kernbench2/docs/adr-proposed/ADR-XXXX-gqa-fused-attention-ahbm.md

# ADR-001: 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; SP (Ring KV) for long-context prefill.

**Algorithm lineage.** This kernel is **FlashAttention** (tiling + online/streaming softmax with fused P·V — no full score matrix materialized). The KV-parallel split-and-combine in §4 is **FlashDecoding** (split-KV with log-sum-exp merge). The SP path in §5.5 is **Ring Attention** (block-wise KV rotated around the ring, accumulated by the same online softmax). No new math is introduced; this ADR maps those known algorithms onto AHBM composite commands + IPCQ.

---

## 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**.
- **IPCQ**: PE↔PE queues. Each PE holds 4 neighbor queue-pairs (one per mesh direction).
- **Composite command**: a fused multi-stage command (load → matmul → vector op → ...) executed as one unit. *Cannot* express a data-dependent `pop` as an internal dependency (see §7). It *can* take a precomputed mask tile as an input and apply it as a stage.
- **Allocation policy (SP):** one query head per CUBE. For GQA-8, one KV head's 8 query heads map to 8 CUBEs.

**Two orthogonal mapping layers** (decided in design discussion):
- **Layer 1 (KV-parallel, intra-request):** within a request, KV token `i` lands on PE `(start_pe + i) mod N` — round-robin so a single long request is split across `N` PEs and all PEs stay balanced (chunk length differs by ≤1 token).
- **Layer 2 (inter-request):** `start_pe = request_id mod N` rotates the "PE-0 role" per request to spread write/start load.
- Combined destination PE for a token: `pe = (request_id + global_token_idx) mod N`.

Here `N` = number of PEs participating in the KV-parallel reduction group for one (query head, request). Within a CUBE the reduction group is the set of PEs splitting that head's sequence; reduction stays **intra-CUBE** (query head never spans CUBEs — explicit non-goal).

---

## 0.5 Kernel boundary, preconditions, and I/O contract

### 0.5.1 Where this kernel sits 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, post-RoPE K-cache, V-cache → O)
6. Output projection (GEMM)        out_proj kernel (SEPARATE, downstream)
7. residual add → FFN ...
```

**Preconditions (responsibilities of the upstream `qkv_rope` kernel, NOT this kernel):**
- **P1.** Q is already RoPE-rotated. This kernel does **no** rotation on Q.
- **P2.** K-cache stores **post-RoPE** K. Past tiles are never re-rotated at attention time (this is 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.** For prefill, the whole query block's K is post-RoPE in cache. ⇒ this kernel is **pure read** on the KV cache; it never writes KV.
- **P4.** V is **not** rotated (RoPE applies to Q,K only). V-cache holds raw projected V.
- **P5.** RoPE position used upstream is the token's **absolute global position**, i.e. `global_idx = local_slot*N + ((pe_id - start_pe) mod N)` (§2.1). Round-robin placement must not be confused with RoPE position — the angle depends on global index, never on the local slot.

(If a fused megakernel is ever desired, stages 2–4 would prepend to §5.1; the chosen design keeps them separate so KV cache is the clean interface and Ring Attention only ever passes post-RoPE tensors.)

### 0.5.2 Symbols for shapes
`T_q` = query length this launch (decode: 1; prefill/chunk: chunk width). `S` = total context length (keys seen). `S_pe` = keys owned by this PE = `valid_len` (§2.2), `≈ ceil(S/N)`. `bf16` storage, `fp32` for `m,l,O` accumulators.

### 0.5.3 INPUTS (per kernel launch)

| Input | Shape (per head) | Layout / location | Notes |
|---|---|---|---|
| `Q` | `[G, T_q, d]` | on-chip regs/SRAM of the PE | post-RoPE (P1). `G=8` query rows of the GQA group batched together. |
| `K_cache` | `[S_pe, d]` | per-PE HBM buffer, **contiguous**, base = `K_base[pe]` | post-RoPE (P2). Read-only. Strided in global index, dense locally (§2.1). |
| `V_cache` | `[S_pe, d]` | per-PE HBM buffer, 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` | scalar = `request_id mod N` | launch arg | Layer-2 rotation. |
| `pe_id`, `N` | scalars | known to PE / launch | reduction-group geometry. |
| `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). |
| `softmax_scale` | scalar | launch arg | `1/sqrt(d)` (=1/√128). |

For **Ring Attention (§5.5)** add: incoming `K_block, V_block` per ring step arrive via IPCQ/comms into ping-pong receive buffers (post-RoPE), plus `step_kv_global_range` so the kernel can apply the causal step-skip.

### 0.5.4 OUTPUTS

| Output | Shape (per head) | Location | Notes |
|---|---|---|---|
| `O` (final) | `[G, T_q, d]` | `O_base`, **written by tree-root PE only** | normalized: `O_acc / l_acc`. fp32→bf16 cast on store. |

**Intermediate (per non-root PE, on IPCQ, not a kernel-visible output):**

| Partial | Shape | Channel | Notes |
|---|---|---|---|
| `(m_i, l_i, O_i)` | `m,l`: `[G, T_q]` scalars; `O_i`: `[G, T_q, d]` unnormalized | pushed to `tree_parent` via neighbor IPCQ | log-sum-exp merge payload (§4). `O_i` is the heavy part. |

**No-SP cases (`N=1`):** there are no IPCQ partials; the single PE's running `(m,l,O)` is normalized in place and written to `O_base`. The kernel's only output is `O`.

**Explicitly NOT outputs of this kernel:** KV cache writes (done upstream, P3), output projection (downstream stage 6), the score matrix `S` and probabilities `P` (never materialized — FlashAttention).

---

## 1. Decision

Fuse the attention inner pipeline into a single composite per KV tile:

