# ADR-0060: AHBM GQA Fused Attention Kernel (Llama3-70B) ## Status Proposed **Context model:** Llama3-70B. **Decision drivers:** agentic workload → low batch, long context; KV-load-bound decode; sequence-parallel (Ring KV) for long-context prefill. **Supersedes / extends:** pre-existing mesh-native attention kernels and their `milestone-gqa-llama70b` eval bench (removed when this ADR's kernels landed). See *§A. Relationship to existing kernbench work* — that code was the baseline this ADR upgrades to a real GQA, causal, long-context kernel. **Supporting ADRs** (efficiency / scale enablers — *not* GQA blockers; see §8 correction): **ADR-0063** `tl.scratch_scope` (per-tile scratch recycling — required for realistic context length), **ADR-0062** lazy `tl.load` (non-blocking load with auto-wait on first use → load/compute overlap), **ADR-0061** `tl.broadcast` (optional mask/general convenience). The two GEMMs (Q·Kᵀ, P·V) are issued as scheduler-managed `tl.composite` commands (the existing `CompositeCmd`; no new command kind); real GQA itself needs only kernel restructuring (§5.2). **Algorithm lineage.** This kernel is **FlashAttention** (tiling + online/streaming softmax with fused P·V — no full score matrix materialised). The KV-parallel split-and-combine in §4 is **FlashDecoding** (split-KV with log-sum-exp merge). The Ring path in §5.5 is **Ring Attention** (KV blocks rotated around the mesh, folded by the same online softmax). No new math is introduced; this ADR maps those known algorithms onto the kernbench **greenlet `tl` programming model** (ADR-0020, ADR-0046) and the **IPCQ** PE↔PE collective (ADR-0023/0025). --- ## TL;DR — two SP kernels (decode = reduce, prefill = ring) Decode-SP and prefill-SP are **structurally different** and are **two kernels** — one kernel cannot do both. The principle is *move the smaller thing*: - **Decode** (T_q=1): the output `O = [G, d]` is tiny, the KV cache is big. → keep KV **statically sharded & resident**, do the local sweep, and move only the small `(m,ℓ,O)` via a **2-level reduce** (§4). **Q is replicated** — all `G` query heads stacked into the GEMM M-dim (**M-fold**), so one `Q·Kᵀ` does all heads sharing one `K`. No KV movement. - **Prefill** (T_q=S): the output `O = [S, d]` per head is big — reducing it would move `[S,d]` per rank. → instead make **each CUBE own one Q head** (head-parallel, `C=G`) and **rotate the KV** so each head sees all KV (**Ring KV**, §5.5). No `(m,ℓ,O)` reduce (each CUBE outputs a different head). Only KV blocks move. Memory has room, so **replicate Q/weights to avoid communicating them**; only the irreducible data moves — `(m,ℓ,O)` (decode) or KV blocks (prefill). Both share §3's composite-hybrid inner tile (GEMMs → `tl.composite`, softmax merge in kernel, lazy `tl.load`). ### Kernel 1 — DECODE + SP (head-replicated, KV static shard, 2-level reduce; NO ring) The decode inner tile has a hard chain `Q·Kᵀ → softmax → P·V`: softmax (`tl.max(Sj)`) waits for the first GEMM, so a naïve loop stalls the CPU on `Sj` and **leaves the GEMM engine idle during softmax** (a bubble). Three variants trade CPU/HW complexity against that bubble (ship **opt3** now; **opt2** needs a new command kind — revisit with the cost model, §8/ADR-0064): ```python # OPTION 1 — current CompositeCmd (today; HAS the GEMM-engine bubble) def gqa_decode_v1(q_ptr, k_ptr, v_ptr, o_ptr, S_kv_local, d, C, P, scale, *, tl): cube_id = tl.program_id(axis=1); pe_id = tl.program_id(axis=0) kv = head_of_group(cube_id) # CUBE → its KV head q_g = tl.load(q_base(kv), (G * 1, d)) # T_q=1; Q replicated: G heads stacked into M (M-fold) m, l, O = init_running(G, d) # persistent arena (-inf, 0, 0) for j in range(ceil(S_kv_local / TILE)): # sweep ONLY my KV shard (resident, no move) with tl.scratch_scope(): Sj = tl.composite("gemm", a=q_g, b=tl.ref(k_tile(j), (d, TILE)), epi=[scale]) # ↓ CPU auto-waits on Sj → GEMM engine IDLE during softmax (bubble) m2 = tl.maximum(m, tl.max(Sj, -1)); P = tl.exp(Sj - m2); corr = tl.exp(m - m2) l = l * corr + tl.sum(P, -1) O = O * corr + tl.composite("gemm", a=P, b=tl.ref(v_tile(j), (TILE, d))); m = m2 hierarchical_reduce_and_store(m, l, O, cube_id, pe_id, C, P, o_base(kv)) # §4 2-level reduce ``` ```python # OPTION 3 — software pipelining (current primitives; bubble hidden, not provably removed) ← SHIP THIS def gqa_decode_v3(q_ptr, k_ptr, v_ptr, o_ptr, S_kv_local, d, C, P, scale, *, tl): cube_id = tl.program_id(axis=1); pe_id = tl.program_id(axis=0) kv = head_of_group(cube_id); q_g = tl.load(q_base(kv), (G * 1, d)) m, l, O = init_running(G, d); n = ceil(S_kv_local / TILE) Sb = double_buffer() # 2 persistent Sj buffers (outside scratch_scope) h = tl.composite("gemm", a=q_g, b=tl.ref(k_tile(0), (d, TILE)), out=Sb[0], epi=[scale]) # prime for j in range(n): Sj = Sb[j % 2] if j + 1 < n: # ← issue NEXT Q·Kᵀ before softmax → fills GEMM engine h = tl.composite("gemm", a=q_g, b=tl.ref(k_tile(j+1), (d, TILE)), out=Sb[(j+1)%2], epi=[scale]) with tl.scratch_scope(): m2 = tl.maximum(m, tl.max(Sj, -1)); P = tl.exp(Sj - m2); corr = tl.exp(m - m2) l = l * corr + tl.sum(P, -1) O = O * corr + tl.composite("gemm", a=P, b=tl.ref(v_tile(j), (TILE, d))); m = m2 hierarchical_reduce_and_store(m, l, O, cube_id, pe_id, C, P, o_base(kv)) ``` ```python # OPTION 2 — ex_composite, 2-split (NEW flash-epilogue cmd; gives K-before-V DMA priority) def gqa_decode_v2(q_ptr, k_ptr, v_ptr, o_ptr, S_kv_local, d, C, P, scale, *, tl): cube_id = tl.program_id(axis=1); pe_id = tl.program_id(axis=0) kv = head_of_group(cube_id); q_g = tl.load(q_base(kv), (G * 1, d)) acc = init_running(G, d) # (m,l,O): scheduler-updated flash accumulator for j in range(ceil(S_kv_local / TILE)): Sj = tl.composite("gemm", a=q_g, b=tl.ref(k_tile(j), (d, TILE)), epi=[scale]) # #1: reads K (priority) tl.ex_composite("softmax_pv", s=Sj, v=tl.ref(v_tile(j), (TILE, d)), acc=acc, scale=scale) # #2: reads V # ↑ both non-blocking; CPU never waits intra-tile → max run-ahead, fewest issues tl.wait() # ← drain ALL composites: acc is updated async (no auto-wait, # #2 is a serial chain through acc); only final after the last #2 hierarchical_reduce_and_store(*acc, cube_id, pe_id, C, P, o_base(kv)) ``` | | new HW cmd | GEMM bubble | CPU intra-tile wait | issues | now | |---|---|---|---|---|---| | **opt1 current** | no | **yes** | yes | `O(tiles·ops)` | ✓ | | **opt3 sw-pipe** | no | hidden\* | yes (reordered) | `O(tiles·ops)` | ✓ | | **opt2 ex_composite** | **#2 only** | hidden\* | **no** | `O(tiles)` | ✗ (build #2) | \* "hidden" not "removed": filling the GEMM engine during softmax depends on the scheduler/engine balance (softmax-vs-GEMM time, K DMA readiness, queue depth) — it *reduces/hides* the bubble, not provably eliminates it. (`#1` = the *existing* GEMM composite + `scale`; only `#2` = softmax + P·V + the stateful online-softmax accumulator is new. MATH engine already has max/sum/exp — the new part is the flash accumulator, not the ops.) ### Kernel 2 — PREFILL + SP (1 Q head per CUBE, head-parallel; Ring KV, NO reduce) ```python def gqa_prefill_sp(q_ptr, k_ptr, v_ptr, o_ptr, T_q, S_kv_local, d, C, scale, q_block, cube_start, *, tl): i = tl.program_id(axis=1) - cube_start # this CUBE's Q head = its start KV slice q = tl.load(q_ptr, (T_q, d)) # MY Q head's query rows (resident, TCM) Kc = tl.load(k_ptr, (d, S_kv_local)) # my K slice, pre-stored transposed [d, S/C] → TCM Vc = tl.load(v_ptr, (S_kv_local, d)); src = i # my V slice [S/C, d] → TCM (K/V in TCM so the ring can send them) m, l, O = init_running(T_q, d) for step in range(C): # ── Ring KV: rotate blocks around C CUBEs over IPCQ ── f = None if step < C - 1: # send current TCM block, recv next (overlap) tl.send("ring+", Kc); tl.send("ring+", Vc) f = (tl.recv_async("ring-", (d, S_kv_local)), tl.recv_async("ring-", (S_kv_local, d))) if not block_all_future(q_block, slice_pos(src)): # causal skip whole-future blocks S = tl.composite("gemm", a=q, b=Kc, epi=[scale]) # [T_q,d]·[d,S/C] → [T_q,S/C]; Kc is TCM-resident if block_partial(q_block, slice_pos(src)): S = S + causal_mask(q_block, slice_pos(src)) m2 = tl.maximum(m, tl.max(S, -1)); P = tl.exp(S - m2); corr = tl.exp(m - m2) l = l * corr + tl.sum(P, -1) O = O * corr + tl.composite("gemm", a=P, b=Vc); m = m2 # [T_q,S/C]·[S/C,d] → [T_q,d] if f: Kc, Vc = tl.wait(f[0]), tl.wait(f[1]); src = (src - 1) % C tl.store(o_ptr, O / l) # MY Q head's rows — NO reduce ``` > **Why two shapes.