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🧮 Napkin Math & Capacity
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Communication Volume Estimates

Every parallelism strategy is a promise to move a certain number of bytes between GPUs every step, and the fabric either affords it or it does not. This page derives the per-rank volume for data parallelism, ZeRO/FSDP, tensor parallelism, pipeline parallelism and expert parallelism, works each for a 70B model at 8 and 64 ranks, and turns the bytes into seconds on NVLink and on a 400 Gb/s NIC. The result is the rule that decides every 3D layout: per-layer traffic stays on NVLink, per-step traffic can cross the fabric.

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