From bb668a3ac3b505699b9b5d711f9539c80badf4f3 Mon Sep 17 00:00:00 2001 From: Mukesh Garg Date: Thu, 18 Jun 2026 15:38:20 -0700 Subject: [PATCH] paper(gqa): derive (m,l,O) AR per-PE cost from kernel topology Replaces the unsourced 32 KB/layer placeholder in the analytical chart with T*(N-1)/N where T = h_q * S_q * (d_head*2 + 8) ~ 2.1 KB (per-PE (m, l, O) payload) and N is the participant count of the reduce-only chain per stage. Cases 2/3/6 analytical bars now match the simulator-measured numbers within ~10% (was 6-30x over). Also: - Bumps the measurement S_kv from 8 K to 64 K to verify Cases 1, 2, 3, 6 are genuinely S_kv-independent and Cases 4, 5 scale linearly. - In-bar descriptor on the paired chart is now wrapped to fit the bar width, black, no background box, and centered between the analytical and measured bars so the label applies to both. Co-Authored-By: Claude Opus 4.7 --- ...long_ctx_6cases_memory_comm_analytical.png | Bin 137072 -> 134741 bytes ...gqa_long_ctx_6cases_memory_comm_paired.png | Bin 186918 -> 187343 bytes .../figures/gqa_long_ctx_6cases_summary.png | Bin 189103 -> 186570 bytes .../measure_gqa_decode_placement_comm.py | 2 +- .../paper/paper_plot_gqa_4cases_summary.py | 68 +++++++++++++----- .../gqa_long_ctx_6cases_measured_comm.json | 22 +++--- ...long_ctx_6cases_memory_comm_analytical.png | Bin 137072 -> 134741 bytes ...gqa_long_ctx_6cases_memory_comm_paired.png | Bin 186918 -> 187343 bytes .../long_ctx/gqa_long_ctx_6cases_summary.png | Bin 189103 -> 186570 bytes 9 files changed, 62 insertions(+), 30 deletions(-) diff --git a/docs/report/1H-codesign-paper/figures/gqa_long_ctx_6cases_memory_comm_analytical.png b/docs/report/1H-codesign-paper/figures/gqa_long_ctx_6cases_memory_comm_analytical.png index 3241151bc0d316e1e30a6210581da9fffb9c6cee..41ff5db639ddbd5c19287446fbfb07cdbc1071da 100644 GIT binary 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Per-cube S_kv share for the d_head-TP partial-score AR cost. diff --git a/scripts/paper/paper_plot_gqa_4cases_summary.py b/scripts/paper/paper_plot_gqa_4cases_summary.py index b5b9a37..584ea46 100644 --- a/scripts/paper/paper_plot_gqa_4cases_summary.py +++ b/scripts/paper/paper_plot_gqa_4cases_summary.py @@ -115,6 +115,7 @@ Output PNG: from __future__ import annotations import json +import textwrap from pathlib import Path import matplotlib.patches as mpatches @@ -187,9 +188,36 @@ _WV_GB = _WV_MB_PER_LAYER * _N_LAYERS / 1000 # 0.16 GB _WO_GB = _WO_MB_PER_LAYER * _N_LAYERS / 1000 # 0.16 GB _WEIGHTS_GB = _WQ_GB + _WK_GB + _WV_GB + _WO_GB # 1.76 GB -# (m, ℓ, O) AR payload — used by Cases 1, 3, 4 (different axes per case). -_MLO_INTRA_BYTES_PER_LAYER = 32 * 1024 # ~32 KB intra-cube AR -_MLO_INTER_BYTES_PER_LAYER = 32 * 1024 # ~32 KB inter-cube AR +# (m, ℓ, O) AR cost per layer, derived from the kernel topology. +# +# Per-PE payload T for one (m, ℓ, O) merge step: +# O — h_q · S_q · d_head · 2 bytes (FP16) +# m — h_q · S_q · 4 bytes (FP32) +# ℓ — h_q · S_q · 4 bytes (FP32) +# T = h_q · S_q · (d_head · 2 + 8) ≈ 2.1 KB +# +# Reduce algorithm: the decode kernels use hierarchical reduce-only +# (chain / tree) rather than ring all-reduce, because the merged result +# only needs to land on the cube that runs the downstream Wo gemm — +# not on every PE. For a chain of N participants the total traffic is +# (N-1)·T and the per-PE average is (N-1)/N · T. +# +# The previous version used a hard-coded 32 KB / layer placeholder which +# overestimated the per-PE cost by ~6× (and ~3× even under a hypothetical +# ring-AR assumption). See `gqa_long_ctx_6cases_measured_comm.json` for +# the measured numbers this matches against. +_MLO_PAYLOAD_BYTES = _H_Q * _S_Q * (_D_HEAD * _BYTES_PER_ELEM + 8) + + +def _reduce_chain_per_pe_bytes(n_participants: int) -> int: + """Per-PE average bytes for a single-stage chain/tree reduce of T.""" + if n_participants <= 1: + return 0 + return _MLO_PAYLOAD_BYTES * (n_participants - 1) // n_participants + + +_MLO_INTRA_BYTES_PER_LAYER = _reduce_chain_per_pe_bytes(_P) # PE-axis +_MLO_INTER_BYTES_PER_LAYER = _reduce_chain_per_pe_bytes(_C) # cube-axis # Cases — renumbered in MEMORY-DESCENDING ORDER (left to