** Decode keeps KV put and moves the tiny `(m,ℓ,O)` > (§4 2-level reduce); prefill moves KV (Ring, §5.5) and keeps each head's > big output local. Both use §3's composite-hybrid tile. `K` is pre-stored > transposed to sidestep the reshape-not-transpose caveat (§3, §B); no > bespoke "flash-composite" kind on the decode critical path (§8 item 4). > **Output head distribution differs** — decode lands all `G` heads at the > CUBE-Group root; prefill leaves one Q head per CUBE (§0.5.4). > The opt2/opt3 variants are a **decode** concern: in prefill the causal `if` > is kernel control flow that **cannot enter a composite**, and the ring > already overlaps via `recv_async`. --- ## A. Relationship to existing kernbench work (read first) kernbench previously ran FlashAttention with an online-softmax `(m, ℓ, O)` merge over IPCQ via two pre-ADR-0060 mesh kernels (now removed): | Role | Mechanism | |---|---| | prefill (Ring K/V) | per-rank partial attention, bidirectional K/V fan-out, online-softmax fold | | decode (split-KV) | per-rank one-shot partial attention, bidirectional `(m,ℓ,O)` fan-out, log-sum-exp merge | Both were driven by `milestone-gqa-llama70b` (4 panels: `{single,multi}_user × {prefill,decode}`). **They are written in the greenlet `tl` API:** `tl.load`, `tl.dot`, `tl.softmax`/`tl.max`/`tl.sum`/`tl.exp`, `tl.send`/`tl.recv`, and Python `-`/`*`/`/` on `TensorHandle` (each emits a `MathCmd`) — the GEMMs as **blocking `tl.dot`**, not composites. The running `(m, ℓ, O)` is just Python `TensorHandle`s threaded through the loop. This ADR keeps the running state and the softmax merge in the kernel but **moves the two GEMMs onto the scheduler-managed `tl.composite` path** (see §1) — this **matters for the design**. **Three deliberate limitations of the baseline** — exactly what an *efficient GQA* kernel must lift: 1. **No GQA reuse.** Baseline was capped at `h_q == h_kv == 1`. The baseline test attributed this to a MemoryStore byte-conservation failure on a *broadcast view*, but that failure is a property of the baseline's **head-packing hack** (`_view(K, (h_q·d, S_kv))`, which conflates all heads into one matmul dim and only conserves bytes when `h_q == h_kv`). The correct fix is **kernel restructuring**, not a broadcast op: process **one KV head at a time** and fold the `G` group rows into the matmul **M** dimension (§5.2). That uses only byte-conserving reshapes, so real GQA (`h_q = G·h_kv`) runs with **no new primitive** — see §8. 2. **O(N) reduction.** The baseline does an all-to-all bidirectional fan-out so *every* rank ends with the full answer (`n_ranks − 1` steps). Attention only needs `O` at the query owner → a **2-level reduce-to-root** (intra-CUBE tree + intra-CUBE-Group center-mesh, §4) is `⌈log₂ P⌉` + center-mesh-over-`C` steps. 3. **Validation scale only.** `S = 16` because the 1 MiB scratch bump allocator leaks per-tile temporaries (baseline test capped S at 16 for this reason) and there is no causal masking / tiling → fixed by **ADR-0063** (recycling) + §5 (tiling, causal skip) + composite K/V streaming (§3) + **ADR-0062** (lazy load overlap). **Documentation debt (out of scope but recorded):** the baseline cites ADR-0055/0056/0057/0058/0059, **none of which exist as files** — they are ghost references. This ADR does not retro-write them; see the Detailed Design Document's *Open Decisions* for the recommendation. --- ## 0. Reference dimensions (Llama3-70B) | Symbol | Meaning | Value | |---|---|---| | `H_q` | query heads | 64 | | `H_kv` | KV heads | 8 | | `G` | GQA group size = `H_q / H_kv` | 8 | | `d` | head dim | 128 | | `L` | layers | 80 | | `D` | model dim | 8192 | Hardware recap: - **AHBM (chip)** = set of **CUBE**s (memory cubes, each with a logic die containing **PE**s) + **IO die** (ADR-0003). - **IPCQ**: PE↔PE queues, 4 mesh-direction queue-pairs per PE (`N/S/E/W`, ADR-0023 D3; `global_*` for inter-SIP, ADR-0032). Kernel API: `tl.send(dir, src)` / `tl.recv(dir, shape, dtype)` (`tl_context.py:402-499`). - **Composite command** (`CompositeCmd`, `pe_commands.py:144-162`): a single GEMM (or MATH) *head* plus element-wise *epilogue* stages (`bias/relu/scale/add/...`), issued **non-blocking** to PE_SCHEDULER, which generates a tile plan and streams DMA→GEMM→write per tile (ADR-0014 D6; `pe_scheduler.py:104-143`). It is **not** a general multi-op DAG: it cannot chain two GEMMs, cannot carry register state across instances, and cannot pop/wait on IPCQ. This ADR therefore issues **each** of the two attention GEMMs (Q·Kᵀ, P·V) as its own composite and keeps the cross-GEMM softmax merge + the IPCQ reduction in the kernel — it does **not** need a new "flash-composite" command kind (see §1, §8). ### CUBE Group — the placement unit (hierarchical SP) **A `CUBE Group` is `C` CUBEs (within one SIP) that jointly own one KV head and its `G` query heads.** One KV head's KV sequence is **sharded two levels** of sequence-parallelism (SP): - **Level-1 (inter-CUBE, within the CUBE Group):** the head's sequence is split across the `C` CUBEs of the group. - **Level-2 (intra-CUBE, across PEs):** each CUBE's slice is split again across its `P` PEs. So one KV head maps to **`C × P` ranks**, all within one SIP. A **rank** is not memory — it is one **SP participant** = a specific **PE in a specific CUBE** (`rank = cube_local·P + pe_local`); its KV shard *resides in* that PE's owned HBM region (`K_base[rank]`) and is DMA'd to the PE's TCM for compute. **How the `G` query heads map onto those ranks differs by case** (the two kernels, TL;DR / §5): - **Decode** (§4): **Q is replicated** — every rank holds all `G` query heads, **M-folded** (stacked into the matmul M / row dimension: `Q` for the group `[G, T_q, d]` → `[G·T_q, d]`, so one `Q·Kᵀ` GEMM computes all `G` heads while sharing the single `K` — the GQA reuse). KV is sequence-sharded `C × P` ways; outputs reduce. - **Prefill** (§5.5): **Q is head-parallel** — with `C = G`, **CUBE `i` owns exactly one query head `i`**; KV rotates (Ring); no reduce. `Q` is small, so replicating it (decode) or distributing it one-head-per-CUBE (prefill) is cheap — only the irreducible data moves (decode: `(m,ℓ,O)`; prefill: KV blocks). `C` is a **tuning knob**: for prefill set `C = G` (one Q head per CUBE); for decode `C` trades inter-CUBE reduction against KV-parallel breadth (small `C`, even `C = 1` single-CUBE, for short context where reduction dominates). **Topology grounding** (`topology.yaml`): a SIP is a `4×4` CUBE mesh (16 CUBEs, ADR-0017 NOC); a CUBE has `P = 8` PEs (`hbm_pseudo_channels/hbm_channels_per_pe = 64/8`). With `C = 8` a SIP holds **2 CUBE Groups = 2 KV heads**; the full `H_kv = 8` model therefore spans **4 SIPs** (8/2). Each CUBE Group is **intra-SIP**, so one head's reduction uses the CUBE NOC (Level-1) + PE IPCQ (Level-2) — never UCIe. (The shipped `topology.yaml` has `sips: 2`; full scale needs a 4-SIP config — §B.) **`--device` enumerates SIPs** (CLI semantics): one SIP-device bench drives its 2 CUBE Groups (2 KV heads) — the head is selected spatially by CUBE coordinate, **not** an in-kernel `for kv` loop. The CLI runs the 4 SIP-devices logically in parallel to cover all 8 heads. **Token → rank placement** within a CUBE Group is **contiguous block sharding**: rank `r` owns the position block `[r·B, (r+1)·B)`, `B = ⌈S/(C·P)⌉` (Level-1 picks the CUBE, Level-2 the PE within it). A contiguous block is **required** so prefill can causal-skip whole future blocks **and** so prefill + decode share one KV cache (§2.1). (Round-robin — interleaved `token i → rank (start+i) mod (C·P)` — gives better short-context decode balance but cannot causal-skip and cannot be shared with prefill; it is the **rejected** alternative, §2.1.) Reduction is **hierarchical and intra-SIP**: a KV head **does** span the `C` CUBEs of its group (Level-1), reduced over the CUBE NOC; this **reverses** the earlier "a query head never spans CUBEs" non-goal, which existed only because the `H_kv=1` baseline never needed it. Crossing **SIPs** for one head remains a non-goal (a head stays in one SIP). --- ## 0.5 Kernel boundary, preconditions, I/O contract ### 0.5.1 Position in the decoder layer ``` 1. RMSNorm 2. QKV projection (GEMM) ─┐ qkv_rope kernel (SEPARATE, upstream) 3. RoPE on Q and K ─┤ 4. write new K,V → KV cache ─┘ 5. ===== THIS KERNEL: FlashAttention ===== (post-RoPE Q, K-cache, V-cache → O) 6. Output projection (GEMM) out_proj kernel (SEPARATE, downstream) 7. residual add → FFN ... ``` **Preconditions (upstream `qkv_rope`, NOT this kernel):** - **P1.