinery built for \S\ref{sec:gqa} is reused unchanged---and to
work out the resulting design across three implementation layers. The
central claim, stated once here and defended throughout, is:

\begin{quote}
\emph{The proposed agentic execution does not change the semantics of
transformer attention; it changes only how independent query rows are
scheduled over a shared KV cache.}
\end{quote}

\noindent Attention stays identical; only the scheduling differs. What
follows is a \emph{design} built on the measured \S\ref{sec:gqa} kernel; it
is not yet a KernBench measurement, and points that go beyond the
implemented path are flagged as such.

\subsection{Motivation: from one attention stream to many}
\label{sec:agentic-why}

Agentic execution has two recurring shapes: a \emph{loop} (an agent that
repeatedly generates, calls a tool, and continues) and a \emph{fan-out /
fan-in} (a parent agent forks several specialised sub-agents and later
synthesises their results). The loop is ordinary autoregressive decoding
and needs nothing new. The fan-out is the interesting case, because the
branches are \emph{structurally related} rather than independent:
\[
\begin{aligned}
  \text{context}_i \;=\;& \underbrace{\text{shared prefix}}_{\text{common}} \\
  &+\; \underbrace{\text{private role}_i + \text{private suffix}_i}_{\text{branch-specific}} .
\end{aligned}
\]
Ordinary batching groups unrelated requests that merely arrive together;
agentic fan-out groups requests that share an identical prefix KV cache and
differ only in a short private suffix. That structure creates two levers
that unrelated-request batching cannot pull:

\begin{enumerate}
  \item \textbf{Shared-prefix KV reuse.} All branches attend to the same
  prefix KV, so it is read (and stored) once, not once per branch.
  \item \textbf{Query-row batching.} The new query rows of many sub-agents
  read the \emph{same} shared KV, so they can be concatenated into one
  taller GEMM.
\end{enumerate}

\noindent Both levers land directly on the \S\ref{sec:gqa} design, which
already multicasts a (small) query against a stationary KV cache and merges
the result hierarchically. Fan-out simply makes the query taller, and
fan-in adds a join step; neither touches the attention math.

\subsection{Architecture: three execution layers}
\label{sec:agentic-arch}

Before the mechanics, we fix the layering, because the recurring reader
question is ``whose job is this?''. Agentic execution divides cleanly along
the request-flow layers already used in this report: the \textbf{agentic
framework} decides \emph{what} to run and how to combine it, the
\textbf{runtime} decides \emph{how} to map it onto the hardware without
copying shared state, and the \textbf{kernel} does the actual math and
reduction on the PEs.

\[
\text{Framework} \;\longrightarrow\; \text{Runtime}
\;\longrightarrow\; \text{Kernel}
\]

\noindent Keeping the split this way preserves the topology-agnostic
runtime boundary: the framework never sees the SIP/CUBE/PE hierarchy, and
the kernel never sees the agent tree. The remainder of the section walks
the fan-out $\rightarrow$ runtime $\rightarrow$ kernel $\rightarrow$ fan-in
path through exactly these three layers.
Table~\ref{tab:agentic-levels} states each layer's responsibilities; the
kernel row is unchanged from \S\ref{sec:gqa}.

