long context

Standard attention writes an N by N score matrix to HBM and reads it back twice. At 8k context that is 134 MB per head. The traffic arithmetic before and after tiling, the online-softmax identity that makes one pass possible, where the kernel lands on the roofline, and why the memory saving matters more than the speed.

A bug that scales with the number of tiles is invisible in a unit test that fits in one tile. The three candidates that produce exactly this signature, the measurement that separates them, and a test design that would have caught all three before the kernel shipped.

At 128k tokens one layer's activations are 73 GB per sequence and attention grows with the square of the length. The arithmetic that forces the sequence onto sixteen GPUs, what a ring of KV chunks costs per layer, why the communication hides, and where Ulysses and Megatron sequence parallelism fit around it.

At 128k tokens one request's cache is 43 gigabytes and its prefill is measured in seconds. Capacity breaks first, then TTFT, then the scheduler. Each has a fix, and the numbers say which fix you need at which length.

Four things break in order and only one of them is the attention math everyone expects. What a single million-token sequence costs in memory, why the first token takes minutes, and what the model's own architecture already did about the parts that would otherwise be impossible.

Every constraint in this bank meets in one design and they conflict. What has to be true of the model before the deployment is possible at all, the four mechanisms that make the latency usable, and the honest statement of what the first request still costs.