** Q is already RoPE-rotated. No rotation here. - **P2.** K-cache stores **post-RoPE** K (never re-rotated at attention time — the reason for post-RoPE caching). - **P3.** For decode, the new step's K row is RoPE-rotated and appended to its owning PE's K-cache slot **by `qkv_rope` before this kernel launches.** ⇒ this kernel is **pure read** on the KV cache. - **P4.** V is not rotated; V-cache holds raw projected V. - **P5.** RoPE position upstream is the token's **absolute global position** `global_idx = rank·B + local_slot` (`B = ⌈S/(C·P)⌉`, contiguous block, `rank = cube_local·P + pe_local`, §2.1). Placement ≠ RoPE position. ### 0.5.2 Shape symbols `T_q` = query length this launch (decode: 1; prefill/chunk: chunk width). `S` = total context length. `R = C·P` = ranks per CUBE Group; `S_rank` = keys owned by this rank ≈ `⌈S/R⌉`. Storage `bf16` (numpy proxy `f16`, `memory_store.py:16`); `m,ℓ,O` accumulators `f32` where precision matters. ### 0.5.3 INPUTS (per kernel launch) | Input | Shape (per KV head) | Location | Notes | |---|---|---|---| | `Q` | `[G, T_q, d]` | per-rank HBM (loaded to TCM) | post-RoPE (P1). `G` query rows of the group batched. | | `K_cache` | `[S/(C·P), d]` | per-rank HBM, base `K_base[rank]`, contiguous | post-RoPE (P2). Read-only. A **contiguous** global position block `[r·B,(r+1)·B)` (§2.1). | | `V_cache` | `[S/(C·P), d]` | per-rank HBM, base `V_base[rank]` | raw V (P4). Read-only. | | `global_token_counter` | scalar | launch arg | kernel derives local len, slot↔global, causal bounds. | | `start_cube`, `start_pe` (= `f(request_id)`) | scalars | launch arg | Level-1/Level-2 rotation. | | `cube_id`, `pe_id`, `C`, `P` | scalars | launch / `tl.program_id` 1/0 | CUBE-Group reduction geometry (`R = C·P`). | | `q_block_meta` `{q_start, T_q}` | launch arg | prefill/SP causal masking & skip. | | `O_base` | address | launch arg | where final O is written (CUBE-Group root only). | | `softmax_scale` | scalar | launch arg | `1/√d`. | For **Ring Attention (§5.5)** add per ring step: incoming `K_block, V_block` via IPCQ into ping-pong buffers (post-RoPE), plus `step_kv_global_range` for the causal step-skip. ### 0.5.4 OUTPUTS **The output head distribution differs by kernel** — downstream out-projection must consume them accordingly: | Kernel | Output | Location | Notes | |---|---|---|---| | **Decode** (§4 reduce) | `O = [G, 1, d]` (all heads) | `O_base` at the **CUBE-Group root** | head-replicated → all `G` heads end on one rank after the 2-level reduce. | | **Prefill** (§5.5 ring) | `O_i = [1, T_q, d]` (one head each) | per-CUBE `O_base[i]`, **distributed** | head-parallel → CUBE `i` writes head `i`'s rows in place; no reduce. | **Handoff contract to out-projection (downstream, separate kernel).** This ADR *guarantees* the two layouts above; designing out-proj is out of scope, but the handoff must match: **decode** delivers all `G` heads co-located at the Group root (out-proj reads them locally, or scatters per its own SP); **prefill** leaves head `i` on CUBE `i` (out-proj is itself head-parallel, or must **gather** the `G` heads first). Pin this per-kernel in the `out_proj` launch contract (§B decode-split item 2). **Decode intermediate** (non-root rank, on IPCQ — not kernel-visible): `(m_i, ℓ_i, O_i)` pushed up the 2-level tree to the parent (Level-2 PE parent, then Level-1 CUBE parent) via `tl.send` (§4). `O_i` is the heavy part. **Prefill** has no such partials (no reduce); instead KV blocks circulate (§5.5). **No-SP (`C=P=1`):** no IPCQ partials; the single rank's running `(m,ℓ,O)` is normalised in place and written to `O_base`. **Explicitly NOT outputs:** KV-cache writes (upstream, P3), output projection (downstream), score `S` and probs `P` (never materialised). --- ## 1. Decision (mechanism) **Implement the kernel as a *hybrid*: issue the two GEMMs (Q·Kᵀ and P·V) as scheduler-managed `tl.composite(op="gemm")` commands, and keep the online-softmax merge and the cross-PE reduction as kernel-level `tl` ops.** `tl.load` is **lazy** (non-blocking; the wait is auto-inserted at first use of the loaded data — ADR-0062), so explicit HBM loads overlap the compute that follows. Rationale grounded in kernbench's execution + latency model: - **GEMM tiling is offloaded to PE_SCHEDULER.** A `CompositeCmd` is non-blocking (`kernel_runner.py:182-191`, `pe_scheduler.py:104-121`): the kernel pushes **one coarse descriptor** (M = `G·T_q`, the whole per-rank tile sweep) and the scheduler generates the tile plan and streams DMA→GEMM→write per tile (ADR-0014 D6). K/V are `tl.ref` operands the scheduler streams from HBM, so per-tile **K/V prefetch is the scheduler's job** — no explicit prefetch op. The CPU (greenlet) is freed to issue the **next** composite while the current one runs, so the scheduler keeps the GEMM engine saturated across tiles. - **This reflects the hardware** and decouples CPU issue-rate from execution-rate. The blocking per-op `tl.dot` path, by contrast, stalls the CPU on every GEMM and leaves GEMM-engine **bubbles** during the interleaved softmax MATH ops; it is realistic only if the CPU can keep up with fine-grained per-tile issue. - **The running `(m, ℓ, O)` flash state stays Python `TensorHandle`s** threaded through the loop (the baseline already does this); the softmax merge (max/exp/sum/rescale) is kernel-level `tl` MATH **between** the two GEMM composites. The existing `CompositeCmd` cannot chain two GEMMs or carry cross-tile register state (§0), so the merge necessarily lives in the kernel — this is the hybrid split, not a limitation worked around. - **Cross-PE combination** is a log-sum-exp **tree** over `(m, ℓ, O)` after P·V, via kernel-level `tl.send`/`tl.recv` (§4) — unchanged. So the per-tile inner pipeline is: ``` q_g = tl.load(Q group) # lazy; auto-wait at first use per tile j: Sⱼ = tl.composite("gemm", a=q_g, b=tl.ref(Kⱼ)) → Sⱼ # scheduler streams Kⱼ DMA + GEMM Sⱼ += maskⱼ # kernel MATH, boundary tile only online-softmax: mⱼ, m_new, P, corr, ℓ # kernel MATH Oⱼ = tl.composite("gemm", a=P, b=tl.ref(Vⱼ)) → Oⱼ # scheduler streams Vⱼ DMA + GEMM O = O*corr + Oⱼ; m = m_new # kernel MATH (running merge) ``` with each tile's MATH temporaries wrapped in `tl.scratch_scope` (ADR-0063) so scratch stays O(1), and the next tile's composites issued before the current tile's results are waited on (non-blocking handles) so the scheduler pipelines across tiles. Control flow (tile skip, mask generation, reduction scheduling, address arithmetic) lives in the **kernel** (plain Python `if`/arithmetic in the greenlet body). This is exactly what kernbench's greenlet model already permits (`kernel_runner.py`, ADR-0020 D3). > **What this supersedes.** An earlier iteration proposed a pure > primitive-op path (all `tl.dot`, no composite — both are issued from the > greenlet, so the contrast is *scheduler-managed composite* vs > *kernel-issued ops*, not "greenlet vs composite") on the argument that > "composite yields no latency benefit." That holds **only because** the > simulator currently charges **zero** per-op CPU issue cost > (`dispatch_cycles=0`, `pe_cpu.py`) — it models away exactly the CPU > issue-rate / DMA-program cost that descriptor offload exists to hide. > The hybrid is the faithful representation of an efficient kernel. The > **measurable** size of the win (can the CPU saturate the engines for > many tiles?) is gated on modelling an op-type-differentiated issue cost, > tracked as future work (cost model; §9). Even at `dispatch_cycles=0` the > non-blocking composite path fills the GEMM-engine bubbles the blocking > `tl.dot` path leaves. > > **Why this is the efficient choice.