```
K_j load → Q·Kjᵀ → (+ mask stage) → online-softmax update → V_j load → P·V → running (m,l,O) update → downstream IPCQ push
```

Cross-PE combination (KV-parallel / SP) is a **log-sum-exp tree reduction** over `(m, l, O)` performed **after P·V**, flowed through IPCQ with a **kernel-driven async-submit + bounded-polling loop** (no hardware `pop`-as-dependency change required for the target workload).

Control flow (tile skip, mask generation, reduction scheduling, address arithmetic) lives in the **kernel**; the **composite** only executes already-decided work.

---

## 2. Memory layout & driver responsibilities

### 2.1 KV cache allocation
- Pre-allocate per-PE KV buffers sized to **per-PE max context** = `ceil(max_context / N)` tokens × `d` × dtype, for K and V separately.
- Within a PE, tokens assigned to it are **appended contiguously** (slot 0,1,2,...). Even though global indices are strided (`i, i+N, i+2N, ...`), the per-PE buffer is dense ⇒ DMA stays contiguous, bandwidth not fragmented.
- Slot → global index is implicit: `global_idx = local_slot * N + ((pe_id - start_pe) mod N)`.

### 2.2 Driver per-step duties (kept minimal)
The driver does **not** compute write slots or read ranges. It supplies, per kernel launch:

| Launch arg | Purpose |
|---|---|
| `K_base[pe]`, `V_base[pe]` | base address of each PE's KV buffer |
| `O_base` | attention output destination (separate from KV write) |
| `global_token_counter` | current sequence position; kernel derives everything from it |
| `start_pe` (= `request_id mod N`) | Layer-2 rotation |
| `pe_id` | known to PE; used with counter for `mod`/`div` |
| `q_block_meta` | for prefill/SP: query block start + length |

From `global_token_counter`, `start_pe`, `pe_id` the kernel derives:
- **"is it 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 + ( ((pe_id - start_pe) mod N) < rem ? 1 : 0 )`
- **write offset:** `my_len` (next free slot) — kernel computes `K_base[pe] + my_len*d`.
- **read range:** tiles `0 .. ceil(my_len / TILE)`.
- **causal bounds & per-tile skip:** from global positions of query block vs each tile.

Driver = address bases + counter + rotation. One formula (`(request_id + token_idx) mod N`) is the entire placement policy.

---

## 3. Composite structure

One composite instance = one KV tile's worth of work on one PE.

