Matmul for symmetric matrices
4 eligible runs
gemm
KernelBench level1 problem 13: Matmul for symmetric matrices. 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
2.66ms±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.
Current records
HardwareBest knownImplementationRuns
NVIDIA H100 · env 12.66 msPyTorch eager2NVIDIA H100 · env 23.69 msPyTorch eager2Not measured on B200 for this workload. Challenges →
Source-native comparison · GPU NVIDIA H100 · Workload n = 4096 · fp32 · Protocol KernelBench timing scripts · mean · 2 results · last observed 2026-03-05Record history →
Estimated floor 277.7 µs · record 9.58× above itestimate, not evidence ›
DRAM 40.1 µs · compute 277.7 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=4096, N=4096, K=4096 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
12.66ms±0.001.00×Reported · MIT · source2026-03-05stale
Measured exactly what you asked. The source's designated baseline implementation. Reported by source; not independently reproduced.
source mirroredMITno install recipeView source →Run detail →
2torch.compile (inductor)PyTorch2.67ms±0.011.00×Reported · MIT · source2026-03-05stale
1.00× 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
Semantics
Inputs and outputs
afp32 [n, n]
bfp32 [n, n]
outfloat [out]
Axes and behavior
nvariable
outvariable
determinismunspecified
constraintsNo mutation or aliasing
Identity
sha2564ca573d82d48…
Sources: KernelBench baseline timings (2026-03-05) · MITlast observed 2026-03-05How records are decidedJSON