Skip to content
KernelIndex
Search⌘K

Attention QKV with QK norm single kernel backward

65 eligible runs
rmsnorm

Backward pass for Gemma3 fused QKV projection with Q/K RMSNorm normalization. Computes gradients for hidden_states, Q/K/V projection weights, and Q/K normalization weights.

Fastest reported
2.35µsmean · 100% of SOL
jonathanc.netLicense unknown · unknown

Reported evidence · last observed 2026-07-11. Reported by source; not independently reproduced. No public source. License unknown.

No public sourceRun detail →

Current records

Workloadsuite of 16 cases · mean latencyhead_dim = 256 · hidden_size = 640 · q_proj_size = 1024 · kv_proj_size = 256 · num_attention_heads = 4 · num_key_value_heads = 116 cases

Not measured on H100 for this workload. Challenges →

Source-native comparison · GPU NVIDIA B200 · Workload suite of 16 cases · mean latency · Protocol SOL-ExecBench evaluation stack v1.1 · mean · 52 results · last observed 2026-08-24Record history →
#
Implementation
Latency
vs #1
Trust
Observed
1
2.35µs100% SOL
1.00×
Reported · license unknown · no source
2026-07-11

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
2
25.0µs85% SOL
10.64×
Reported · license unknown · no source
2026-08-02

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
3
25.4µs85% SOL
10.81×
Reported · license unknown · no source
2026-07-10

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
4
26.1µs84% SOL
11.09×
Reported · license unknown · no source
2026-08-02

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
5
27.4µs84% SOL
11.66×
Reported · license unknown · no source
2026-08-03

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
6
27.4µs84% SOL
11.68×
Reported · license unknown · no source
2026-08-24

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
7
27.7µs84% SOL
11.78×
Reported · license unknown · no source
2026-08-23

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
8
28.1µs83% SOL
11.97×
Reported · license unknown · no source
2026-08-21

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
9
28.7µs83% SOL
12.23×
Reported · license unknown · no source
2026-08-22

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
10
28.9µs83% SOL
12.29×
Reported · license unknown · no source
2026-08-22

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
11
29.2µs83% SOL
12.44×
Reported · license unknown · no source
2026-07-16

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
12
29.3µs82% SOL
12.48×
Reported · license unknown · no source
2026-07-10

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
13
31.4µs82% SOL
13.36×
Reported · license unknown · no source
2026-08-21

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
14
31.4µs82% SOL
13.38×
Reported · license unknown · no source
2026-08-20

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
15
31.5µs82% SOL
13.42×
Reported · license unknown · no source
2026-08-19

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
16
31.6µs81% SOL
13.44×
Reported · license unknown · no source
2026-08-16

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
17
32.3µs81% SOL
13.77×
Reported · license unknown · no source
2026-07-26

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
18
33.6µs81% SOL
14.30×
Reported · license unknown · no source
2026-07-10

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
19
34.0µs80% SOL
14.49×
Reported · license unknown · no source
2026-08-14

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
20
34.1µs80% SOL
14.50×
Reported · license unknown · no source
2026-08-14

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
21
34.1µs80% SOL
14.51×
Reported · license unknown · no source
2026-08-15

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
22
34.8µs80% SOL
14.79×
Reported · license unknown · no source
2026-07-12

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
23
34.8µs80% SOL
14.80×
Reported · license unknown · no source
2026-08-14

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
24
34.8µs80% SOL
14.83×
Reported · license unknown · no source
2026-08-11

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
25
34.9µs80% SOL
14.86×
Reported · license unknown · no source
2026-08-15

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
26
35.0µs80% SOL
14.89×
Reported · license unknown · no source
2026-08-11

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
27
37.2µs78% SOL
15.82×
Reported · license unknown · no source
2026-07-11

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
28
37.4µs78% SOL
15.90×
Reported · license unknown · no source
2026-07-22

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
29
37.6µs78% SOL
15.99×
Reported · license unknown · no source
2026-08-13

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
30
38.5µs78% SOL
16.38×
Reported · license unknown · no source
2026-08-12

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
31
39.0µs78% SOL
16.59×
Reported · license unknown · no source
2026-08-05

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
32
39.3µs77% SOL
16.73×
Reported · license unknown · no source
2026-08-09

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
33
40.0µs77% SOL
17.02×
Reported · license unknown · no source
2026-08-11