** GEMM tiling + DMA streaming + > cross-tile pipelining are offloaded to the proven `CompositeCmd` > scheduler path; the softmax merge and the proven IPCQ collective stay in > the kernel. The only genuinely new machinery is two small, general > primitives (ADR-0062 lazy `tl.load`, ADR-0063 `tl.scratch_scope`); the > reduction reuses `tl.send`/`tl.recv`. A bespoke "flash-composite" > command (one kind internalising the softmax merge + carried register > state + an IPCQ-push epilogue) is **not** built — large, special-purpose, > and its only delta over this hybrid (full softmax offload) is not > justified at the current modelling fidelity; see §8. --- ## 2. Memory layout & driver responsibilities ### 2.1 KV cache allocation (2-level SP) One KV head's sequence is sharded across `C × P` ranks (Level-1 inter-CUBE × Level-2 intra-CUBE PE, §0). In kernbench this is a `DPPolicy` whose **both** the `cube` axis (`row_wise` over `C`) **and** the `pe` axis (`row_wise` over `P`) shard the sequence dimension, with Q `replicate` (`policy/placement/dp.py`). The baseline's single-axis `DPPolicy(pe="row_wise")` becomes a two-axis `row_wise` over (cube, pe). - Per-rank KV buffers sized to `⌈max_context / (C·P)⌉ × d × dtype`, K and V separately. - Each rank's **contiguous position block** is stored dense (`B = ⌈max_context/(C·P)⌉` slots) ⇒ DMA stays contiguous. - Slot → global (**contiguous block**): `rank = cube_local·P + pe_local` where `cube_local = (cube_id − start_cube) mod C`, `pe_local = (pe_id − start_pe) mod P`; then `global_idx = rank·B + local_slot`. > **Why the placement is *contiguous* blocks (rationale).** Because > prefill *writes* the KV cache (`qkv_rope`, > upstream) and decode *reads + extends* the same cache, both kernels share > one physical layout — no reshard at the prefill→decode boundary. Prefill's > **causal skip needs contiguous position blocks** (a late contiguous block > can be wholly future and skipped; a round-robin block spans all positions > and can never be skipped). So the shared layout shards each KV head into > **contiguous `C × P` position blocks** (rank `r` owns `[r·B, (r+1)·B)`, > `B = ⌈max_context/(C·P)⌉`). Decode reads its block + reduces; prefill rings > the `C` CUBE-level blocks. *Caveat:* contiguous under-uses ranks for > **short** context (only frontier ranks hold data) — acceptable given the > long-context target; short-context balance is a separate study (§B). > **Fallback:** for short/early decode where contiguous-block sharding > under-utilizes ranks, the driver may select a smaller `C` (or `C=P=1`); SP > is enabled only past the context-length threshold where KV-sweep time > dominates reduction and placement imbalance. > **Rejected: round-robin** (interleaved `token i → rank (start+i) mod (C·P)`) > — better short-context decode balance *alone*, but a round-robin block > spans all positions so it cannot causal-skip and cannot be shared with > prefill. ### 2.2 Driver per-launch duties (minimal) The driver supplies, per launch, the bases + counter + rotation; the kernel derives the rest: | Launch arg | Purpose | |---|---| | `K_base[rank]`, `V_base[rank]` | per-rank KV buffer bases (from tensor VA) | | `O_base` | attention output destination | | `global_token_counter` | current sequence position | | `start_cube`, `start_pe = f(request_id)` | Level-1/Level-2 rotation | | `cube_id`, `pe_id` (`tl.program_id` 1/0), `C`, `P` | CUBE-Group geometry | | `q_block_meta` | prefill/SP query block start + length | Let `R = C·P`, `B = ⌈max_context/R⌉`, `cube_local = (cube_id − start_cube) mod C`, `pe_local = (pe_id − start_pe) mod P`, and this rank's index `rank = cube_local·P + pe_local`. Kernel-derived (plain arithmetic, with `counter` = # filled tokens): - **my valid length** (contiguous block `[rank·B, (rank+1)·B)`): `my_len = clamp(counter − rank·B, 0, B)`. - **my turn to write this step:** the new decode token (position `counter`) lands on rank `counter // B` (its contiguous block). - **read range:** tiles `0 .. ⌈my_len / TILE⌉`. - **causal bounds / per-tile skip:** from global positions of the query block vs each tile. Driver = bases + counter + rotation. The placement policy is the single contiguous-block map `token t → rank ⌊t/B⌋` (rotated by `start_*`). --- ## 3. Per-tile op sequence (greenlet `tl`) One iteration = one KV tile on one PE. The two GEMMs are `tl.composite(op="gemm")` (scheduler-managed tiling + K/V DMA streaming); the softmax merge is kernel `tl` MATH between them. Real `tl` names (`tl_context.py`), with lazy `tl.load` (ADR-0062), `tl.scratch_scope` (ADR-0063): ```python # running state (persistent arena — allocated once, outside the scope) # m: [G, T_q] l: [G, T_q] O: [G, T_q, d] q_g = tl.load(Q_group_ptr, (G*T_q, d)) # lazy; auto-wait at first use (ADR-0062) with tl.scratch_scope(): # per-tile MATH temporaries recycled Sj = tl.composite("gemm", a=q_g, # [G·T_q, TILE]; scheduler streams Kⱼ DMA b=tl.ref(K_base + j*TILE*d, (TILE, d))) * softmax_scale if mask_j is not None: Sj = Sj + mask_j # additive causal mask (boundary tile) m_j = tl.max(Sj, axis=-1) m_new = tl.maximum(m, m_j) P = tl.exp(Sj - m_new) # no full-matrix softmax; streaming corr = tl.exp(m - m_new) # rescale factor for old accumulators l = l * corr + tl.sum(P, axis=-1) Oj = tl.composite("gemm", a=P, # [G·T_q, d]; scheduler streams Vⱼ DMA b=tl.ref(V_base + j*TILE*d, (TILE, d))) O = O * corr + Oj # running merge (kernel MATH) m = m_new ``` Notes: - `q_g` is the GQA-batched query reshaped to `[G·T_q, d]` (the `G` group rows folded into the matmul M dim; byte-conserving). One K/V tile serves all `G·T_q` rows — the GQA reuse lever — with no broadcast. - **K/V are `tl.ref` operands** the composite scheduler streams from HBM per tile (`pe_scheduler.py:104-143`): that *is* the prefetch/pipeline, so there is no explicit prefetch op. Issuing tile `j+1`'s composites before waiting on tile `j` (non-blocking handles) keeps the scheduler pipelined across tiles and the GEMM engine saturated. - `tl.trans` is **metadata-only** in kernbench (`tl_context.py:390`) and `MemoryStore.read` *reshapes* rather than transposes (`memory_store.py:73`). For zero/structural runs this is harmless; for non-trivial numeric data it yields a reshape-not-transpose, so Q·Kᵀ via a transposed K needs care (§11) — store K pre-transposed `[d, TILE]`, or add a real `tl.transpose` (a candidate further primitive, likely unnecessary given the simulator's performance-modeling purpose). - Masking: the kernel builds the boundary-tile mask from query/KV global offsets and adds it (`Sj + mask_j`); full-past tiles pass `None`; full-future tiles are **skipped** (the `if` never enqueues them). - A **new** "flash-composite" command kind (one that internalises the softmax merge + carried `(m,ℓ,O)`) is **not** used; the existing `CompositeCmd` covers each GEMM and the merge stays in the kernel (§1, §8 item 4). --- ## 4. Reduction (KV-parallel / SP combine) — 2-level reduce-to-root **Scope: this is the DECODE-SP path** (head-replicated, KV statically sharded, small `O`). Prefill-SP does **not** reduce — it rotates KV (Ring, §5.5). Reduce is chosen for decode because `O = [G, d]` is tiny, so moving `(m,ℓ,O)` beats moving the resident KV. After its tile sweep each rank holds `(m_i, ℓ_i, O_i)` (unnormalised) over its `1/(C·P)` shard. Combine via the associative/commutative log-sum-exp merge (identical math to the baseline's fold): ```python def merge(m_a, l_a, O_a, m_b, l_b, O_b): m = tl.maximum(m_a, m_b) sa, sb = tl.exp(m_a - m), tl.exp(m_b - m) return m, l_a*sa + l_b*sb, O_a*sa + O_b*sb # final: O = O_root / l_root # normalise once at the CUBE-Group root ``` Because the merge is associative **and** commutative, the combine is **reduce-to-root** (attention needs `O` at one place — the rank that writes `O_base` — not an all-reduce) and proceeds in **two levels**: ### 4.1 Level-2 — intra-CUBE (P PEs → CUBE root PE) - The CUBE's KV slice is itself **sequence-SP-split across its `P` PEs** (decision (a): the only way decode, `T_q=1`, can use all `P` PEs — there is no query axis to split). Each PE sweeps its `1/(C·P)` sub-shard, then a **reduce-to-root tree** over the `P` PEs, depth `⌈log₂ P⌉` (3 for `P=8`), over the PE IPCQ `N/S/E/W` mesh (`configure_sfr_intracube_pe_ring`). Each tree pair is a 1-hop physical neighbour. Result lands on the CUBE's root PE. ### 4.2 Level-1 — intra-CUBE-Group (C CUBE