```
COMPOSITE attn_tile(q_reg, K_base, V_base, tile_idx, mask_tile_or_null,
                    m_reg, l_reg, O_reg, push_target):
  S1: DMA  K_tile  ← K_base + tile_idx*TILE*d          # contiguous load
  S2: MM   S = q_reg · K_tileᵀ            (scale 1/sqrt(d))
  S3: VEC  if mask_tile != null: S += mask_tile        # masked boundary tile
  S4: VEC  online softmax:
             m_new = max(m_reg, rowmax(S))
             P     = exp(S - m_new)
             l_reg = l_reg*exp(m_reg - m_new) + rowsum(P)
             O_reg = O_reg*exp(m_reg - m_new)          # rescale accumulator
             m_reg = m_new
  S5: DMA  V_tile  ← V_base + tile_idx*TILE*d          # issued early, hidden behind S2-S4
  S6: MM   O_reg += P · V_tile
  S7: (tail) PUSH (m_reg,l_reg,O_reg) → push_target    # only on reduction-producing composite
```

Notes:
- `m_reg, l_reg, O_reg` are **carried across composites** (running state), so consecutive tile composites form an in-order chain on one PE.
- S5 (V load) is scheduled so its latency overlaps S2–S4; with prefetch depth ≥ 2 the next tile's K/V are already in flight.
- S7 push is only on the **last** composite of a PE's tile sweep (when its `O_local` is final). Push is a tail *action*, not a dependency — composites can express push, not pop.
- Mask handling: composite only **applies** a mask tile it is *given*. The kernel generates the boundary-tile mask from query/KV offsets and passes it in. Full-past tiles get `null`; full-future tiles are never enqueued (skipped in kernel).

---

## 4. Reduction (KV-parallel / SP combine)

After every PE finishes its tile sweep it holds `(m_i, l_i, O_i)` (unnormalized). Combine via associative/commutative log-sum-exp merge:

```
merge((m_a,l_a,O_a),(m_b,l_b,O_b)):
  m = max(m_a,m_b)
  l = l_a*exp(m_a-m) + l_b*exp(m_b-m)
  O = O_a*exp(m_a-m) + O_b*exp(m_b-m)
  return (m,l,O)
final O = O_root / l_root      # normalize once at tree root
```

- **Timing: exchange is AFTER P·V** (each PE must finish its `O_local`).
- **Topology:** mesh tree, depth `ceil(log2(N))`. For `N=8`: level-0 pairs (0↔1,2↔3,4↔5,6↔7), level-1 (1↔3,5↔7), level-2 (3↔7), root = PE matching last-in-group. PE↔mesh-neighbor numbering must be chosen so each tree pair is a physical 4-direction neighbor (tuning item, §9).
- **Payload:** `O` is the heavy part (`d`-vector = 128 elems); `m,l` are scalars appended.

---

## 5. Kernel pseudocode

### 5.1 Common loop skeleton (all four cases share this)

```python
def attn_kernel(pe_id, start_pe, counter, K_base, V_base, O_base, q_block):
    # ---- derive geometry ----
    my_len  = valid_len(counter, start_pe, pe_id, N)
    n_tiles = ceil(my_len / TILE)
    q_reg   = load_Q(q_block)                 # decode: 1 row; prefill: q_block rows
    m,l,O   = -inf, 0, zeros(d)

    PREFETCH = 2
    issued = 0
    # prime prefetch
    for j in range(min(PREFETCH, n_tiles)):
        if not tile_all_future(j, q_block):           # kernel-level if (§7)
            enqueue(build_composite(j, q_block)); issued += 1

