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4D tensor matrix multiplication

4 eligible runs
gemm

KernelBench level1 problem 11: 4D 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).

Fastest reported
10.9ms±0.21 · mean of 100 · 1.01× faster than baseline
torch.compile (inductor)PyTorch · MIT · python

Reported evidence · last observed 2026-03-05. Reported by source; not independently reproduced.

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

Current records

HardwareBest knownImplementationRuns
NVIDIA H100 · env 110.9 mstorch.compile (inductor)2NVIDIA H100 · env 212.6 msPyTorch eager2

Not measured on B200 for this workload. Challenges →

Source-native comparison · GPU NVIDIA H100 · Workload b = 8 · i = 256 · j = 512 · k = 768 · l = 256 · fp32 · Protocol KernelBench timing scripts · mean · 2 results · last observed 2026-03-05Record history →
Estimated floor 320.8 µs · record 33.98× above itestimate, not evidence ›
DRAM 320.8 µs · compute 3.25 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=512, N=768, K=256 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
torch.compile (inductor)PyTorch
10.9ms±0.21
1.00×
Reported · MIT · source
2026-03-05stale

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

source mirroredMITno install recipeView source →Run detail →
2
PyTorch eagerbaselinePyTorch
11.0ms±0.20
1.01×
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 →

Implementations

Implementation
Runtime
Best latency
Evidence
Availability
PyTorch eagerPyTorch
python · torch_eager
11.0ms
1.01×
Reported
MIT · source
torch.compile (inductor)PyTorch
python · torch_compile_inductor
10.9ms
1.00×
Reported
MIT · source

Semantics

Inputs and outputs
afp32 [b, i, j, l]
bfp32 [l, k]
outfloat [out]
Axes and behavior
bvariable
ivariable
jvariable
kvariable
lvariable
outvariable
determinismunspecified
constraintsNo mutation or aliasing
Identity
sha2567b72882069ac…
Sources: KernelBench baseline timings (2026-03-05) · MITlast observed 2026-03-05How records are decidedJSON