roofline

Decode reads every weight once per token. The answer turns that sentence into a millisecond floor, then accounts for the three things that keep a real server above it.

Two FLOPs per parameter is the number everyone quotes. The answer interviewers want rebuilds it from the config, finds the parameters that do no arithmetic, and names the context length where the rule breaks.

Decode and prefill run the same weights through the same kernels, yet one waits on memory and the other on tensor cores. The answer finds the prompt length where they trade places and turns it into a TTFT.

Batching rescues the weight GEMMs at decode but never the attention kernel, and one head-count ratio explains why. The answer derives it, then shows how MLA moves attention to within a hair of the H100 ridge.

One division tells you whether a headline number is physics or marketing. The answer runs it, then works out which unstated condition would make the claim true and what to ask the vendor for.

The datasheet ratios are close to each other, so the lazy answer is one speedup for everything. The answer splits it into three regimes, and the biggest win turns out to come from capacity, not bandwidth.

Active parameters describe one token. A decode step serves a batch, and the batch decides how many experts get pulled through HBM. The answer computes that number and shows where the MoE cost advantage actually comes from.

The crossover falls out of one division, and the number it gives lines up exactly with something else on the GPU. Spotting that coincidence is what the interviewer is waiting for.

Step time is a straight line in batch size, so throughput is a hyperbola with a ceiling. The answer finds the knee in closed form and shows why the ceiling usually comes from the KV cache, not the tensor cores.

Every weight GEMM ties, attention sits at a constant the batch cannot move, and the ranking flips at batch 8. The answer then separates what fusion can fix from what only the model architecture or the batch can.

Twenty lines of roofline arithmetic get within striking distance of a real server, and the interviewer knows it. What they are scoring is the list of places the model breaks, and how you would catch each one before a capacity plan rests on it.

Absorption is one line of matrix associativity. The part interviewers score is the bill: attention gets more expensive per cached token, and the kernel lands in a roofline regime GQA never visits.

The textbook IO count says FlashAttention re-reads K and V once per query block, which at 8K is only 2x better than naive. The answer explains why the real HBM number is 65x lower, and which cache makes the difference.

Weight-only INT4 shrinks the bytes but keeps the arithmetic in BF16. The answer finds the batch size where that bargain flips, which does not depend on the model, then explains why a code benchmark notices before perplexity does.

The same drafter that triples speed at 3 a.m. costs a third of peak throughput at 6 p.m. if left alone. The answer builds a step-time model for Llama 3.3 70B on eight H100s, derives a draft length per batch bucket, and shows why context length moves the whole table.