roots → Group root) - A **center-root bidirectional CUBE-mesh reduce** over the `C` CUBEs of the group (PE-root-only, `program_id(axis=1)` = `cube_id`), over the CUBE NOC 2D mesh (ADR-0017). This **adapts the proven inter-CUBE pattern of `lrab_hierarchical_allreduce.py` (Phases 1–2: row-then-col converge at the center CUBE)** — but **reduce-only** (drop its broadcast-back Phases 4–5; attention needs root-only) and with the **log-sum-exp `merge`** replacing its plain `+`. Center-root halves the critical path vs a corner root (`lrab_hierarchical_allreduce.py:113-116`). No inter-SIP phase — the CUBE Group is intra-SIP (§0). ### 4.3 Data-driven overlap, no global barrier - A rank sends up the tree the **instant its own local P·V finishes** — it does **not** wait for sibling ranks; internal nodes `merge` children as they arrive. So the reduction **overlaps the compute of slower ranks** (causal prefill imbalance, batched decode tokens). - The two levels **pipeline**: a CUBE whose Level-2 reduction is done feeds Level-1 immediately, while other CUBEs are still doing Level-2 — **no barrier between levels**. (A rank cannot send before its *own* local sweep completes; sending pre-final partials would multiply the heavy `O` payload and is not worth it.) - **Why reduce-to-root, not the baseline fan-out / an all-reduce:** the baseline replicates the answer to every rank (`R−1` steps); attention needs it once. Reduce-to-root is `⌈log₂ P⌉ + (center-mesh depth over C)` — for decode (short sweep, reduction-dominated) this is the dominant win. ### 4.4 Configurable topology Each level's collective is **selectable** (a tuning item, §9): the defaults above (Level-2 tree, Level-1 center-root mesh) suit the latency-bound, small-`O` decode case; a **ring** variant (chunked) is available if a specific reduction proves bandwidth-bound. (Note: this is the *reduce* collective for **decode**; **prefill** does not reduce at all — it uses the Ring-KV kernel of §5.5.) `C=1` degenerates to Level-2 only (single-CUBE SP). **Payload:** `O_i` (`[G·1, d]` for decode) is the heavy part; `m,ℓ` are light. Sent as separate `tl.send`s (baseline pattern). Kernel structure (greenlet), both levels reuse `merge`: ```python def hierarchical_reduce_and_store(m, l, O, cube_id, pe_id, C, P, o_base): # ---- Level-2: PE tree within the CUBE → CUBE root PE ---- for child in tree_children_dirs(pe_id, P): # PE IPCQ N/S/E/W m, l, O = merge(m, l, O, *recv_triplet(child)) if not is_cube_root(pe_id, P): send_triplet(parent_dir(pe_id, P), m, l, O); return # ---- Level-1: CUBE-mesh center-root reduce → Group root (cube roots only) ---- for child in mesh_children_dirs(cube_id, C): # CUBE NOC, center-root m, l, O = merge(m, l, O, *recv_triplet(child)) if is_group_root(cube_id, C): tl.store(o_base, O / l) # normalise once else: send_triplet(parent_dir_mesh(cube_id, C), m, l, O) ``` The reduction tree/mesh is **static** (fixed at compile time), so the recv order is data-independent — no data-dependent `pop`, plain blocking `tl.recv` suffices, and **no hardware/composite `pop`-as-dependency change is required** (§6). --- ## 5. Per-case kernels All cases share §3's composite-hybrid inner tile, but split into **two kernels** (TL;DR): the **decode-reduce** skeleton below (§5.2/§5.3) and the **prefill-ring** kernel (§5.5). They differ in head mapping, KV strategy, and cross-rank communication — see §10. ### 5.1 Decode skeleton (head-replicated, static shard, reduce) ```python def gqa_decode_sp(q_ptr, k_ptr, v_ptr, o_ptr, counter, start_pe, start_cube, C, P, *, tl): cube_id = tl.program_id(axis=1); pe_id = tl.program_id(axis=0) kv = head_of_group(cube_id) # CUBE coord → KV head (no for-kv loop) my_len = valid_len_2level(counter, start_cube, start_pe, cube_id, pe_id, C, P) n_tiles = ceil(my_len / TILE) q_g = load_Q_group(q_ptr, kv) # [G·1, d]; lazy tl.load, G folded into M (replicated) m, l, O = init_running() # persistent arena: -inf, 0, zeros for j in range(n_tiles): # sweep ONLY my static KV shard (resident, no move) run_tile(j) # §3: 2 composites + softmax MATH, in tl.scratch_scope if C == 1 and P == 1: tl.store(o_base(kv), O / l) # no reduction (single rank) else: hierarchical_reduce_and_store(m, l, O, cube_id, pe_id, C, P, o_base(kv)) # §4 reduce ``` (Prefill-no-SP is this same shape with `C=P=1`, `T_q>1`, and causal masking; **prefill-with-SP is the separate Ring kernel of §5.5**, not this skeleton.) ### 5.2 DECODE, no SP (`C=P=1`, one PE owns the head's KV) - `T_q = 1`, attends to all past KV ⇒ no future tiles, mask only on the final ragged tile. - **GQA reuse is the whole game** (decode is KV-load-bound): the `G=8` query rows of the KV head are folded into the matmul **M** dimension (`q_g` reshaped `[G, T_q, d] → [G·T_q, d]`, a byte-conserving reshape). Then `Q·Kᵀ` is `composite([G·T_q, d], Kᵀ[d, TILE]) → [G·T_q, TILE]` and `P·V` is `composite([G·T_q, TILE], V[TILE, d]) → [G·T_q, d]`. The KV tile (`[TILE, d]`) is the shared `K`/`V` operand — **streamed once, reused by all `G·T_q` rows automatically** because they are the M rows of the GEMM. No broadcast of K/V is needed; `m = G·T_q` in the composite's tile plan also makes the timing count all `G` rows' work correctly (a leading batch axis would *not* be counted — see §8). - If `S_rank` fits in scratch (small/medium context) this degenerates to a **one-shot** partial attention (one composite for Q·Kᵀ, one softmax, one composite for P·V) — exactly the baseline `_partial_attention` shape, just GQA-batched and on the composite path. Tiling (§3) only kicks in when `S_rank` exceeds the scratch scope's tile budget. ### 5.3 DECODE, with SP / KV-parallel (`C × P` ranks) - One request's KV is **contiguous-block sharded** across the `C·P` ranks of the CUBE Group (Level-1 over `C` CUBEs, Level-2 over `P` PEs); each rank owns its `B`-token block and GQA-batches its `G=8` query rows over its local tiles. - `T_q=1` ⇒ short per-rank sweep ⇒ **reduction dominates** ⇒ the §4 2-level reduce (`⌈log₂ P⌉` + center-mesh over `C`) is the structurally important part. Reduction latency is hidden by other concurrent decode tokens when batched, by the long per-rank sweep for long single-stream context, and by the §4.3 level-pipelining. For short decode prefer a **small `C`** (less inter-CUBE reduction); push `C` up only when context length demands the extra KV-parallelism. ### 5.4 PREFILL, no SP - Whole prompt resident; query is a block of `T_q` tokens (chunked). - Causality is real, per query block `[qs, qe)` vs KV tile `[ks, ke)`: - `ke ≤ qs` → `tile_all_past` → `mask=None`, full compute. - `ks ≥ qe` → `tile_all_future` → **skip** (kernel `if`). - overlap → `tile_partial` → kernel builds a triangular additive mask, the tile op sequence adds it (`Sj + mask_j`). - GQA batches the group's query heads along the same axis as decode. ### 5.5 PREFILL, with SP (Ring KV) — head-parallel, NO reduce This is the **second kernel** (Kernel 2 in the TL;DR), structurally distinct from the decode reduce path (§4). The output `O = [T_q, d]` per head is **big**, so reducing it across ranks would move `[T_q,d]` per rank; instead we **shard the heads** and **move the (also big) KV**, which each head needs in full anyway. > **When ring beats reduce (cost model — the choice is *not* just "O is > big").