Amazon·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

Amazon ML Engineer interview, got a numpy-only implementation question on top-p sampling. Pretty technical, felt like a take-home style problem but was likely part of a coding round. No behavioral stuff from what I could tell.

Questions Asked (1)

Implement top-p (nucleus) sampling from scratch using only NumPy. Given raw logits, a cumulative probability threshold p, and a temperature parameter, return the index of a sampled token drawn from the renormalized nucleus distribution.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

This one took me a minute to get fully right.

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AI HintsAI Generated

Suggested Approach

Start by explaining the purpose of top-p sampling: to sample from the smallest set of tokens whose cumulative probability exceeds p, after applying temperature scaling. Then, walk through the implementation steps: temperature scaling, softmax, sorting, cumulative sum, truncation, renormalization, and sampling. Finally, discuss trade-offs and edge cases.

Pro tip: Mention that top-p sampling is often preferred over top-k because it adapts to the model's confidence, and highlight the importance of numerical stability (e.g., subtracting max logit before softmax).

1. Apply temperature scaling

Divide the logits by the temperature parameter to control the randomness of the distribution. Higher temperature increases randomness, lower temperature makes it more deterministic.

2. Compute probabilities

Apply softmax to the scaled logits to obtain a probability distribution over the vocabulary. Ensure numerical stability by subtracting the maximum logit before exponentiation.

3. Sort and compute cumulative probabilities

Sort the probabilities in descending order and compute their cumulative sum. This allows identifying the smallest set of tokens whose cumulative probability exceeds p.

4. Truncate and renormalize

Remove tokens beyond the cumulative threshold p, then renormalize the remaining probabilities so they sum to 1. This forms the nucleus distribution.

5. Sample from the nucleus

Draw a random sample from the renormalized nucleus distribution using np.random.choice or inverse transform sampling, and return the index of the sampled token.

Key Points to Mention

Temperature scaling affects the sharpness of the distribution before top-p filtering.
Numerical stability: subtract max logit before softmax to avoid overflow.
Sorting is necessary to identify the nucleus; use argsort to keep track of original indices.
Renormalization ensures the truncated distribution sums to 1.
Edge cases: p=1 includes all tokens, p=0 should include at least one token (the highest probability).
Trade-offs: top-p vs top-k, computational complexity, and suitability for different tasks.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.