tensor parallelism

Decode reads every weight once per token. The answer turns that sentence into a millisecond floor, then accounts for the three things that keep a real server above it.

Decode and prefill run the same weights through the same kernels, yet one waits on memory and the other on tensor cores. The answer finds the prompt length where they trade places and turns it into a TTFT.

A 60% MBU number is a symptom, not a diagnosis. The answer rebuilds the floor from bytes, then splits the missing 40% into buckets a profiler can confirm and a team can own.

Doubling the GPUs past the KV head count halves the weights per GPU and leaves the KV per GPU exactly where it was. The answer derives that, prices the duplicate copy, and picks the parallelism that does not pay it.

The per-token formula gives a scary number for GQA and a reassuring one for MLA. Put both on real GPUs with tensor parallelism and the reassuring one is the request that does not fit.

Tensor parallelism divides the weight bytes but not the all-reduce count, so each doubling buys less than the one before. The answer prices that fixed cost, then finds the workload where TP=8 wins anyway.

Two matrix multiplies in a row, and the order of the splits decides whether you communicate once or twice per block. The answer places every split for a 70B layer and prices what the remaining all-reduces send per token.

A ring all-reduce is bandwidth-optimal and takes fourteen synchronized steps on eight GPUs. At 16 KB per call, the steps are the cost. The answer builds the latency-bandwidth model, finds the crossover size, and checks it against the threshold vLLM ships.

Same eight GPUs, same weights per GPU, same KV capacity. One layout pays 252 all-reduces per token, the other pays for every layer twice in wall-clock time. The answer works both, then finds the precision choice that forces the second.