gqa(adr): ADR-0060 hierarchical CUBE-Group SP — 2-level reduce-to-root

Placement pivot (user-approved): a CUBE Group = C CUBEs within one SIP that
jointly own one KV head + its G=8 query heads. KV sequence sharded 2 levels
(Level-1 inter-CUBE over C, Level-2 intra-CUBE PE over P=8 = C*P ranks); G
folded into matmul M. C is a knob (8/4; C=1 = single-CUBE). Reverses the old
'a query head never spans CUBEs' non-goal (held only because the baseline
was H_kv=1). device=SIP; the for-kv loop is gone (head picked by CUBE coord).

Reduction is a 2-level reduce-to-root (not all-reduce): Level-2 PE tree ->
Level-1 center-root CUBE-mesh reduce, adapting lrab_hierarchical_allreduce's
inter-CUBE pattern as reduce-only + log-sum-exp. Data-driven (send on local
P.V completion, no global barrier) + level-pipelined; per-level topology
configurable (tree for decode, ring for long prefill).

Rewrites SS0/2/4/5/0.5/8-11, pseudocode, and adds SSB items (4-SIP config,
mesh partition, C knob, invariant-reversal check, index-math test). KO mirror
updated. Topology grounded in topology.yaml (4x4 CUBE mesh/SIP, 8 PE/cube).
Docs only; no production code changed.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
This commit is contained in:
2026-06-04 17:35:43 -07:00
parent f009ba7b1f
commit a61fed3ce0
2 changed files with 604 additions and 342 deletions
@@ -37,63 +37,66 @@ known algorithms onto the kernbench **greenlet `tl` programming model**
## TL;DR — final GQA kernel (composite hybrid) pseudocode
The decision (§1) in one place: **GEMMs → `tl.composite`; softmax merge +
tree reduction → kernel; `tl.load` is lazy.** Per-KV-head, `G` folded into
the matmul M dim (real GQA, no broadcast). This is the reference shape; the
prose sections elaborate each piece.
2-level reduction → kernel; `tl.load` is lazy.** The KV head is selected by
**CUBE coordinate** (one CUBE Group per head, §0) — **no `for kv` loop**.
`G` is folded into the matmul M dim (real GQA, no broadcast). The KV
sequence is sharded `C × P` ranks (Level-1 inter-CUBE × Level-2 intra-CUBE
PE); the combine is a 2-level reduce-to-root (§4). Reference shape:
```python
def gqa_attention(q_ptr, k_ptr, v_ptr, o_ptr,
counter, start_pe, N, q_block, scale, *, tl):
# ---- geometry (kernel arithmetic, §2) ----
pe_id = tl.program_id(axis=rank_axis)
G = H_q // H_kv # query heads per KV head (=8)
counter, start_pe, q_block, scale, *, tl):
# ---- geometry: this rank within its CUBE Group (§0, §2) ----
cube_id = tl.program_id(axis=1) # which CUBE in the SIP mesh
pe_id = tl.program_id(axis=0) # which PE in the CUBE
kv = head_of_cube(cube_id) # CUBE coord → KV head (no for-kv loop)
C, P = cube_group_size, pes_per_cube # Level-1 × Level-2 SP extents
G = H_q // H_kv # query heads per KV head (=8)
causal = q_block.is_prefill
for kv in range(H_kv): # one KV head per iteration (§5.2)
# Q group: G rows folded into M → [G·T_q, d]. Lazy load (ADR-0062):
# issue now, auto-wait at first use inside the first composite.
q_g = tl.load(q_base(kv), (G * q_block.T_q, d)) # [G·T_q, d]
my_len = valid_len(counter, start_pe, pe_id, N) if not causal else S_kv
n_tiles = ceil(my_len / TILE)
