sampling

These are the knobs every LLM product tunes, and the interviewer wants to know what each does to the probability distribution and which setting fits which task. Including why factual and creative tasks want opposite settings.

How you decode from the model's probabilities shapes the output as much as the model. The signal is knowing the deterministic vs sampling methods and when each fits (factual vs creative). Here is the answer.

Neural text degeneration is a known failure of likelihood-maximizing decoding, not a broken model. The fixes are specific decode-time knobs. Here is which lever to pull and what each one costs.

Most people know MCP exposes tools. The deeper signal is the full primitive set (resources, prompts, sampling, roots) and the patterns: server composition, sampling for nested LLM calls, and scoping access safely.

Sampling uniformly from a stream you cannot fit in memory (or whose length you never learn) is a real data-engineering problem. The signal is the replace-with-decreasing-probability trick and a proof that telescopes. Here is the answer.

Every chat model's 'temperature' and 'top_p' knobs are a few lines of logit surgery. Implementing them shows you understand decoding, not just call it. Here is the from-scratch version.

Negative sampling in word2vec and recommendation draws millions of weighted samples; doing each in O(log n) is a bottleneck. The alias method makes each draw O(1) after an O(n) setup. Here it is.

If labels only exist for the cases you already acted on, the model learns a distorted world: great offline, blind to everyone you never saw. Worse, its own decisions pick the next labels. Here is how to spot it and counter it.

Bayesian inference needs an intractable normalizing constant, and MCMC sidesteps it. The signal is explaining the acceptance ratio, detailed balance, and why you can skip the constant entirely. Here is the answer.

Building a training set from a billion-row table means sampling, and the naive 'ORDER BY random() LIMIT n' sorts the whole table. Stratified sampling needs more care still. Here are both, done efficiently.