\begin{table*}[t]
\centering
\caption{Division of responsibilities for agentic attention. Only the
framework and runtime rows are new work; the kernel is the
\S\ref{sec:gqa} fused GQA kernel, unchanged in its math and reduction.}
\label{tab:agentic-levels}
\small
\begin{tabular}{@{}p{0.16\textwidth}p{0.40\textwidth}p{0.36\textwidth}@{}}
\toprule
\textbf{Level} & \textbf{Responsibilities} & \textbf{Explicitly not its job} \\
\midrule
\textbf{Agentic framework}
& Manage the agent tree: fork sub-agents and assign roles; identify the
shared prefix; mark which branches are co-schedulable (same shared prefix).
Fan-in: enforce schema-constrained results, deduplicate/rank findings,
hold evidence behind pointers, insert hierarchical reducers, and drive the
main agent's final synthesis.
& No topology, routing, KV placement, or scheduling. Sees agents and text,
not CUBEs or PEs. \\
\addlinespace
\textbf{Runtime}
& Fork the logical context by page table (shared-prefix pages $+$ private
suffix pages) with \emph{no copy} of shared KV. Concatenate co-scheduled
sub-agent query rows into $Q_{\text{cmb}}$. Select the execution policy
(Stationary-KV vs.\ Distributed-Q, \S\ref{sec:agentic-choice}) from the
cost model. Launch the
fused GQA kernel (composite command $+$ PE\_IPCQ) and hand the batched work
and policy to the simulation engine.
& No attention math and no per-hop routing (delegated to the engine and
policy); no agent-level semantics. \\
\addlinespace
\textbf{Kernel}
& Multicast $Q_{\text{cmb}}$ to all PEs; per-PE local attention over the
stationary KV shard via composite-command $Q\!\cdot\!K^{\top}$ and
$P\!\cdot\!V$; produce per-row online-softmax state; merge that state
hierarchically over PE\_IPCQ by matching row index (row-parallel, not
serialised).
& No knowledge of agents, page tables, or policy selection. Identical to
\S\ref{sec:gqa}; a taller $Q$ is the only difference. \\
\bottomrule
\end{tabular}
\end{table*}

\subsection{Stationary-KV Execution Policy}
\label{sec:agentic-policyA}

The core attention operation is $Q\!\cdot\!K^{\top}$, and under fan-out
multiple sub-agents contribute different query rows while reading a common
$K$. Rather than issuing $Q_A\!\cdot\!K_{\text{shared}}$,
$Q_B\!\cdot\!K_{\text{shared}}$, \dots\ as separate small GEMMs, the runtime
concatenates the rows,
\[
  Q_{\text{cmb}} = \begin{bmatrix} Q_A \\ Q_B \\ \vdots \end{bmatrix},
  \qquad
  Q_{\text{cmb}}\!\cdot\!K_{\text{shared}},
\]
and issues one taller GEMM. The arithmetic is unchanged---each row is still
independent---but the $M$ dimension grows. For a representative fan-out of
$8$ sub-agents at $20$ new tokens each, $M = 8\times20 = 160$; with a per-PE
KV shard of $256$ sequence positions this is a $160\times d$ by $d\times256$
local product---an $M{=}160$, $N{=}256$ shape that sits well above the
per-command issue overhead the composite command (\S\ref{sec:gemm}) is built
to amortise. Fan-out is therefore especially valuable during \emph{prefill}
of the private suffixes, where the combined $M$ is large; during decode the
query stays short and the workload remains, as \S\ref{sec:gqa} found,
KV-bandwidth bound.

The Stationary-KV policy maps onto the \S\ref{sec:gqa} placement
essentially unchanged: logically replicated $Q$ over a stationary,
sequence-sharded KV cache. One
KV head spans four CUBEs and 32 PEs, with each PE owning a different KV
\emph{sequence} shard $K_p[S_p,d]$, $V_p[S_p,d_v]$. The combined $Q$ is
multicast to all of them; each PE forms a complete local score
$Q_{\text{cmb}}\!\cdot\!K_p^{\top}$ over its own shard, and the per-row
online-softmax state is reduced hierarchically---8-PE merge inside each
CUBE, then a 4-CUBE merge---using the same PE\_IPCQ merge primitive from
\S\ref{sec:allreduce}.

\paragraph{The reduction algorithm does not change.} This is the point to
emphasise. Agentic batching does \emph{not} require a new reduction
algorithm: the hierarchical online-softmax reduction of \S\ref{sec:gqa}
remains exactly as-is, and only the query batch becomes larger. The
reduction is always \emph{same row index across sequence shards}, never
\emph{different query rows against each other}, so $M$ batched rows do
\emph{not} become $M$ serialised communication rounds; the $(m,\ell,O)$ row
states are exchanged as vectors/tiles and merged in parallel. Because the
merge is row-indexed, a taller $Q$ widens each payload but adds no rounds.
This is what makes agentic support a reuse of \S\ref{sec:gqa} rather than a
redesign.

