xAI (SpaceXSI) KV Cache & GPU Memory interview questions

Forty layers, and only four of them own a global KV cache. The answer counts what those four store, finds the one dtype choice and the page padding that separate the model card from the engine, and says which number to plan capacity on.

Weights and KV are the two numbers everyone knows. The answer that gets the offer accounts for the other few gigabytes, says which ones vLLM measures and which it guesses, and knows where an OOM comes from when the sum looks fine.

FP8 halves the cache and the attention bytes, and on short prompts it looks free. The answer explains why the scale matters less than people think for rounding and more than they think for clipping, and why the failures hide at 128K.

Doubling the GPUs past the KV head count halves the weights per GPU and leaves the KV per GPU exactly where it was. The answer derives that, prices the duplicate copy, and picks the parallelism that does not pay it.

The bound is a one-line argument about where a sequence can be partly full. The block size is a three-way trade between that waste, kernel efficiency and how finely the prefix cache can match.

The formula takes one line. The answer interviewers score is the memory budget around it: what the engine reserves first, what tensor parallelism does to the heads, and why the count you get is a ceiling.

Half the layers capped at a 128-token window sounds like a big saving at 128K. The arithmetic says the saving is set by the layer ratio, not the window, and the allocator decides whether you get it at all.

Compare KV transfer and recompute costs, then add the restore delays the copy timer misses. Derive a prefix-length crossover, test changed load, and preserve block ownership until asynchronous work completes.

A prefix cache only hits from the first token forward, so evicting the wrong block can strand gigabytes that stay resident and can never be hit. The answer derives how much, and which eviction order guarantees it never happens.

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.

Count the blocks with and without sharing and the saving looks large. The answer that scores also knows when the copy fires, what a misaligned prompt does, and the workload where the saving all but disappears.

All three policies keep the server alive. They differ in who waits, who redoes work, and which percentile absorbs the damage, and the numbers for a 6K-token victim make the choice for you.

The transfer looks like gigabytes per request until you divide by prefill time. Then the prompt length cancels, and the real question becomes which models and which GPUs break the link.

The per-token formula gives a scary number for GQA and a reassuring one for MLA. Put both on real GPUs with tensor parallelism and the reassuring one is the request that does not fit.

Keys and values take the same bytes, yet their errors reach the output by different roads. Trace both roads and the scale layout for each tensor follows, along with the bookkeeping that makes per-channel keys awkward to serve.

Each tier is worth exactly the recompute it avoids minus the fetch it costs. Work that out per token and the design writes itself, including the tier that should not exist for small models and the SSD that wears out in a week.