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3D tensor matrix multiplication

4 eligible runs
gemm

KernelBench level1 problem 10: 3D tensor 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
1.04ms±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 11.04 msPyTorch eager2NVIDIA H100 · env 21.54 msPyTorch eager2

Not measured on B200 for this workload. Challenges →

Source-native comparison · GPU NVIDIA H100 · Workload k = 2048 · l = 768 · m = 1024 · n = 16 · fp32 · Protocol KernelBench timing scripts · mean · 2 results · last observed 2026-03-05Record history →
Estimated floor 41.9 µs · record 24.8× above itestimate, not evidence ›
DRAM 41.9 µs · compute 136 ns · 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=1024, N=16, K=2048 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
1.04ms±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
1.05ms±0.01
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
1.04ms
1.00×
Reported
MIT · source
torch.compile (inductor)PyTorch
python · torch_compile_inductor
1.05ms
1.01×
Reported
MIT · source

Semantics

Inputs and outputs
afp32 [n, m, k]
bfp32 [k, l]
outfloat [out]
Axes and behavior
kvariable
lvariable
mvariable
nvariable
outvariable
determinismunspecified
constraintsNo mutation or aliasing
Identity
sha256e6ecca672016…
Sources: KernelBench baseline timings (2026-03-05) · MITlast observed 2026-03-05How records are decidedJSON