\paragraph{Logical vs.\ physical $Q$ replication.} ``Replicated $Q$'' is a
\emph{logical} statement. Because the shard axis is the KV \emph{sequence}
dimension $S$, every PE must form the full score $Q\!\cdot\!K_p^{\top}$
against its local $K_p$ and therefore needs $Q$'s \emph{entire} hidden
dimension $d$; what is partitioned across PEs is $K$/$V$ along $S$, never
$Q$ along its columns. Splitting $Q$ (and $K$) on the hidden dimension
would instead make each PE's product \emph{partial} and force a pre-softmax
hidden-dimension reduction ($QK^{\top}=\sum_i Q_iK_i^{\top}$)---that is
tensor-/head-parallel attention, a different structure from the
sequence-parallel one assumed here, and one that cannot coexist with using
the PE axis for sequence shards. Logical replication also does not mean 32
physical copies: $Q$ can be multicast once into a CUBE-local shared buffer
(shared SRAM) that all PEs in the CUBE read, and a large $Q$ can further be
\emph{row}-tiled in time ($Q[0{:}16,:],\,Q[16{:}32,:],\dots$)---row tiling
splits the $M$ dimension, not the hidden-dimension columns. In short:
the Stationary-KV policy uses logically replicated $Q$ across
sequence-parallel PEs while $K$ and $V$ are partitioned along the sequence
dimension; $Q$ may be
temporally row-tiled or physically shared through multicast buffers, but it
is not partitioned along the hidden-dimension columns.

\paragraph{Replication is not $32\times$ the compute work (attention
FLOPs).} Multicasting $Q$ to 32 PEs does not multiply attention FLOPs,
because each PE computes against a different KV sequence shard rather than
the same one. Let the KV sequence length be $S$; with sequence parallelism
over 32 PEs, each PE owns $S/32$ positions. The score GEMM
$Q[M,d]\!\cdot\!K^{\top}[d,S]$ costs $\propto M\,d\,S$, so each PE performs
$M\,d\,(S/32)$ and the 32 shards sum to
\[
  32 \cdot M\,d\,\tfrac{S}{32} \;=\; M\,d\,S,
\]
identical to attention over one undivided sequence. Replication therefore
changes $Q$ distribution, reduction traffic, buffering, and scheduling---not
the total attention FLOPs.

\subsection{Distributed-Q Execution Policy (alternative)}
\label{sec:agentic-policyB}

The natural alternative is to partition (distribute) the query rows across
PE groups (\emph{the Distributed-Q policy}) rather than replicate them. It
is not automatically
better. Because the 32 PEs already shard the KV \emph{sequence}, every query
row must still attend to \emph{all} shards; partitioning $Q$ across PE
groups therefore forces each group to reach every KV shard, which requires
one of: regrouping KV shards per $Q$ group, replicating KV across groups, or
reading remote KV through symmetric memory. Each of these adds
memory-system complexity that the Stationary-KV policy avoids entirely.
Time-multiplexing the same PEs over $Q$ groups is the fourth option, but
that is temporal tiling---already available under the Stationary-KV policy
as row tiling---not true spatial $Q$ partitioning. The Distributed-Q policy
is thus a proposed adaptive extension, not the
baseline, and is only worth its complexity when $Q$ grows large enough that
multicast and reduction traffic dominate remote/regrouped-KV cost.