# Q group: G rows folded into M → [G·T_q, d]. Lazy load (ADR-0062).
q_g = tl.load(q_base(kv), (G * q_block.T_q, d)) # [G·T_q, d]
my_len = valid_len_2level(counter, start_pe, cube_id, pe_id, C, P) \
if not causal else S_kv_local
n_tiles = ceil(my_len / TILE)
# persistent arena (outside scratch_scope, ADR-0063): -inf, 0, zeros
m, l, O = init_running(G * q_block.T_q, d)
# persistent arena (outside scratch_scope, ADR-0063): -inf, 0, zeros
m, l, O = init_running(G * q_block.T_q, d)
for j in range(n_tiles):
if causal and tile_all_future(j, q_block):
continue # causal skip (kernel if)
with tl.scratch_scope(): # per-tile temporaries (ADR-0063)
# --- GEMM #1 on the scheduler: Q·Kⱼᵀ; K streamed by composite ---
Sj = tl.composite("gemm", a=q_g,
b=tl.ref(k_tile(kv, j), (d, TILE))) * scale # Kᵀ pre-stored [d,TILE]
if causal and tile_partial(j, q_block):
Sj = Sj + causal_mask(j, q_block) # additive boundary mask
# --- online softmax merge in the kernel (MATH ops) ---
m_new = tl.maximum(m, tl.max(Sj, axis=-1))
P = tl.exp(Sj - m_new)
corr = tl.exp(m - m_new)
l = l * corr + tl.sum(P, axis=-1)
# --- GEMM #2 on the scheduler: P·Vⱼ; V streamed by composite ---
Oj = tl.composite("gemm", a=P,
b=tl.ref(v_tile(kv, j), (TILE, d)))
O = O * corr + Oj # running merge
m = m_new
for j in range(n_tiles):
if causal and tile_all_future(j, q_block):
continue # causal skip (kernel if)
with tl.scratch_scope(): # per-tile temporaries (ADR-0063)
# --- GEMM #1 on the scheduler: Q·Kⱼᵀ; K streamed by composite ---
Sj = tl.composite("gemm", a=q_g,
b=tl.ref(k_tile(kv, j), (d, TILE))) * scale # Kᵀ pre-stored [d,TILE]
if causal and tile_partial(j, q_block):
Sj = Sj + causal_mask(j, q_block) # additive boundary mask
# --- online softmax merge in the kernel (MATH ops) ---
m_new = tl.maximum(m, tl.max(Sj, axis=-1))
P = tl.exp(Sj - m_new)
corr = tl.exp(m - m_new)
l = l * corr + tl.sum(P, axis=-1)
# --- GEMM #2 on the scheduler: P·Vⱼ; V streamed by composite ---
Oj = tl.composite("gemm", a=P,
b=tl.ref(v_tile(kv, j), (TILE, d)))
O = O * corr + Oj # running merge
m = m_new
# ---- cross-PE combine (§4): log-sum-exp tree to root, or store ----
if N == 1:
tl.store(o_base(kv), O / l)
else:
tree_reduce_and_store(m, l, O, pe_id, N, o_base(kv)) # tl.send/tl.recv
# ---- 2-level combine to the CUBE Group root (§4); data-driven, no barrier ----
hierarchical_reduce_and_store(m, l, O, cube_id, pe_id, C, P, o_base(kv))
```
> **Why this shape:** the two `tl.composite` calls offload tiling + K/V DMA
> streaming + cross-tile pipelining to PE_SCHEDULER (CPU issues coarse
> descriptors and runs ahead → engines stay saturated, §1); the softmax
> merge and the IPCQ tree reduction stay in the kernel because the existing
> `CompositeCmd` cannot carry cross-tile state. `K` is pre-stored
> transposed `[d, TILE]` to sidestep the reshape-not-transpose caveat
> (§3, §B). A bespoke "flash-composite" command kind is **not** introduced
> (§8 item 4).
> merge and the IPCQ reduction stay in the kernel because the existing
> `CompositeCmd` cannot carry cross-tile state. The reduction is **2-level**
> (Level-2 PE tree within a CUBE → Level-1 CUBE-mesh reduce within the CUBE
> Group), both reduce-to-root, log-sum-exp, sent as each rank finishes its
> local sweep (§4). `K` is pre-stored transposed `[d, TILE]` to sidestep the
> reshape-not-transpose caveat (§3, §B). A bespoke "flash-composite" command
> kind is **not** introduced (§8 item 4).
