Skip to content
KernelIndex
Search⌘K
Sign in

Matrix vector multiplication

4 eligible runs
gemm

KernelBench level1 problem 4: Matrix vector multiplication. The computation is the reference PyTorch module's forward pass; the output shape follows the module (mirrored as each implementation's source).

Source baseline · unbeaten
2.77ms±0.00 · mean of 100
PyTorch eagerPyTorch · MIT · python

Reported evidence · last observed 2026-03-05. The source's designated baseline implementation. Reported by source; not independently reproduced.

No package · vendor the source →View source →Run detail →

Current records

HardwareBest knownImplementationRuns
NVIDIA H100 · env 12.77 msPyTorch eager2NVIDIA H100 · env 24.51 msPyTorch eager2

Not measured on B200 for this workload. Challenges →

Source-native comparison · GPU NVIDIA H100 · Workload k = 1048576 · m = 2048 · fp32 · Protocol KernelBench timing scripts · mean · 2 results · last observed 2026-03-05Record history →
Estimated floor 2.57 ms · record 1.08× above itestimate, not evidence ›
DRAM 2.57 ms · compute 8.68 µs · bandwidth-bound on H100 SXM
every declared tensor crosses HBM exactly once (3,350 GB/s, H100 SXM datasheet)
2·M·N·K with M=2048, N=1, K=1048576 at the dense tf32 peak (495 TFLOP/s)
headroom-v1: a lower bound from declared tensors and datasheet peaks. A kernel can sit well above it for good reasons.
#
Implementation
Latency
vs #1
Trust
Observed
1
PyTorch eagerbaselinePyTorch
2.77ms±0.00
1.00×
Reported · MIT · source
2026-03-05stale

Measured exactly what you asked. The source's designated baseline implementation. Reported by source; not independently reproduced.

source mirroredMITno install recipeView source →Run detail →
2
torch.compile (inductor)PyTorch
2.79ms±0.00
1.01×
Reported · MIT · source
2026-03-05stale

1.01× slower than the baseline. Measured exactly what you asked. Reported by source; not independently reproduced.

source mirroredMITno install recipeView source →Run detail →

Implementations

Implementation
Runtime
Best latency
Evidence
Availability
PyTorch eagerPyTorch
python · torch_eager
2.77ms
1.00×
Reported
MIT · source
torch.compile (inductor)PyTorch
python · torch_compile_inductor
2.79ms
1.01×
Reported
MIT · source

Semantics

Inputs and outputs
afp32 [m, k]
bfp32 [k, 1]
outfloat [out]
Axes and behavior
kvariable
mvariable
outvariable
determinismunspecified
constraintsNo mutation or aliasing
Identity
sha2565fb3f81b873d…
Sources: KernelBench baseline timings (2026-03-05) · MITlast observed 2026-03-05How records are decidedJSON