\subsection{Why the Stationary-KV policy is the baseline}
\label{sec:agentic-choice}

The choice reduces to a cost comparison the runtime can estimate. The
Stationary-KV policy pays for $Q$ multicast and a hierarchical reduction;
the Distributed-Q policy pays for moving or replicating KV plus extra
scheduling:
\[
  T_{\text{SK}} = T_{Q\text{-mcast}} + T_{\text{local GEMM}} + T_{\text{hier.\ reduce}},
\]
\[
\begin{aligned}
  T_{\text{DQ}} = {}& T_{Q\text{-part}} + T_{\text{remote/repl.\ KV}} + T_{\text{local GEMM}} \\
        &+ T_{\text{grp.\ reduce}} + T_{\text{remap}}.
\end{aligned}
\]
For the assumed mapping (one KV head $=$ 4 CUBEs $=$ 32 PEs), the KV cache
is large and stationary while $Q$ is comparatively small, so $T_{\text{SK}}$
is the lower cost and the Stationary-KV policy is the recommended baseline.
A future runtime can compute both estimates per launch---from the current
agent count, $Q$ size, KV-head mapping, and interconnect state---and switch
to the Distributed-Q policy only in the regime where a very large $Q$ batch
makes multicast and reduction traffic outweigh the cost of remote or
regrouped KV. Until that regime is measured, the Distributed-Q policy
remains a designed, not-yet-implemented option.

\subsection{Fan-in: joining sub-agent branches}
\label{sec:agentic-fanin}

Fan-out is only half of the pattern; after it, each branch produces a
private continuation and the parent must synthesise them. We treat fan-in
as a runtime/framework design problem with a clear optimization ladder.

\paragraph{Problem.} The branch KV caches \emph{cannot} be concatenated.
Each token's K/V depends on its full causal history, so stacking several
branches' private KV does not form the cache of any single valid
sequence. Join must therefore happen at the token/text level, and its cost
is dominated by the number of join-input tokens, because the new main-agent
KV grows in proportion to them.

\paragraph{Baseline.} A naive full-text gather concatenates every branch's
raw output: $8$ agents $\times\ 1000$ tokens $=\ 8000$ tokens pushed through
every layer during continuation prefill---inflating prefill work, KV
allocation, and later decode-time KV reads. This is the cost the ladder
below drives down.

\paragraph{Optimization 1 --- schema-constrained results.} Constrain each
sub-agent to emit a compact structured result (claim, confidence, evidence
handles) instead of free text, cutting join input by an order of magnitude
($8\times1000 \to 8\times50$).

\paragraph{Optimization 2 --- deduplication and ranking.} Overlapping
findings across branches are merged and ranked in the framework before they
reach the main context. This is preprocessing, not reasoning, and shrinks
the input further without involving the main model.

\paragraph{Optimization 3 --- pointer-based evidence.} Detailed evidence
stays outside the main context behind handles, materialised only when the
main agent actually requests it, so the effective input is summaries plus
only the evidence truly used.

\paragraph{Optimization 4 --- hierarchical reducers.} For wide fan-out,
intermediate reducer agents summarise groups of branches, shrinking the
final join prompt and organising fan-in traffic hierarchically---mirroring
how the hierarchical online-softmax merge organises attention reduction.

\paragraph{Future --- latent-state join.} A more aggressive step replaces
text outputs with a few learned latent tokens, further cutting join prefill
and KV growth. This requires training the main model to consume latent
tokens and aligning branch representations; it is a model--system co-design
direction, not a drop-in runtime optimization, and is out of scope here.

\medskip
\noindent Throughout, the shared prefix KV is reused by page-table
reference and only the join suffix is new, so shortening join input is the
primary lever on continuation-prefill cost, KV growth, and later
decode-time KV reads. Taken together, \S\ref{sec:agentic-policyA}--\ref{sec:agentic-fanin}
show why this workload is a natural extension of the 1H design rather than a
new one: the decisive hardware levers of this report---cheap composite
issue and a fast on-device reduction path---are exactly what make agentic
fan-out efficient, and no part of the attention math is altered to get
there. Quantifying the fan-out speedup and the fan-in join savings on
KernBench is left as measured 2H work.