---
@@ -136,8 +139,9 @@ GEMMs onto the scheduler-managed `tl.composite` path** (see §1) — this
(`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 **tree
reduction** to root is `⌈log₂ N⌉` steps (§4).
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
(`test_milestone_gqa_llama70b.py:123-148`) and there is no causal
@@ -180,20 +184,48 @@ Hardware recap:
**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).
- **Allocation policy (SP):** one query head per CUBE in the multi-user
panels; the `G` query heads of a KV group map within a CUBE's PEs.
**Two orthogonal mapping layers** (round-robin placement):
- **Layer 1 (KV-parallel, intra-request):** KV token `i` lands on PE
`(start_pe + i) mod N` — round-robin so one long request is split
across `N` PEs, balanced to ≤1 token.
- **Layer 2 (inter-request):** `start_pe = request_id mod N` rotates the
"PE-0 role" per request.
- Combined: `pe = (request_id + global_token_idx) mod N`.
### CUBE Group — the placement unit (hierarchical SP)
`N` = number of PEs in the KV-parallel reduction group for one
(query head, request). Reduction stays **intra-CUBE** (a query head never
spans CUBEs — explicit non-goal).
**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 the KV-parallel reduction group for one (KV head, request) is **`C × P`
ranks**, all within one SIP. The `G` query heads are folded into the
matmul M dim (replicated across all ranks). `C` is a **tuning knob**
(e.g. 8 or 4): large `C` for long-context prefill, small `C` (→ 1 = a
single CUBE, intra-CUBE SP only) for short decode 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 (round-robin SP, balanced
to ≤1 token): KV token `i` lands on Level-1 rank `(start + i) mod C`, then
Level-2 rank `((i // C) + start_pe) mod P` — a hierarchical round-robin so
each of the `C × P` ranks owns a dense, contiguous local slice.
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).
---
@@ -220,27 +252,28 @@ spans CUBEs — explicit non-goal).
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 = local_slot·N + ((pe_id start_pe) mod N)`
(§2.1). Round-robin placement ≠ RoPE position.
position** `global_idx = local_slot·(C·P) + rank` where `rank =
cube_local·P + pe_local` (§2.1). Round-robin placement ≠ RoPE position.
### 0.5.2 Shape symbols
`T_q` = query length this launch (decode: 1; prefill/chunk: chunk width).
`S` = total context length. `S_pe` = keys owned by this PE ≈ `⌈S/N⌉`.
Storage `bf16` (numpy proxy `f16`, `memory_store.py:16`); `m,,O`
accumulators `f32` where precision matters.
`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,,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-PE HBM (loaded to TCM) | post-RoPE (P1). `G` query rows of the group batched. |
| `K_cache` | `[S_pe, d]` | per-PE HBM, base `K_base[pe]`, contiguous | post-RoPE (P2). Read-only. Dense locally, strided in global index (§2.1). |
| `V_cache` | `[S_pe, d]` | per-PE HBM, base `V_base[pe]` | raw V (P4). Read-only. |
| `global_token_counter` | scalar | launch arg | kernel derives `S_pe`, slot↔global, causal bounds. |
| `start_pe` (= `request_id mod N`) | scalar | launch arg | Layer-2 rotation. |
| `pe_id`, `N` | scalars | launch / `tl.program_id` | reduction-group geometry. |
| `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. Dense locally, strided by `C·P` in global index (§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 (root PE only). |
| `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,
@@ -251,14 +284,15 @@ V_block` via IPCQ into ping-pong buffers (post-RoPE), plus
| Output | Shape | Location | Notes |
|---|---|---|---|
| `O` (final) | `[G, T_q, d]` | `O_base`, **root PE only** | normalised `O_acc / _acc`, cast to storage dtype. |
| `O` (final) | `[G, T_q, d]` | `O_base`, **CUBE-Group root only** | normalised `O_acc / _acc`, cast to storage dtype. |
**Intermediate (non-root PE, on IPCQ — not a kernel-visible output):**
**Intermediate (non-root rank, on IPCQ — not a kernel-visible output):**
`(m_i, _i, O_i)` (`m,`: `[G, T_q]`; `O_i`: `[G, T_q, d]` unnormalised)
pushed to `tree_parent` via `tl.send` (§4). `O_i` is the heavy part.