    # main sweep
    for j in range(n_tiles):
        wait_complete(j)                              # in-order; running m,l,O updated
        nxt = j + PREFETCH
        if nxt < n_tiles and not tile_all_future(nxt, q_block):
            enqueue(build_composite(nxt, q_block))
        # opportunistic reduction progress (see 5.5) — only when this PE
        # already produced O_local AND has spare queue depth
        try_drain_reduction()

    # ---- reduction phase ----
    push_local((m,l,O), to=tree_parent(pe_id))
    if is_tree_internal_or_root(pe_id):
        reduce_tree_node(pe_id)                       # async-submit + bounded poll
    if is_root(pe_id):
        O_final = O_acc / l_acc
        store(O_base, O_final)

def build_composite(j, q_block):
    if tile_partial(j, q_block):       # boundary / diagonal tile
        mask = make_mask_tile(j, q_block)   # kernel computes from offsets
    else:                              # tile_all_past
        mask = null
    return composite.attn_tile(q_reg, K_base, V_base, j, mask, m,l,O, push_target)
```

`tile_all_future / tile_partial / tile_all_past` are pure position comparisons (query global pos vs tile's KV global-pos range). Decode degenerates them (see below).

### 5.2 DECODE, **no SP** (single PE owns the whole head's KV)

- `N = 1` for the reduction group → no cross-PE merge, no tree.
- Query length = 1; it attends to **all** past KV ⇒ `tile_all_future` never true, `tile_partial` only on the final ragged tile, no real masking.
- GQA reuse: the `G=8` query heads sharing one KV head are processed in the **same** PE/composite stream so each K/V tile is loaded once and reused by 8 query rows (Q·Kᵀ becomes an 8×TILE GEMV-batch, P·V an 8×d). This is the main lever; decode is KV-load-bound, so amortizing K/V load over the group is where the win is.
- Bottleneck = K/V tile DMA. Tune `PREFETCH` (≥2) so the queue never starves.

```
load q_reg = [8 query rows for this KV head]      # GQA group batched
for j in 0..n_tiles:
    composite.attn_tile(...)                      # 8×TILE Q·Kᵀ, mask=null (except last)
store O[8 rows]                                   # no reduction
```

### 5.3 DECODE, **with SP / KV-parallel** (N=8, head split across 8 PEs)

- One request's KV is round-robin across 8 PEs; each PE owns ~`my_len` tokens (≤1 apart).
- Each PE still batches its `G=8` query rows (GQA) over its local tiles.
- Query length 1 ⇒ no future tiles, minimal mask ⇒ tile sweep is short per PE; **reduction is the structurally interesting part**, done once per token at sweep end.
- Reduction latency for a single token is hidden by the remaining tiles of *other* concurrent decode tokens if batched; for strict batch=1 long-context, hidden by the fact that each PE still has many tiles (long context) — sweep work >> reduction handshake.

```
per PE:
  my tiles sweep (short, GQA-batched) → (m_i,l_i,O_i)
  push to tree_parent
  tree merge (depth 3)  → root normalizes → O[8 rows] for this KV head
```

### 5.4 PREFILL, **no SP**

- Whole prompt resident on the PE(s) for the head; query is a block of `T` tokens (chunked).
- Now causality is real: for query block `[qs, qe)` and KV tile covering `[ks, ke)`:
  - `ke <= qs`  → `tile_all_past`  → mask=null, full compute.
  - `ks >= qe`  → `tile_all_future`→ **skip enqueue** (kernel `if`).
  - overlap     → `tile_partial`   → kernel builds triangular mask tile, composite applies it.
- Chunked prefill walks query blocks; for each query block runs the tile sweep with the skip/mask decisions above.
- GQA: 8 query heads of a group share K/V tiles within the block ⇒ batched along the same axis as decode.

