Total variation distance loss
36 eligible runs
tvd
Total variation distance between two tokens×vocab probability distributions (batchmean reduction); the benchmark generates fp32 inputs.
Fastest reported · usable today
275.7µsmedian · 2.64× faster than baseline
LigerLiger-Kernel · BSD-2-Clause · triton
Reported evidence · last observed 2026-03-03. Reported by source; not independently reproduced.
pip install "liger-kernel==0.7.0"Fastest by languagetriton · Liger · 275.7 µs · #1python · PyTorch · 728.8 µs · 2.64×
Current records
Workloadvocab = 8192 · tokens = 16384 · fp32vocab = 16384 · tokens = 16384 · fp32vocab = 32768 · tokens = 16384 · fp32vocab = 65536 · tokens = 16384 · fp32vocab = 131072 · tokens = 16384 · fp32vocab = 4096 · tokens = 16384 · fp32
HardwareBest knownImplementationRuns
NVIDIA H100 · env 1275.7 µsLiger2NVIDIA H100 · env 2850.2 µsLiger2NVIDIA H100 · env 31.12 msLiger2Not measured on B200 for this workload. Challenges →
Source-native comparison · GPU NVIDIA H100 · Workload vocab = 4096 · tokens = 16384 · fp32 · Protocol Liger-Kernel benchmark scripts · median · 2 results · last observed 2026-03-03Record history →
Estimated floor 160.3 µs · record 1.72× above itestimate, not evidence ›
DRAM 160.3 µs · bandwidth-bound on H100 SXM
every declared tensor crosses HBM exactly once (3,350 GB/s, H100 SXM datasheet)
no arithmetic formula for this family: bandwidth floor only
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
1LigerLiger-Kernel275.7µs1.00×Reported · BSD-2-Clause · source2026-03-03stale
2.64× faster than the baseline. Measured exactly what you asked. Reported by source; not independently reproduced.
source mirroredBSD-2-ClauseinstallableView source →Run detail →
2PyTorchbaseline728.8µs2.64×Reported · BSD-3-Clause · source2026-03-03stale
Measured exactly what you asked. The source's designated baseline implementation. Reported by source; not independently reproduced.
source mirroredBSD-3-Clauseno install recipeView source →Run detail →
Scaling by vocab
Implementations
Semantics
Inputs and outputs
pfloat [tokens, vocab]
qfloat [tokens, vocab]
lossfloat [1]
Axes and behavior
vocabvariable
tokensvariable
determinismunspecified
constraintsNo mutation or aliasing
Identity
sha256ae6b46f63ebb…
Sources: Liger-Kernel benchmarks (2026-03-03) · BSD-2-Clauselast observed 2026-03-03How records are decidedJSON