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.
**No-SP (`N=1`):** no IPCQ partials; the single PE's running `(m,,O)` is
normalised in place and written to `O_base`.
**No-SP (`C=P=1`):** no IPCQ partials; the single rank's running `(m,,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).
@@ -278,7 +312,7 @@ 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-PE tile sweep) and the scheduler generates the tile plan and streams
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
@@ -348,16 +382,24 @@ permits (`kernel_runner.py`, ADR-0020 D3).
## 2. Memory layout & driver responsibilities
### 2.1 KV cache allocation
- Per-PE KV buffers sized to per-PE max context `⌈max_context / N⌉ × d ×
dtype`, for K and V separately. In kernbench these are deployed with a
`DPPolicy` whose `pe` (or `cube`) axis is `row_wise` over the sequence
dimension (`policy/placement/dp.py`; the baseline uses
`DPPolicy(pe="row_wise")` for K/V and `replicate` for Q).
- Within a PE, assigned tokens are **appended contiguously** (slot
0,1,2,…). Global indices are strided (`i, i+N, …`) but the per-PE
buffer is dense ⇒ DMA stays contiguous.
- Slot → global: `global_idx = local_slot·N + ((pe_id start_pe) mod N)`.
### 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.
- Within a rank, assigned tokens are **appended contiguously** (slot
0,1,2,…); the per-rank buffer is dense ⇒ DMA stays contiguous, even
though global indices are strided by `C·P`.
- Slot → global (hierarchical round-robin): `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 = local_slot·(C·P) + rank`.
### 2.2 Driver per-launch duties (minimal)
The driver supplies, per launch, the bases + counter + rotation; the
@@ -365,23 +407,26 @@ kernel derives the rest:
| Launch arg | Purpose |
|---|---|
| `K_base[pe]`, `V_base[pe]` | per-PE KV buffer bases (from tensor VA) |
| `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_pe = request_id mod N` | Layer-2 rotation |
| `pe_id` (`tl.program_id`), `N` | geometry |
| `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 |
Kernel-derived (plain arithmetic):
- **my turn to write this step:** `(start_pe + counter) mod N == pe_id`
- **my valid length:** `base = counter // N; rem = counter % N;
my_len = base + (1 if ((pe_id start_pe) mod N) < rem else 0)`
Let `R = C·P`, `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):
- **my turn to write this step:** `(start_rank + counter) mod R == rank`
- **my valid length:** `base = counter // R; rem = counter % R;
my_len = base + (1 if rank < rem else 0)`
- **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 single formula
`(request_id + token_idx) mod N` is the entire placement policy.
`(request_id + token_idx) mod (C·P)` over the two SP axes is the entire
placement policy.
---
@@ -440,84 +485,124 @@ Notes:
---
## 4. Reduction (KV-parallel / SP combine) — tree to root
## 4. Reduction (KV-parallel / SP combine) — 2-level reduce-to-root
After its tile sweep each PE holds `(m_i, _i, O_i)` (unnormalised).
Combine via the associative/commutative log-sum-exp merge (identical math
to the baseline's fold, `_attention_mesh_mlo.py:117-122`):
After its tile sweep each rank holds `(m_i, _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, `_attention_mesh_mlo.py:117-122`):
```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 tree root
# final: O = O_root / l_root # normalise once at the CUBE-Group root
```
- **Timing:** exchange is **after P·V** (each PE has its final `O_i`).
- **Topology:** mesh tree, depth `⌈log₂ N⌉`, over physical neighbours.
For `N=8`: level-0 `(0↔1,2↔3,4↔5,6↔7)`, level-1 `(1↔3,5↔7)`, level-2
`(3↔7)`, root = `7`. Each tree pair must be a physical `N/S/E/W`
neighbour so `tl.send(dir)`/`tl.recv(dir)` use a real link
(tuning item §9; the SFR install that wires neighbours is
`configure_sfr_intracube_pe_ring`, used by the baseline).