right): # Case 1 (40 GB) : no sharding @@ -225,11 +253,11 @@ _CASE_COLOR = { } _ATTN_DESC = { 1: "none", - 2: "online-softmax\nmerge of\n(m,ℓ,O)\ninter-cube", - 3: "online-softmax\nmerge of\n(m,ℓ,O)\nintra-cube", - 4: "partial\nscores\n+ (m,ℓ,O)\nmerge\n(d_head-TP)", - 5: "partial\nscores\n+ (m,ℓ,O)\nmerge\n(d_head-TP)", - 6: "online-softmax\nmerge of\n(m,ℓ,O)\nintra + inter", + 2: "online-softmax (m,ℓ,O) — inter-cube", + 3: "online-softmax (m,ℓ,O) — intra-cube", + 4: "partial scores + (m,ℓ,O) merge (d_head-TP)", + 5: "partial scores + (m,ℓ,O) merge (d_head-TP)", + 6: "online-softmax (m,ℓ,O) — intra + inter", } _WO_COLOR = "#9EC5E8" @@ -498,21 +526,25 @@ def _plot_comm(ax, *, mode: str = "analytical") -> None: fontsize=8 if paired else 9, weight="bold", linespacing=1.05) - # In-bar attention-time AR description (online-softmax (m,ℓ,O) - # merge, partial-score AR, intra/inter-cube). Placed on the - # analytical bar; with paired mode it lives on the solid bar so - # the hatched measured bar stays uncluttered. + # Attention-time AR descriptor — placed at the attention-segment + # midpoint, centered between the analytical and measured bars so + # it visually spans both. Coloured the same as the attention bar + # (no background box) so it lives within the case's bar zone. + # Wrapped narrow so each line fits inside the bar-pair width. + wrapped = textwrap.fill(_ATTN_DESC[c], width=14) if attn_mb[i] > 0: mid = bottoms_attn[i] + attn_mb[i] / 2 - ax.text(x_ana[i], mid, _ATTN_DESC[c], + ax.text(x[i], mid, wrapped, ha="center", va="center", - fontsize=6 if paired else 7, - color="black", weight="bold") + fontsize=7 if paired else 8, + color="black", weight="bold", + linespacing=1.0) else: - ax.text(x_ana[i], totals_ana[i] * 0.4, _ATTN_DESC[c], + ax.text(x[i], totals_ana[i] * 0.4, wrapped, ha="center", - fontsize=6.5 if paired else 7.5, - color="grey", style="italic") + fontsize=7 if paired else 8, + color="grey", style="italic", + linespacing=1.0) legend_handles = [ mpatches.Patch(facecolor=_WO_COLOR, edgecolor="black", diff --git a/src/kernbench/benches/1H_milestone_output/gqa/long_ctx/gqa_long_ctx_6cases_measured_comm.json b/src/kernbench/benches/1H_milestone_output/gqa/long_ctx/gqa_long_ctx_6cases_measured_comm.json index e527aea..c37d1d6 100644 --- a/src/kernbench/benches/1H_milestone_output/gqa/long_ctx/gqa_long_ctx_6cases_measured_comm.json +++ b/src/kernbench/benches/1H_milestone_output/gqa/long_ctx/gqa_long_ctx_6cases_measured_comm.json @@ -1,5 +1,5 @@ { - "S_kv_measured": 8192, + "S_kv_measured": 65536, "S_kv_headline": 1048576, "n_layers": 80, "num_pes": 64, @@ -31,19 +31,19 @@ }, "4": { "label": "Case 4 (Cube-SP x PE-TP d_head)", - "total_ipcq_bytes_one_layer": 1851136, - "per_pe_partial_score_bytes_one_layer": 16384, - "per_pe_mlo_bytes_one_layer": 12540, - "per_pe_attn_bytes_per_token_at_1M": 168775360, - "per_pe_total_bytes_per_token_at_1M": 170086080 + "total_ipcq_bytes_one_layer": 14696192, + "per_pe_partial_score_bytes_one_layer": 131072, + "per_pe_mlo_bytes_one_layer": 98556, + "per_pe_attn_bytes_per_token_at_1M": 175656640, + "per_pe_total_bytes_per_token_at_1M": 176967360 }, "5": { "label": "Case 5 (Cube-TP d_head x PE-SP)", - "total_ipcq_bytes_one_layer": 1851136, - "per_pe_partial_score_bytes_one_layer": 16384, - "per_pe_mlo_bytes_one_layer": 12540, - "per_pe_attn_bytes_per_token_at_1M": 168775360, - "per_pe_total_bytes_per_token_at_1M": 170086080 + "total_ipcq_bytes_one_layer": 14696192, + "per_pe_partial_score_bytes_one_layer": 131072, + "per_pe_mlo_bytes_one_layer": 98556, + "per_pe_attn_bytes_per_token_at_1M": 175656640, + "per_pe_total_bytes_per_token_at_1M": 176967360 }, "6": { "label": "Case 6 (Cube-SP x PE-SP) [*]", diff --git a/src/kernbench/benches/1H_milestone_output/gqa/long_ctx/gqa_long_ctx_6cases_memory_comm_analytical.png b/src/kernbench/benches/1H_milestone_output/gqa/long_ctx/gqa_long_ctx_6cases_memory_comm_analytical.png index 3241151bc0d316e1e30a6210581da9fffb9c6cee..41ff5db639ddbd5c19287446fbfb07cdbc1071da 100644 GIT binary patch literal 134741 zcmeFZ^;cAJ|1U~OC<7=;45>&A-Q6fi%K!q>(%oGOGAP}hl0$c=NH+}KF@SVP*V%l} 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