** Compare **total cross-rank bytes**, head dim `d` factored out: > > - **reduce** ≈ `G·T_q · ⌈log₂(C·P)⌉` — the payload is `(m,ℓ,O)` but **`O` > dominates** (`m,ℓ` are `[G·T_q]` scalars vs `O` = `[G·T_q, d]`), so this > is `O`-bytes × tree hops; head-replicated, so the `G` factor is present. > - **ring** ≈ `2·S` — the **total K+V bytes one CUBE injects** over the > `C−1` rotations (`2·(S/C)·(C−1) ≈ 2·S`); `recv_async` **pipelines** the > rotations so *latency* ≈ the slowest single step, but *traffic* is the > sum. **No `G` factor, no log** — one KV slice is *shared* across all `C` > heads by the rotation. > > So **ring < reduce (by total bytes) when `T_q > 2S / (G·⌈log₂(C·P)⌉)`** — > decode (`T_q=1`) → **reduce**, prefill (`T_q≈S`, RHS `≈ 2/(G·log) ≪ 1`) → > **ring**. KV is big, but the reduce's `O` carries the extra `G·log` factor, > so ring still wins for prefill. (Threshold sweep: §9.) - **Head-parallel placement:** within a CUBE Group, **CUBE `i` owns exactly one query head `i`** (the `G` query heads → the `C=G` CUBEs, one Q head per CUBE) and KV slice `i`. Each CUBE computes **its one Q head's** full attention. Because each CUBE produces a *different* head, there is **no `(m,ℓ,O)` reduce** — each CUBE normalises and writes its own head's rows. - **Ring KV:** the `C` KV slices **rotate** around the CUBE ring; each CUBE folds the incoming block into its head's running `(m,ℓ,O)` (online-softmax, carried across ring steps as Python handles). After `C` steps every head has seen all KV. **GQA reuse comes from the rotation** — slice `j` visits all `C` CUBEs, serving all `G` heads. - IPCQ overlaps the next step's KV receive with the current step's compute via `tl.recv_async`/`tl.wait` (`tl_context.py:543-560` — already exists); receive buffers ping-pong (persistent arena, not recycled). - **Causal ring skip:** if the incoming KV block is entirely *after* this head's query block, skip its compute — eliminates ≈half the steps. - **Within a CUBE (P PEs):** the head's query rows `[T_q, d]` and/or the current KV block tile across the `P` PEs (a query-axis split exists here, unlike decode); details in §B. The (now-removed) baseline already implemented the ring fold; this ADR adds GQA reuse, the head-parallel placement, causal step-skip, and the composite-hybrid inner tile (§3). ### 5.6 Decode CPU-pipelining variants (opt1 / opt3 / opt2) The three decode variants are shown **in full in the TL;DR** (Kernel 1): **opt1** current `CompositeCmd` (has a GEMM-engine bubble while the CPU auto-waits on `Sj`), **opt3** software pipelining (issue the next tile's `Q·Kᵀ` before this tile's softmax, `Sj` in a persistent double buffer — *hides* the bubble subject to scheduler+engine balance, no new command kind), **opt2** `ex_composite` (split into `#1` Q·Kᵀ = existing composite reading K first, `#2` softmax+P·V+ accumulator = the only new flash-epilogue machinery, reading V later). **Recommend:** ship **opt3** now (no new machinery, hides the bubble subject to scheduler+engine balance); revisit **opt2** once the cost model (ADR-0064) makes the fewer-CPU-issues win measurable (§8 item 4). The MATH engine already has max/sum/exp — the only genuinely new part of opt2 is the composite's **stateful `(m,ℓ,O)` accumulator**, not the ops. These variants are a **decode** concern: in prefill (§5.5) the causal `if` is kernel control flow that cannot enter a composite, and the ring already overlaps via `recv_async`. --- ## 6. Why no hardware / composite change is needed - The only place a HW/composite `pop`-as-dependency would help is a lone reduction with no other work to hide a poll — i.e. batch=1 **and** short context. The target is **agentic = low batch, long context** ⇒ each rank has many KV tiles; the §4 reduce's `tl.recv` blocks are covered by the sweep work of concurrent tokens / long context / the §4.3 level-pipeline. - The §4 reduction uses a **static** 2-level tree/mesh, so the recv order is fixed at compile time — no data-dependent pop. `tl.recv` (blocking) suffices. - **Decision: ship with the greenlet `tl.send`/`tl.recv` collective.** Revisit a HW `pop` only if a short-context, single-stream, latency-critical target emerges. --- ## 7. Control vs execution split (the load-bearing principle) | Concern | Owner | |---|---| | tile skip (future), mask generation, causal bounds | **kernel** (Python `if` + arithmetic in greenlet body) | | address / offset / valid-length arithmetic | **kernel** (from counter) | | reduction scheduling, IPCQ send/recv ordering | **kernel** (static 2-level tree/mesh) | | Q·Kᵀ, P·V (incl. per-tile K/V DMA streaming + tiling) | **`tl.composite`** → PE_SCHEDULER | | Q load, mask add, softmax math, running `(m,ℓ,O)` merge | **`tl` ops** on PE engines (kernel-issued) | The kernel decides; the GEMMs are offloaded to the scheduler as composites; the remaining `tl` ops execute already-decided work. This is exactly the greenlet + composite model kernbench already supports — no new control abstraction. --- ## 8. Required kernbench changes **Correction from design iteration:** real GQA (`h_q > h_kv`) needs **no new primitive** — only the kernel restructuring in §5.2 (per KV head, `G` folded into M, byte-conserving reshapes). The supporting ADRs are *efficiency / scale* enablers, not GQA blockers. **Algorithm work in the kernel (no new primitive; existing `tl` API):** - **GQA Q-axis batching** (the reuse lever) — fold `G·T_q` into the matmul M dim per KV head (§5.2); `_view`-style byte-conserving reshape; the GEMM is a `tl.composite(op="gemm")` with M = `G·T_q`. Runs today in both timing and data mode. - **GEMMs via composite** (§1/§3) — Q·Kᵀ and P·V each issued as a non-blocking `tl.composite(op="gemm")`; PE_SCHEDULER tiles them and streams the `tl.ref` K/V operands' DMA (existing `CompositeCmd`; no new command kind). - **2-level reduce-to-root** (§4) replacing the baseline all-to-all fan-out — Level-2 PE tree (intra-CUBE) + Level-1 center-root CUBE-mesh reduce (intra-CUBE-Group, adapting the `lrab_hierarchical_allreduce` inter-CUBE pattern as reduce-only + log-sum-exp), data-driven and level-pipelined, pure kernel control flow over `tl.send`/`tl.recv`. - Causal tile skip + additive boundary mask (§3/§5.4) — kernel `if` + a mask tensor added with `+`. - 2-level contiguous-block KV placement / valid-length arithmetic (§0, §2) — launch-arg arithmetic + `DPPolicy` `row_wise` over both `cube` and `pe`. **New primitives for efficiency / scale (each has a supporting ADR):** 1. **Per-tile scratch recycling** — **ADR-0063** (`tl.scratch_scope`). *Required for scale*: removes the `S=16` ceiling (1 MiB bump allocator) so realistic context lengths run. Highest-value of the three. 2. **Lazy `tl.load`** — **ADR-0062** (non-blocking load + auto-wait on first use; API surface unchanged). *Efficiency*: overlaps explicit loads (the Q group, non-composite kernels) with following compute. The per-tile **K/V** prefetch is handled by the composite scheduler (§1), so this covers the remaining explicit loads. Global semantics change → existing goldens regenerate (ADR-0062 D3). 3. **GQA head / mask broadcast** — **ADR-0061** (`tl.broadcast`). *Optional convenience*, not a GQA blocker (see correction above). Useful for additive-mask construction across the `G·T_q` rows and for general kernels; `np.matmul` already broadcasts in data mode, so it is not needed for correctness. Lowest priority. **Explicitly REJECTED (efficient alternative chosen):** 4. ~~A bespoke "flash-composite" command kind that internalises the whole inner loop — DMA→MM→VEC→DMA→MM→VEC with carried `(m,ℓ,O)` register state and a tail IPCQ push.~~ The two GEMMs **do** use the existing `CompositeCmd` (§1/§3) — that gives scheduler-managed tiling, K/V DMA streaming, and cross-tile pipelining. What is rejected is a **new** command kind that also absorbs the softmax merge + cross-tile register lifetime. **Sizing note (§5.6 opt2):** if revisited, split it into **two** composites — `#1` = Q·Kᵀ (the *existing* composite + `scale`; lets DMA prioritise K), `#2` = softmax + P·V + the online-softmax accumulator merge (the *only* genuinely new machinery: reduction epilogues + a stateful `(m,ℓ,O)` accumulator). MATH engine already has max/sum/exp — the new part is the composite's stateful flash accumulator, not the ops. **Revisit when the cost model (ADR-0064) makes the fewer-CPU-issues win measurable** (§5.6); until then ship §5.6 opt3 (software pipelining, no new cmd). 5. ~~Hardware `pop`-as-dependency.~~ Out of scope (§6). 6. ~~RoPE / QKV projection / KV-cache write inside this kernel.~~ Upstream `qkv_rope` (P1–P5). Folding RoPE in would force re-rotating past tiles every decode step and break Ring Attention's post-RoPE pass-through. --- ## 9. Open tuning items (measured in kernbench, not blocking) 1. **Composite tile-pipeline depth** — dominant for KV-load-bound; how far ahead the kernel issues non-blocking composites before waiting, and the scheduler's per-tile streaming depth. 2. **Reduction topology per level (§4.4)** — Level-2 (intra-CUBE PE) and Level-1 (intra-CUBE-Group CUBE-mesh) each selectable tree/center-mesh (and a ring variant) — **decode reduce only**; prefill uses the §5.5 Ring-KV kernel, not a reduce. Also the decode `C` knob (small `C` for short context where reduction dominates). Ensure each tree pair is a 1-hop physical neighbour; verify against the SFR install. 