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
34
44.6µs75% SOL
18.99×
Reported · license unknown · no source
2026-08-07

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
35
50.6µs72% SOL
21.53×
Reported · license unknown · no source
2026-07-11

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
36
50.7µs72% SOL
21.59×
Reported · license unknown · no source
2026-08-11

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
37
52.5µs72% SOL
22.36×
Reported · license unknown · no source
2026-08-07

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
38
53.0µs71% SOL
22.58×
Reported · license unknown · no source
2026-07-10

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
39
54.9µs71% SOL
23.37×
Reported · license unknown · no source
2026-07-10

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
40
58.6µs69% SOL
24.95×
Reported · license unknown · no source
2026-07-10

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
41
60.4µs68% SOL
25.73×
Reported · license unknown · no source
2026-08-16

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
42
63.4µs67% SOL
26.98×
Reported · license unknown · no source
2026-07-26

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
43
65.4µs66% SOL
27.86×
Reported · license unknown · no source
2026-08-07

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
44
73.0µs63% SOL
31.09×
Reported · license unknown · no source
2026-07-25

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
45
112.0µs53% SOL
47.67×
Reported · license unknown · no source
2026-07-24

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
46
203.8µs38% SOL
86.78×
Reported · license unknown · no source
2026-08-14

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
47
209.7µs37% SOL
89.28×
Reported · license unknown · no source
2026-07-10

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
48
220.3µs36% SOL
93.79×
Reported · license unknown · no source
2026-07-23

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
49
312.1µs30% SOL
132.87×
Reported · license unknown · no source
2026-08-24

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
50
333.6µs29% SOL
142.03×
Reported · license unknown · no source
2026-08-16

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
51
836.2µs16% SOL
356.00×
Reported · license unknown · no source
2026-08-22

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →
52
15.3ms1% SOL
6496.09×
Reported · license unknown · no source
2026-08-23

Measured exactly what you asked. Reported by source; not independently reproduced.

no sourcelicense unknownno install recipeRun detail →

Implementations

Implementation
Runtime
Best latency
Evidence
Availability
unknown
2.35µs
1.00×
Reported
license unknown · no source
unknown
24.5µs
10.41×
Reported
license unknown · no source
unknown
27.4µs
11.68×
Reported
license unknown · no source
unknown
28.0µs
11.93×
Reported
license unknown · no source
unknown
29.2µs
12.44×
Reported
license unknown · no source
unknown
32.9µs
14.02×
Reported
license unknown · no source
unknown
34.0µs
14.49×
Reported
license unknown · no source
unknown
34.1µs
14.50×
Reported
license unknown · no source
Show all 65 implementations ›
unknown
34.8µs
14.80×
Reported
license unknown · no source
unknown
37.4µs
15.90×
Reported
license unknown · no source
unknown
80.8µs
34.38×
Reported
license unknown · no source
unknown
165.4µs
70.42×
Reported
license unknown · no source
unknown
426.6µs
181.62×
Reported
license unknown · no source
unknown
25.4µs
10.81×
Reported
license unknown · no source
unknown
27.7µs
11.78×
Reported
license unknown · no source
unknown
28.1µs
11.97×
Reported
license unknown · no source
unknown
28.7µs
12.23×
Reported
license unknown · no source
unknown
28.9µs
12.29×
Reported
license unknown · no source
unknown
29.3µs
12.48×
Reported
license unknown · no source
unknown
31.4µs
13.36×
Reported
license unknown · no source
unknown
31.4µs
13.38×
Reported
license unknown · no source
unknown
31.5µs
13.42×
Reported
license unknown · no source
unknown
31.6µs
13.44×
Reported
license unknown · no source
unknown
32.3µs
13.77×
Reported
license unknown · no source
unknown
33.6µs
14.30×
Reported
license unknown · no source
unknown
34.1µs
14.51×
Reported
license unknown · no source
unknown
33.9µs
14.45×
Reported
license unknown · no source
unknown
34.9µs
14.86×
Reported
license unknown · no source
unknown
34.8µs
14.79×
Reported
license unknown · no source
unknown
35.0µs
14.89×
Reported
license unknown · no source
unknown
34.8µs
14.83×
Reported
license unknown · no source
unknown
36.1µs
15.37×
Reported
license unknown · no source
unknown
37.6µs
15.99×
Reported
license unknown · no source
unknown
37.2µs
15.82×
Reported
license unknown · no source
unknown
38.5µs
16.38×
Reported
license unknown · no source
unknown
39.0µs
16.59×
Reported
license unknown · no source
unknown
39.3µs
16.73×
Reported
license unknown · no source
unknown
40.0µs
17.02×
Reported
license unknown · no source
unknown
44.6µs
18.99×
Reported
license unknown · no source
unknown
50.7µs
21.59×
Reported
license unknown · no source
unknown
50.6µs
21.53×
Reported
license unknown · no source
unknown
52.5µs
22.36×
Reported
license unknown · no source
unknown
53.0µs
22.58×
Reported
license unknown · no source
unknown
54.9µs
23.37×
Reported
license unknown · no source
unknown
57.1µs
24.29×
Reported
license unknown · no source
unknown
58.6µs
24.95×
Reported
license unknown · no source
unknown
60.4µs
25.73×
Reported
license unknown · no source
unknown
63.4µs
26.98×
Reported
license unknown · no source
unknown
65.4µs
27.86×
Reported
license unknown · no source
unknown
73.0µs
31.09×
Reported
license unknown · no source
unknown
77.7µs
33.06×
Reported
license unknown · no source
unknown
103.4µs
44.01×
Reported
license unknown · no source
unknown
112.0µs
47.67×
Reported
license unknown · no source
unknown
121.9µs
51.91×
Reported
license unknown · no source
unknown
203.8µs
86.78×
Reported
license unknown · no source
unknown
209.7µs
89.28×
Reported
license unknown · no source
unknown
220.3µs
93.79×
Reported
license unknown · no source
unknown
312.1µs
132.87×
Reported
license unknown · no source
unknown
333.6µs
142.03×
Reported
license unknown · no source
unknown
341.9µs
145.57×
Reported
license unknown · no source
unknown
836.2µs
356.00×
Reported
license unknown · no source
unknown
15.3ms
6496.09×
Reported
license unknown · no source
unknown
25.0µs
10.64×
Reported
license unknown · no source
unknown
26.1µs
11.09×
Reported
license unknown · no source
unknown
27.4µs
11.66×
Reported
license unknown · no source