- **Why a tree, not the baseline fan-out:** attention needs `O` at one
place (the PE that writes `O_base`). A tree is `⌈log₂ N⌉` steps
(3 for `N=8`) vs the baseline all-to-all's `N1` (7). For decode, where
the per-PE sweep is short, the reduction is the dominant cost, so this
is a real win. (The baseline's fan-out replicates the answer to all
ranks — unnecessary here.)
- **Payload:** `O_i` (`d`-vector) is heavy; `m,` are scalars per `(g,
T_q)`. Sent as separate `tl.send`s (the baseline sends the triplet as
three sends — same pattern).
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**:
Kernel structure (greenlet):
### 4.1 Level-2 — intra-CUBE (P PEs → CUBE root PE)
- A **reduce-to-root tree** over the `P` PEs of a CUBE, 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 12: row-then-col converge at
the center CUBE)** — but **reduce-only** (drop its broadcast-back Phases
45; 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 (`R1` 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** option (chunked `O`) suits bandwidth-bound
long-context prefill with large `T_q·d` payload. `C=1` degenerates to
Level-2 only (single-CUBE SP).
**Payload:** `O_i` (`[G·T_q, d]`) is heavy; `m,` are light. Sent as
separate `tl.send`s (baseline pattern).
Kernel structure (greenlet), both levels reuse `merge`:
```python
# leaf / internal node: fold children that send to me, then forward up
for child_dir in tree_children_dirs(pe_id, N):
m_c = tl.recv(child_dir, m.shape); l_c = tl.recv(child_dir, l.shape)
O_c = tl.recv(child_dir, O.shape)
m, l, O = merge(m, l, O, m_c, l_c, O_c)
if not is_root(pe_id):
tl.send(parent_dir(pe_id), m); tl.send(parent_dir(pe_id), l); tl.send(parent_dir(pe_id), O)
else:
tl.store(O_base, O / l)
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)
```
`tl.recv` blocks until data arrives (`tl_context.py:446-499`); the merge
order is fixed by the static tree, so no data-dependent `pop` is needed —
which is why **no hardware/composite `pop`-as-dependency change is
required** (§6).
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 four cases share §3 (tile sweep) + §4 (reduction); they differ only
in `N`, query-block width, and which `tile_*` predicates fire.
in the SP extents `C·P`, query-block width, and which `tile_*` predicates
fire.
### 5.1 Common skeleton
```python
def attn_kernel(q_ptr, k_ptr, v_ptr, o_ptr, counter, start_pe, N,
q_block, softmax_scale, *, tl):
pe_id = tl.program_id(axis=rank_axis)
my_len = valid_len(counter, start_pe, pe_id, N)
def attn_kernel(q_ptr, k_ptr, v_ptr, o_ptr, counter, start_pe, start_cube,
C, P, q_block, softmax_scale, *, tl):
cube_id = tl.program_id(axis=1); pe_id = tl.program_id(axis=0)
kv = head_of_cube(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) # [G·T_q, d]; lazy tl.load, G folded into M (no broadcast)
q_g = load_Q_group(q_ptr, kv) # [G·T_q, d]; lazy tl.load, G folded into M (no broadcast)
m, l, O = init_running() # persistent arena: -inf, 0, zeros
for j in range(n_tiles): # K/V streamed per tile by the composite scheduler (§3)
if tile_all_future(j, q_block): # causal skip (kernel if)
continue
run_tile(j, mask_or_null(j, q_block)) # §3: 2 composites + softmax MATH, in tl.scratch_scope
if N == 1:
tl.store(o_ptr, O / l) # no reduction
if C == 1 and P == 1:
tl.store(o_base(kv), O / l) # no reduction (single rank)
else:
tree_reduce_and_store(pe_id, N, o_ptr) # §4
hierarchical_reduce_and_store(m, l, O, cube_id, pe_id, C, P, o_base(kv)) # §4
```
### 5.2 DECODE, no SP (`N=1`, one PE owns the head's KV)
### 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`
@@ -530,19 +615,25 @@ def attn_kernel(q_ptr, k_ptr, v_ptr, o_ptr, counter, start_pe, N,
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_pe` fits in scratch (small/medium context) this degenerates to a
- 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 `_attention_mesh_mlo`
`_partial_attention`, just GQA-batched and on the composite path. Tiling
(§3) only kicks in when `S_pe` exceeds the scratch scope's tile budget.
