optimizer state

Sixteen bytes per parameter is the bill for mixed-precision Adam. ZeRO pays it in three installments: optimizer state, then gradients, then the weights themselves. The per-rank bytes for a 70B at 8, 16, 32 and 64 GPUs, and what each stage adds to the wire.

Sixteen bytes per parameter is 1.1 TB of static state before a single activation; LoRA keeps the 141 GB of frozen weights and shrinks the rest to a few gigabytes. The derivation, the GPU counts, and the activations that both still pay.