sharding

The roofline, the sharding arithmetic and the parallelism trade-offs transfer unchanged, and the numbers are in the same units. What changes is who writes the kernels, how shapes must behave, and the interconnect topology you shard against. The v6e and v7 numbers worked through against an H100.

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.

Same algorithm, two implementations, one of which now lives inside PyTorch and composes with everything else there. The differences that decide it in 2026: per-parameter sharding, DTensor, torch.compile, and the two features DeepSpeed still owns outright.

On a TPU pod you write one program, annotate how each array is sharded across a named mesh, and the compiler inserts and schedules every collective. What that removes from the engineer's job, what the torus changes about layouts, where Pathways fits, and what a compiler-owned schedule costs.

For text training the bytes are trivial and the bottleneck is never bandwidth, so the usual advice about faster storage misses. What the loader actually has to deliver per second, the four things that consume the time instead, and the order to fix them with the measurement that proves each.

A tokenizer moves about a megabyte of text per second per core, which makes this a seven-hundred-core-day batch job rather than something to run during training. The throughput arithmetic per stage, the shard format the loader needs, and the determinism requirements that let you resume without corrupting a run.

Six and a half terabytes leaving sixteen thousand GPUs at once is a burst no shared filesystem absorbs, and the fix is to stop trying. What the barrier actually has to wait for, the per-node arithmetic that makes it seconds, and the manifest rule that decides whether a checkpoint is usable at all.

The bandwidth is effectively unlimited and the first byte takes fifty milliseconds, so throughput is set by how many requests you keep in flight rather than by the network. Little's law applied to a data loader, the request size where the latency stops mattering, and the two design changes that follow.

Fifteen trillion tokens starts as a few petabytes of raw text and ends as 30 TB of shards a training job reads at 1.7 million tokens per second. The stages, the bytes at each boundary, the throughput each one needs to finish in two weeks, and the two stages where the pipeline actually spends its time.