parallelism layout

Sixteen bytes per parameter says 1.6 TB of state against a 640 GB node, so the model spans nodes before the first token. The arithmetic that sizes the fleet, the layout that puts each axis on the right link, and the two numbers that decide FSDP against pipeline across nodes.

Tensor parallel 8, pipeline 16, data parallel 128: the layout Meta trained Llama 3 405B on, rebuilt from the memory floor, the compute budget and the bandwidth of each link. Why the axes go in that order, what each one costs per step, and the bubble that the schedule has to hide.

A 400B dense model on 10 trillion tokens is 2.4 × 10²⁵ FLOPs, 43 days of pure compute on 16,384 H100s, and about 380 interruptions along the way. The order in which to derive every number, the layout and the data rate, the checkpoint and failure budgets, and the schedule that survives its own arithmetic.