(§3) only kicks in when `S_rank` exceeds the scratch scope's tile budget.
### 5.3 DECODE, with SP / KV-parallel (`N=8`)
- One request's KV is round-robin across 8 PEs; each owns ≈`my_len`
tokens. Each PE GQA-batches its `G=8` query rows over its local tiles.
- `T_q=1` ⇒ short per-PE sweep ⇒ **reduction dominates** ⇒ the §4 tree
(3 steps) is the structurally important part. Reduction latency is
hidden by other concurrent decode tokens when batched, or by the long
per-PE tile sweep for long single-stream context.
### 5.3 DECODE, with SP / KV-parallel (`C × P` ranks)
- One request's KV is hierarchical-round-robin across the `C·P` ranks of
the CUBE Group (Level-1 over `C` CUBEs, Level-2 over `P` PEs); each rank
owns ≈`my_len` tokens 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).
@@ -554,17 +645,21 @@ def attn_kernel(q_ptr, k_ptr, v_ptr, o_ptr, counter, start_pe, N,
- GQA batches the group's query heads along the same axis as decode.
### 5.5 PREFILL, with SP (Ring KV)
- KV sharded across `N` PEs (the ring); each step delivers a peer's KV
block over IPCQ. Running `(m,,O)` is carried **across ring steps**
(Python handles, exactly as `_attention_mesh_kv` does today).
- KV sharded across the `C·P` ranks in **ring order**; each step delivers a
peer's KV block over IPCQ. Running `(m,,O)` is carried **across ring
steps** (Python handles, exactly as `_attention_mesh_kv` does today). The
ring is the long-context, bandwidth-bound case where §4.4's **ring**
collective option (not the tree) is the natural choice.
- IPCQ overlaps next step's KV receive with current step's compute via
`tl.recv_async`/`tl.wait` (`tl_context.py:543-560` — already exists).
- **Causal ring skip:** if the incoming step's KV block is entirely
*after* the local query block, skip its compute (don't recv-consume /
don't fold) — eliminates ≈half the steps for causal attention.
- Receive buffers ping-pong (persistent arena, not recycled).
- After the ring, `(m,,O)` is final per query-owning PE; if KV-parallel
splits remain, §4 tree-merges them, then normalise + store.
- After the ring, `(m,,O)` is final per rank; remaining KV-parallel splits
combine via the §4 2-level reduce, then normalise + store at the Group
root.
The baseline `_attention_mesh_kv` already implements the ring fold; this
ADR adds GQA reuse, causal step-skip, and `recv_async` overlap.
@@ -575,11 +670,12 @@ ADR adds GQA reuse, causal step-skip, and `recv_async` overlap.
- 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 PE
has many KV tiles; the §4 tree's `tl.recv` blocks are covered by the
sweep work of concurrent tokens / long context.
- The §4 reduction uses a **static** tree, so the recv order is fixed at
compile time — no data-dependent pop. `tl.recv` (blocking) suffices.
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.
@@ -592,7 +688,7 @@ ADR adds GQA reuse, causal step-skip, and `recv_async` overlap.
|---|---|
| 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 tree) |
| 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,,O)` merge | **`tl` ops** on PE engines (kernel-issued) |
@@ -620,12 +716,15 @@ new primitive** — only the kernel restructuring in §5.2 (per KV head,
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).
- Tree reduction to root (§4) replacing the baseline all-to-all fan-out
- **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 `+`.
- Round-robin KV placement / valid-length arithmetic (§2) — launch-arg
arithmetic + `DPPolicy(pe="row_wise")`.