3. **TILE size** — balance scratch residency (`S/P tiles + O_acc + G-way GQA`) against DMA efficiency; interacts with ADR-0063 and the scheduler's `TILE_M/K/N` (`pe_scheduler.py`). 4. **Ring buffer ping-pong vs `recv_async` depth** in §5.5. 5. **One-shot vs tiled crossover for decode** (§5.2) — the `S_rank` threshold where tiling beats a single composite. 6. **Per-op CPU issue cost (cost model)** — currently `dispatch_cycles=0` (`pe_cpu.py`), so composite-vs-primitive issue overhead is invisible. An op-type-differentiated issue cost (a `tl.composite` descriptor push ≫ a primitive op) is what makes the hybrid's CPU-saturation win **measurable** (§1). Specified in **ADR-0064**; tracked as separate future work. --- ## 10. Coverage summary | Case | Head map | KV strategy | Cross-rank comm | Masking | |---|---|---|---|---| | Decode, no SP | `G` replicated, 1 rank | all KV resident | none | last tile only | | **Decode, SP** | **Q replicated** (all `G` query heads stacked into the GEMM M-dim) | 2-level static shard `C·P` | **§4 2-level reduce** (small `O`) | last tile only | | Prefill, no SP | `G` replicated, 1 rank | resident | none | triangular / skip future | | **Prefill, SP (Ring)** | **1 Q head per CUBE** (`C=G`) | **Ring KV rotate** | **none** (KV blocks move, not `O`) | causal step-skip + boundary | **I/O per case** (full contract §0.5): | Case | Inputs | Output | Cross-rank traffic | |---|---|---|---| | Decode, no SP | `Q[G,1,d]`, full `K/V[S,d]` on 1 rank | `O[G,1,d]` at `O_base` | none | | Decode, SP | `Q[G,1,d]` (replicated), per-rank `K/V[S/(C·P),d]` | `O[G,1,d]` at Group root | `(m,ℓ,O_i)` reduce (small) | | Prefill, no SP | `Q[G,T_q,d]`, `K/V[≤end,d]` | `O[G,T_q,d]` at `O_base` | none | | Prefill, SP (Ring) | `Q[1,T_q,d]` per CUBE, own `K/V[S/C,d]` | `O[1,T_q,d]` per CUBE (distributed) | KV blocks rotate (Ring) | In all cases: KV-cache writes and RoPE happen **upstream**; output projection **downstream**; score `S` and probs `P` are never materialised. --- ## 11. Verification plan (Phase 1 test outline) SPEC/ADR coverage: R5 (PE↔PE IPCQ, PE↔HBM), R2 (latency by traversal), ADR-0023/0025 (IPCQ), ADR-0046 (`tl` contract), ADR-0054 (eval bench). The simulator's contract is **latency by traversal + determinism + structural correctness** (SPEC §0, §0.1), not bit-exact numerics — Phase 2 data exists mainly to exercise the data path, `tl.trans` is reshape-not-transpose, and `bf16` is modelled as `f16`. Verification is therefore **structural/timing-first**, with numeric parity as a bounded secondary check. **Gate type.** *Absolute* latency targets are deferred — they are only meaningful once ADR-0064's cost model lands (`dispatch_cycles=0` today). The gates below are (a) **structural** (op_log shape) and (b) **relative-to- baseline** ratios that *are* testable now and must pass: reduce rounds `⌈log₂P⌉+center-mesh` **vs baseline `C·P−1`**; KV bytes `H_kv·S·d` **vs `H_q·S·d` (G×=8× less)**; causal GEMM count = lower-triangular **vs full grid**; prefill ring traffic = `C` KV rotations **vs** a `[G·T_q,d]` reduce. 1. **Runs in data mode (`enable_data=True`):** the GQA kernel (`h_q = G·h_kv`) completes without the byte-conservation error that the baseline head-packing hits — for all four cases. (This needs the §5.2 restructuring, *not* a new primitive.) **Numeric parity (secondary):** for symmetric/identity inputs where reshape-as-transpose is exact, kernel `O` matches a numpy FlashAttention reference within fp tolerance. Full asymmetric parity is gated on a real `tl.transpose` (out of scope; flagged). 2. **GQA reuse:** with `h_q = G·h_kv`, the K/V `dma_read_count` is independent of `G` (one load per tile, reused across the group), while GEMM work scales with `G`. Asserts the lever actually fires. 3. **SP cross-rank traffic — both kernels:** - *Decode (reduce):* issues `⌈log₂ P⌉` (Level-2, intra-CUBE) + center-mesh-depth-over-`C` (Level-1) reduction rounds — not the baseline's `C·P − 1` all-to-all; op_log `ipcq_send`/`recv` match the static 2-level tree/mesh; result lands at exactly one rank (CUBE-Group root); Level-1 sends use the CUBE NOC, Level-2 the PE IPCQ. - *Prefill (ring):* **no** `(m,ℓ,O)` reduce — instead `C` KV-block rotations (`ipcq_send`/`recv` of K,V per step); each CUBE writes a **distinct** head's `O` in place (no Group root); GQA reuse shows as each KV slice consumed by all `C` heads over the ring. 4. **Causal skip:** prefill skips all `tile_all_future` tiles (and whole future KV blocks in the ring) — GEMM count equals the lower-triangular tile/step count, not the full grid. 5. **Long context (ADR-0063):** a sweep at `S` that overflows 1 MiB without scopes completes and matches the reference. 6. **Load/compute overlap:** end-to-end latency of the tiled sweep is below the serial `Σ(load+compute)` — from the composite scheduler streaming K/V per tile (§1/§3) and lazy `tl.load` (ADR-0062) overlapping the Q load. (Overlap is real modelled concurrency, not a subtraction.) 7. **Composite GEMM offload (structural):** each tile's Q·Kᵀ and P·V emit a `CompositeCmd` (non-blocking) to PE_SCHEDULER, not a blocking `tl.dot`; op_log shows the composite tile plan and the kernel issues the next tile's composites before waiting (cross-tile pipelining). 8. **Determinism:** identical inputs → identical op_log + latency (SPEC §0.1). --- ## B. Open design items from the hybrid pivot (review later) These arose when the decision moved from a pure primitive-op (`tl.dot`) path to the **composite hybrid + lazy `tl.load`** (this revision). None blocks the design; each needs a verification pass during implementation. Recorded here (rather than asked) per the working agreement — the recommendation is my predicted default; revise on review. 1. **DDD-0060 synced (this revision).** The Detailed Design Document has been rewritten to match the two-kernel composite-hybrid + CUBE-Group SP design (file plan, placement, phase plan P1–P8, verification, risks). The ADR remains the authoritative design record; the DDD is the implementation how-to and points back here (and to §B) for rationale. 2. **K operand orientation for the composite GEMM.** Q·Kᵀ needs `b = [d, TILE]`, but the KV cache stores K as `[S_rank, d]`. `tl.trans` is metadata-only and `MemoryStore.read` reshapes, not transposes (`memory_store.py:73`) — so a runtime transpose is wrong for non-trivial data. **Recommend:** store K **pre-transposed** `[d, S_rank]` in the cache (the pseudocode and §3 assume this), making `tl.ref(k_tile, (d, TILE))` a contiguous slice. Verify the upstream `qkv_rope` write layout supports this, or add a real `tl.transpose` (heavier; deferred). 3. **Composite output buffer vs `tl.scratch_scope`.** Each Q·Kᵀ composite writes `Sj` to an `out_addr`; the kernel then reads it for the softmax MATH. That output buffer, and the in-flight composites' targets, must live where the per-tile `scratch_scope` (ADR-0063) will **not** recycle them before they are consumed — same discipline as in-flight lazy loads (ADR-0062 D-Negative). **Recommend:** composite outputs for the *current* tile live in the scoped arena (consumed same iteration); the persistent `(m,ℓ,O)` stays outside. Verify no use-after-recycle when the next tile's composites are issued early (cross-tile pipelining). 4. **GQA `dma_read_count` lever under composite streaming.** The lever (§11.2: K/V `dma_read_count` independent of `G`) assumes the composite emits **one** K/V tile DMA reused across all `G·T_q` M-rows. The scheduler's `generate_gemm_plan` tiles by `TILE_M/K/N` (`pe_scheduler.py:35-37`, 32/64/32) — confirm the M-tiling over `G·T_q` does **not** re-issue the shared K/V tile DMA per M-tile (i.e. operand DMA is shared across M-tiles, or the lever weakens). **Recommend:** assert it in the levers test; if violated, the GQA win is in compute only, not DMA — still correct, but the headline changes. 5. **Kernel TILE vs scheduler `TILE_M/K/N`.