Semantics

Inputs and outputs
grad_querybf16 [batch_size, num_attention_heads, seq_len, head_dim]
grad_keybf16 [batch_size, num_key_value_heads, seq_len, head_dim]
grad_valuebf16 [batch_size, num_key_value_heads, seq_len, head_dim]
hidden_statesbf16 [batch_size, seq_len, hidden_size]
q_weightbf16 [q_proj_size, hidden_size]
k_weightbf16 [kv_proj_size, hidden_size]
v_weightbf16 [kv_proj_size, hidden_size]
q_norm_weightbf16 [head_dim]
k_norm_weightbf16 [head_dim]
query_transposedbf16 [batch_size, num_attention_heads, seq_len, head_dim]
key_transposedbf16 [batch_size, num_key_value_heads, seq_len, head_dim]
q_rstdfp32 [batch_size, num_attention_heads, seq_len, 1]
k_rstdfp32 [batch_size, num_key_value_heads, seq_len, 1]
q_normedbf16 [batch_size, num_attention_heads, seq_len, head_dim]
k_normedbf16 [batch_size, num_key_value_heads, seq_len, head_dim]
rms_norm_epsfp32 scalar
grad_hidden_statesbf16 [batch_size, seq_len, hidden_size]
grad_q_weightbf16 [q_proj_size, hidden_size]
grad_k_weightbf16 [kv_proj_size, hidden_size]
grad_v_weightbf16 [kv_proj_size, hidden_size]
grad_q_norm_weightfp32 [head_dim]
grad_k_norm_weightfp32 [head_dim]
Axes and behavior
seq_lenvariable
head_dimconstant = 256
batch_sizevariable
hidden_sizeconstant = 640
q_proj_sizeq_proj_size = num_attention_heads * head_dim
kv_proj_sizekv_proj_size = num_key_value_heads * head_dim
num_attention_headsconstant = 4
num_key_value_headsconstant = 1
determinismunspecified
constraintsNo mutation or aliasing
Identity
alias051_attention_qkv_with_qk_norm_single_kernel_backwardmodelgemma-3-270msha2562ed74f1d0e5c…
Sources: NVIDIA SOL-ExecBench (2026-08-24)last observed 2026-08-24How records are decidedJSON