- 2-level round-robin 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):**
@@ -669,14 +768,17 @@ new primitive** — only the kernel restructuring in §5.2 (per KV head,
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. **PE↔mesh-neighbour mapping for the reduction tree** — ensure each
depth-`⌈log₂ N⌉` pair is a physical `N/S/E/W` neighbour; bad mapping
adds hops. Verify against the SFR install.
2. **Reduction topology per level (§4.4)** — Level-2 (intra-CUBE PE) and
Level-1 (intra-CUBE-Group CUBE-mesh) each selectable tree/ring/center-mesh;
sweep tree (latency, small-`O` decode) vs ring (bandwidth, large-`O`
prefill). Also the CUBE-Group size `C` knob (small for decode, large for
long context). 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_pe`
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.
@@ -691,19 +793,19 @@ new primitive** — only the kernel restructuring in §5.2 (per KV head,
| Case | KV placement | Inner loop | Reduction | Masking |
|---|---|---|---|---|
| Decode, no SP | 1 PE, all KV | one-shot or tiled, GQA-batched | none | last tile only |
| Decode, SP | round-robin `N` PEs | tiled, GQA-batched | §4 tree (`⌈log₂ N⌉`) | last tile only |
| Decode, no SP | 1 rank (`C=P=1`), all KV | one-shot or tiled, GQA-batched | none | last tile only |
| Decode, SP | 2-level RR over `C·P` ranks | tiled, GQA-batched | §4 2-level (`⌈log₂P⌉`+mesh over `C`) | last tile only |
| Prefill, no SP | resident | tiled per q-block | none | skip future / triangular boundary |
| Prefill, SP (Ring) | ring-sharded | per ring step (recv_async overlap) | running state + §4 tree | causal step-skip + boundary |
| Prefill, SP (Ring) | ring over `C·P` ranks | per ring step (recv_async overlap) | running state + §4 2-level | causal step-skip + boundary |
**I/O per case** (full contract §0.5):
| Case | Inputs | Output | IPCQ partials |
|---|---|---|---|
| Decode, no SP | `Q[G,1,d]`, full `K/V[S,d]` on 1 PE | `O[G,1,d]` at `O_base` | none |
| Decode, SP | `Q[G,1,d]`, per-PE `K/V[S_pe,d]` | `O[G,1,d]` (root) | `(m,,O_i)` per PE → tree |
| 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]`, per-rank `K/V[S/(C·P),d]` | `O[G,1,d]` (Group root) | `(m,,O_i)` per rank → 2-level |
| 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[G,T_q,d]`, ring-delivered `K/V` blocks | `O[G,T_q,d]` (root) | running `(m,,O)` + tree |
| Prefill, SP (Ring) | `Q[G,T_q,d]`, ring-delivered `K/V` blocks | `O[G,T_q,d]` (Group root) | running `(m,,O)` + 2-level |
In all cases: KV-cache writes and RoPE happen **upstream**; output
projection **downstream**; score `S` and probs `P` are never materialised.
@@ -733,8 +835,12 @@ secondary check.
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. **Tree reduction step count:** decode-SP issues `⌈log₂ N` reduction
rounds (not `N1`); op_log `ipcq_send`/`recv` counts match the tree.
3. **2-level reduction step count:** decode-SP 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` counts
match the static 2-level tree/mesh, and the result lands at exactly one
rank (CUBE-Group root). A separate assertion checks Level-1 sends use the
CUBE NOC and Level-2 the PE IPCQ.
4. **Causal skip:** prefill skips all `tile_all_future` tiles — GEMM
count equals the lower-triangular tile count, not the full grid.
5. **Long context (ADR-0063):** a sweep at `S` that overflows 1 MiB
@@ -769,10 +875,10 @@ predicted default; revise on review.
implementation starts.
2. **K operand orientation for the composite GEMM.** Q·Kᵀ needs `b =
[d, TILE]`, but the KV cache stores K as `[S_pe, d]`. `tl.trans` is
[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_pe]` in the cache
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).
@@ -815,3 +921,39 @@ predicted default; revise on review.
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` / hierarchical round-robin correctness.** The
two-axis `(cube_local·P + pe_local)` 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 slices are contiguous) before the kernel.