** The kernel reasons about a logical KV `TILE`; the scheduler re-tiles internally at fixed `TILE_M/K/N`. Two tiling layers interact (scratch residency, pipeline depth). **Recommend:** treat the kernel TILE as the K/V streaming granularity and let the scheduler sub-tile the GEMM; document the relationship in the DDD and sweep both (§9 items 1, 3). 6. **Cost model is a separate ADR.** The hybrid's CPU-saturation benefit is invisible while `dispatch_cycles=0`. The per-op-type issue-cost model is specified in **ADR-0064**; this ADR's §1/§9 depend on it for the *measurable* (not just structural) win. **Recommend:** land ADR-0064's model before claiming hybrid latency wins in the eval. 7. **Ring path (§5.5) GEMMs.** §5.5 still describes the ring fold with primitive ops + `recv_async`. For consistency the ring's per-step Q·Kᵀ / P·V should also be composites; the IPCQ `recv_async` overlap is orthogonal and stays. **Recommend:** apply the same hybrid shape to the ring step during implementation; low risk, mirrors §3. ### Items from the hierarchical CUBE-Group SP pivot (this revision) 1. **A 4-SIP topology config is needed for full scale.** The shipped `topology.yaml` has `sips: count: 2`; the full `H_kv=8` model at `C=8` needs **4 SIPs** (2 KV heads each, §0). **Recommend:** add a 4-SIP topology config (16-CUBE 4×4 mesh per SIP, 8 PE/CUBE — already the per-SIP shape) for the headline eval; validation-scale runs can use fewer CUBEs/SIPs. The bench must remain single-device per launch (one SIP). 2. **`head_of_cube` / CUBE-Group partition of the 4×4 mesh.** With `C=8`, each SIP's 16-CUBE mesh splits into 2 CUBE Groups of 8. The exact sub-mesh shape (4×2 vs 2×4) sets the Level-1 center-root mesh hop counts and which CUBEs are 1-hop neighbours. **Recommend:** pick the partition that keeps each CUBE Group a contiguous rectangular sub-mesh with a true center CUBE (so `lrab`-style center-root applies); verify against the CUBE NOC routing (ADR-0017). 3. **`C` as a per-operating-point knob.** `C` should differ by case (small for decode where reduction dominates, large for long-context prefill). **Recommend:** expose `C` (and per-level topology, §4.4) as launch/bench config, sweep it in the milestone bench, and report the decode-vs-prefill optimum. Default `C` TBD by measurement. 4. **Reverses the §0 "never spans CUBEs" non-goal — confirm no downstream assumption depends on it.** Earlier text and possibly other ADRs treated intra-CUBE-only reduction as invariant. **Recommend:** grep for that assumption (SFR installs, address policy, diagrams) before implementation; none found in this kernel's scope, but the `configure_sfr_*` neighbour wiring must expose CUBE-NOC `N/S/E/W` for Level-1, not just PE IPCQ. 5. **`valid_len_2level` / contiguous-block correctness.** The two-axis `rank = cube_local·P + pe_local`, block `[rank·B, (rank+1)·B)` placement (§2.1) must tile the sequence with no gaps/overlaps and keep each rank's local buffer dense. **Recommend:** unit-test the index math (every global token maps to exactly one rank; per-rank blocks are contiguous) before the kernel. ### Items from the decode-reduce / prefill-ring split (this revision) 1. **Two kernels, two head mappings.** Decode-SP = head-replicated + static KV shard + 2-level reduce (§4); Prefill-SP = head-parallel (1 Q head/CUBE, `C=G`) + Ring KV + no reduce (§5.5). The principle is *move the smaller thing* — decode's `O` is tiny (reduce it), prefill's `O` is big (move KV instead). **Recommend:** keep them as two kernels; do not re-merge. 2. **Output head distribution differs (downstream impact).** Decode lands all `G` heads at the CUBE-Group root; prefill leaves one Q head per CUBE (distributed). The downstream **out-projection** must consume each layout (gather for decode-root vs in-place per-CUBE for prefill). **Recommend:** pin the O layout per kernel in the `qkv_rope`/`out_proj` contract before implementation (§0.5.4). 3. **Prefill within-CUBE `P` PEs.** §5.5 splits the head's query rows `[T_q, d]` and/or the current KV block across the `P` PEs (a query axis exists, unlike decode). **Recommend:** default to tiling the query rows across PEs (no intra-CUBE reduce needed — disjoint output rows); fall back to KV-block split + intra-CUBE reduce only if `T_q < P`. 4. **`C = G` coupling for prefill.** The head-parallel mapping assumes `C = G = 8` (one Q head per CUBE). If `C ≠ G`, the mapping needs revisiting (multiple heads per CUBE, or heads spanning a partial ring). **Recommend:** fix `C = G` for the prefill kernel at headline scale; treat `C ≠ G` as a separate study. 5. **Reconcile with the prior `_attention_mesh_mlo_2d` impl (now removed).** That 2D kernel was an **AllReduce** over cubes with **Q replicated** — i.e. the decode-reduce family, but all-reduce (broadcast-back) not reduce-to-root, and not yet the prefill head-parallel ring. **Recommend:** (a) move its 2D AllReduce → reduce-to-root (drop broadcast-back) for the decode kernel; (b) add the §5.5 head-parallel Ring-KV kernel for prefill. 6. **Shared KV cache layout (prefill writes, decode reads+extends).** Both kernels share one physical KV cache, so it must use **contiguous `C×P` position blocks** (not round-robin) — prefill's causal skip needs contiguous blocks, and a shared layout avoids a prefill→decode reshard (§2.1). **Recommend:** standardise on the contiguous block layout in the `qkv_rope` write contract; flag that **short-context** decode under-uses ranks under contiguous (acceptable for the long-context target; a short-context balance scheme is a separate study). 7. **Decode CPU-pipelining variant to ship (§5.6).** Three decode variants exist (opt1 current / opt3 software-pipelining / opt2 ex_composite). **Recommend:** implement **opt3** (software pipelining: issue next Q·Kᵀ before this tile's softmax, `Sj` in a persistent double buffer) — hides the GEMM-engine bubble (subject to scheduler+engine balance) with no new command kind. Defer **opt2** (the two-composite `ex_composite`, only `#2` is new) until ADR-0064's cost model makes its fewer-issues win measurable. ### Items from the long/short context split (this revision) The split between the long-context kernels (§5.2 decode, §5.5 prefill — both already specified) and a short-context variant is referenced abstractly in items §B-1 and §B-6 above ("short-context balance is a separate study"). This subsection pins the two open numbers. 1. **Short/long context threshold = 256 K tokens.** Below the threshold, the §5.5 Ring KV prefill pays C-1 ring rotations whose IPCQ cost is not amortised by enough per-rank compute; above it, the per-rank KV sweep dominates and ring is the right choice (§9 line 803). Likewise §5.2's per-rank `S_kv/C·P` shard is small enough at short context that the 2-level reduce-to-root hop count dominates the per-rank compute. The 256 K boundary matches the point at which `S_kv/C·P` (`C=4, P=8 → /32`) crosses the 8 K tokens-per-rank mark above which the per-rank tile sweep (§3 / §B-3 §scratch_scope) becomes the limiting factor rather than collective overhead. **Recommend:** treat 256 K as the bench dispatch threshold; expose it as a launch knob for sweeps. 2. **Short-context kernel design — `kv_per_cube ∈ {1, 2, 4, 8}`.** At short context the §5.5 Ring KV motion is wasted work and the §5.2 cube-SP shard is too thin to feed the engines. The short-context variant therefore drops cube-SP entirely: each CUBE owns `kv_per_cube` *whole* KV heads (no `S_kv` sharding across CUBEs), and the existing PE-SP within a CUBE shards `S_kv` across the `P` PEs for each owned head. For `h_kv = 8` the natural distributions are: | `kv_per_cube` | participating CUBEs | head→CUBE map | |---|---|---| | 1 | `C = 8` | head `i` → CUBE `i` | | 2 | `C = 4` | heads `[2i, 2i+1]` → CUBE `i` | | 4 | `C = 2` | heads `[4i..4i+3]` → CUBE `i` | | 8 | `C = 1` | all heads → single CUBE | No inter-CUBE reduce within a head (each head fully owned by one CUBE), so the kernel runs Level-2 (PE) chain reduce-to-root only; Level-1 (inter-CUBE) collapses to a no-op. The output stays distributed per CUBE (each CUBE writes its owned heads' `O` slice). **Recommend:** ship as a separate kernel file (`_gqa_decode_short.py` / `_gqa_prefill_short.py`) and a separate bench dispatcher that picks short vs long by `S_kv ⋚ 256K`. Keep `kv_per_cube` as a kernel arg so the topology cost trade-off can be measured per workload.