```
for q_block in chunks(prompt):
    m,l,O = reset
    for j in tiles_up_to(q_block.end):
        if tile_all_future(j,q_block): continue        # skip
        composite.attn_tile(..., mask=mask_or_null(j,q_block))
    store O[q_block]
```

### 5.5 PREFILL, **with SP (Ring KV)**

- KV is sharded across `N` PEs (the SP ring); each ring step delivers a different KV block from a peer.
- **Composite is instantiated per ring step's KV block:** `K load → Q·Kᵀ → mask → online-softmax update → V → P·V → running (m,l,O)`. Running `(m,l,O)` is carried **across ring steps**.
- IPCQ overlaps **next step's KV receive (comms)** with **current step's compute**. KV and V of a step arrive together (it's comms, not local DMA) ⇒ V is already present when P·V runs.
- **Causal ring optimization via kernel `if`:** if the incoming step's KV block is entirely *after* the local query block, the whole step's compute is **skipped** (don't enqueue the composite) — can eliminate ~half the ring steps for causal attention.
- Receive buffers ping-pong; buffer swap aligned to composite boundary.
- After the ring completes, `(m,l,O)` is final per PE → same log-sum-exp tree reduction to produce O. (If the ring already linearly accumulated the full sequence on each query-owning PE, the "reduction" is just the running state; if KV-parallel splits remain, tree-merge them.)

```
init m,l,O
recv KV_block[0]
for step in 0..N-1:
    issue_recv(KV_block[step+1])                       # overlap comms
    if step_all_future(step, q_block):                 # causal ring skip
        continue
    mask = step_mask(step, q_block)                    # null if fully past
    composite.attn_tile(q_reg, Kbuf[step%2], Vbuf[step%2], 0, mask, m,l,O, _)
swap buffers each step
# m,l,O now final for this PE's query block
reduce_tree → normalize → store O
```

### 5.6 Reduction drain loop (the no-hardware-change mechanism)

Because composites cannot `pop` as a dependency, the kernel does it explicitly. The poll never sits on the critical path because there is always other tile work to enqueue (long context):

