d-Matrix Quantization & Numerics interview questions

FP4 has no value between 4 and 6, so the largest numbers in a block lose the most. The answer derives the error at the top of the grid for both scale targets, works the selection rule on two blocks, explains the tensor-scale change it forces, and says why MXFP4 cannot do it and where it made results worse.

A handful of channels with huge activations wreck the INT8 grid for every other channel in the token. The answer shows why the obvious fix cannot run on a tensor core, what SmoothQuant does instead, and why FP8 makes most of the problem disappear.

Finer scales buy accuracy, and the bytes they cost are easy to count. The answer counts them for a 70B model, then shows the cost that matters more: which scales can wait for the epilogue and which ones invade the inner loop.

The two methods ship identical file formats and run on identical kernels, so the difference is entirely in how the rounding was chosen. The answer shows the one design choice that makes one of them fragile when traffic stops looking like the calibration set.

Both formats spend the same eight bits. The answer derives where each one's largest and smallest values come from, then explains why inference almost always picks the narrower of the two.

Weight-only INT4 shrinks the bytes but keeps BF16 arithmetic. Derive its compute-bound knee and its crossover against FP8 under a weights-only model, then investigate a coding-quality loss with held-out evidence.

Both formats store the same eight 4-bit values per element. The difference is all in the scale, and the answer shows which of the two scale choices buys more accuracy and what it costs in bits.

Perplexity averages over the tokens a model finds easy and scores it on text it did not write. The answer builds the evaluation that catches what quantization actually breaks, and shows why a one-point drop on a benchmark can be noise or a real regression.

A few matrices cause most of the damage when a model is quantized, and keeping them wide costs little memory. The answer builds the sweep that finds them, prices it in GPU hours, and explains why the sum of single-layer damages is not the damage of the mix.

Fine-grained scales let E4M3 carry every tensor, but they change along the reduction axis, so the tensor cores cannot apply them. The answer walks the main loop where they do get applied, prices that work against the MMA, and explains what Blackwell moves into hardware.

Local-inference formats spend every bit where it buys the most accuracy, and datacenter formats spend them uniformly. The answer works out what a Q4_K_M file actually costs per weight, and explains why the trade that wins on one consumer GPU loses at batch 64.

Reduction order explains the last-bit drift, but a quantized server has a second, much larger leak: a scale computed over the whole batch lets one user's activations change another user's logits. The answer separates the two and fixes both.

FP8 halves the weights and still leaves almost no memory for the cache. The answer does the budget line by line, picks the format pair that leaves room for real concurrency, and says which hardware change makes the opposite choice correct.

QAT never makes a model faster than PTQ at the same format; both produce identical tensors for the kernel. The answer reframes what QAT buys, prices a QAT run in GPU hours against the fleet it could shrink, and names the cases where a serving team should not touch it.

Calibration data reaches each expert only through the router, so the experts that matter for rare domains see almost none of it. The answer counts the tokens, shows the point where a Hessian-based quantizer becomes worse than plain rounding, and builds a recipe that does not depend on luck.

Even a format with the same name differs between the two generations: block-scaled FP8 uses FP32 scales on Hopper and power-of-two scales on Blackwell. The answer designs formats, fallbacks and gates so a user routed to either pool gets a model the team has actually tested.