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Tall skinny matrix multiplication

4 eligible runs
gemm

KernelBench level1 problem 9: Tall skinny matrix 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
2.59ms±0.02 · 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 12.59 msPyTorch eager2NVIDIA H100 · env 24.29 msPyTorch eager2

Not measured on B200 for this workload. Challenges →

Source-native comparison · GPU NVIDIA H100 · Workload m = 32768 · n = 32 · fp32 · Protocol KernelBench timing scripts · mean · 2 results · last observed 2026-03-05Record history →
Estimated floor 138.8 µs · record 18.66× above itestimate, not evidence ›
DRAM 2.50 µs · compute 138.8 µs · compute-bound on H100 SXM
every declared tensor crosses HBM exactly once (3,350 GB/s, H100 SXM datasheet)
2·M·N·K with M=32768, N=32768, K=32 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
2.59ms±0.02
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
2.62ms±0.03
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
2.59ms
1.00×
Reported
MIT · source
torch.compile (inductor)PyTorch
python · torch_compile_inductor
2.62ms
1.01×
Reported
MIT · source

Semantics

Inputs and outputs
afp32 [m, n]
bfp32 [n, m]
outfloat [out]
Axes and behavior
mvariable
nvariable
outvariable
determinismunspecified
constraintsNo mutation or aliasing
Identity
sha2562189973f565d…
Sources: KernelBench baseline timings (2026-03-05) · MITlast observed 2026-03-05How records are decidedJSON