```python
def reduce_tree_node(pe_id):
    children = tree_children(pe_id)
    acc = local_state
    pending = set(children)
    while pending:
        for c in list(pending):
            if ipcq_nonempty(dir_to(c)):       # poll ONLY the child direction
                part = ipcq_pop(dir_to(c))
                acc  = merge(acc, part)
                pending.remove(c)
        if pending:
            # miss → do useful work instead of busy-wait
            if has_unissued_tiles(): enqueue(next_tile_composite())
            else: spin_short()                 # rare: only batch=1 + short ctx
    if not is_root(pe_id):
        ipcq_push(dir_to(parent), acc)
    else:
        global_acc = acc
```

---

## 6. Why no hardware change for the target workload

- The only place a HW `pop`-as-dependency helps is a **lone reduction with no other work to hide the poll** — i.e. batch=1 *and* short context.
- Target is **agentic = low batch but long context** ⇒ each PE has many KV tiles; a reduction poll-miss is always covered by issuing the next tile composite. The handshake cost is hidden, not on the critical path.
- HW `pop` would also **remove the kernel's ability to choose "do another tile instead of waiting"** and complicate buffer-lifetime/deadlock reasoning (a blocked composite holds PE resources). For long-context that flexibility is worth more than the saved handshake.
- **Decision: ship with software async-submit + bounded poll. Revisit 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** (`if`, arithmetic) |
| address/offset/valid-length arithmetic | **kernel** (from counter) |
| reduction scheduling, IPCQ poll/push timing | **kernel** |
| K/V load, Q·Kᵀ, mask-apply, softmax, P·V, push | **composite** (no internal branch) |

Composites never branch on data and never `pop`. They receive fully-decided inputs (which tile, which mask, where to push). This is what lets the design avoid HW changes.

---

## 8. Required changes to the composite command implementation

1. **Multi-stage fusion across DMA + 2×MM + VEC in one command.** Current composites must support the chain `DMA(K) → MM → VEC(mask+softmax) → DMA(V) → MM(P·V) → VEC(accumulate)` as a single fused unit, with the two DMAs schedulable at *different* dependency points (K early, V mid) rather than both up front.
2. **Carried register state across composite instances.** `(m, l, O)` accumulators must persist between consecutive composites on a PE (running flash state) instead of being command-local. Needs a stable register/SRAM binding the kernel passes in and out.
3. **Mask tile as an input operand.** Composite must accept an optional mask tile and apply it as a VEC stage (`S += mask`). No mask generation inside the composite.
4. **Tail push action to a named IPCQ direction.** Composite must be able to, as a terminal action, write `(m,l,O)` to a neighbor queue-pair identified by direction. Push only — **pop remains a kernel operation** (no internal pop-dependency).
5. **Early/decoupled V DMA scheduling.** The V load stage must be issuable so its latency overlaps the preceding MM/VEC stages (prefetch depth ≥ 2 across instances), not serialized after softmax.
6. **GQA batching on the Q axis.** Q·Kᵀ and P·V stages must accept a batched Q of `G=8` rows so one K/V tile load serves the whole query group (single KV-head reuse).
7. **(NOT required) internal data-dependent branch / pop-as-dependency.** Explicitly out of scope; kernel handles all branching. Listed so reviewers don't add it speculatively.
8. **(NOT required here) RoPE / QKV projection.** Handled by the upstream `qkv_rope` kernel (§0.5). This kernel assumes post-RoPE Q and post-RoPE K-cache and performs **no rotation and no KV-cache write**. Listed so reviewers don't fold RoPE into the attention composite (doing so would force re-rotating past tiles every decode step and break Ring Attention's post-RoPE pass-through).

---

## 9. Open tuning items (not blocking; measured in Kernbench)

1. **KV tile prefetch depth** — dominant for KV-load-bound decode/prefill; sweep 2→4.
2. **PE↔mesh-neighbor mapping for the reduction tree** — ensure each depth-3 tree pair is a physical 4-direction neighbor; bad mapping adds hops.
3. **TILE size** — balance SRAM residency (K_tile + S/P + V_tile + O_acc + 8-way GQA) against DMA efficiency.
4. **Ring buffer ping-pong vs prefetch depth** interaction in §5.5.

---

## 10. Coverage summary

| Case | KV placement | Composite unit | Reduction | Masking |
|---|---|---|---|---|
| Decode, no SP | 1 PE, all KV | per tile, GQA-batched | none | last tile only |
| Decode, SP | round-robin N PEs | per tile, GQA-batched | tree (depth 3) | last tile only |
| Prefill, no SP | resident | per tile per q-block | none | skip future / triangular boundary |
| Prefill, SP (Ring) | ring-sharded | per ring step | running state + tree | causal step-skip + boundary |

All four share the §5.1 skeleton and the §3 composite; they differ only in `N`, query-block width, and which `tile_*` predicates fire.

**I/O per case** (see §0.5 for full contract):

| Case | Inputs | Output | Partials on IPCQ |
|---|---|---|---|
| Decode, no SP | `Q[G,1,d]` post-RoPE, full `K_cache[S,d]`, `V_cache[S,d]` on 1 PE | `O[G,1,d]` at `O_base` | none |
| Decode, SP | `Q[G,1,d]`, per-PE `K_cache[S_pe,d]`, `V_cache[S_pe,d]` | `O[G,1,d]` (root PE) | `(m,l,O_i)` per PE → tree |
| Prefill, no SP | `Q[G,T_q,d]` post-RoPE, `K_cache[≤end,d]`, `V_cache` | `O[G,T_q,d]` at `O_base` | none |
| Prefill, SP (Ring) | `Q[G,T_q,d]`, ring-delivered `K_block,V_block` (post-RoPE) per step | `O[G,T_q,d]` (root PE) | running `(m,l,O)` + tree partials |

In all cases: KV-cache writes and RoPE happen **upstream**; output projection happens **downstream**; score `S` and probs `P` are never materialized.