LinkedIn·AI Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

LinkedIn AI Engineer technical screen, one meaty probability/sampling question that took up most of the time. Pretty focused session, no fluff.

Questions Asked (1)

You have an N-sided die where each face has a probability derived from a softmax over a logits vector. Implement an efficient sampler that returns a face index according to those probabilities. Walk through your approach and any alternatives you know.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I went straight for cumulative sum plus binary search, which is the standard inverse-CDF move.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem: given a logits vector, compute softmax probabilities, then sample an index according to those probabilities. Present the standard O(N) prefix-sum + binary search approach, then discuss optimizations like the alias method for O(1) sampling, and trade-offs between preprocessing time and sampling speed.

Pro tip: Mention numerical stability in softmax (subtract max logit) and that for large N, the alias method is often used in production systems like recommendation models. Also, note that if sampling many times from the same distribution, preprocessing pays off.

1. Clarify requirements and constraints

Ask about N (size), number of samples, whether probabilities change frequently, and if memory is a concern. This determines the best approach.

2. Compute softmax probabilities

Given logits, compute probabilities using softmax with numerical stability (subtract max logit). Explain the formula and why stability matters.

3. Implement basic sampler (prefix sum + binary search)

Build cumulative distribution (CDF) array, generate uniform random number in [0,1), then binary search to find the index. This is O(N) preprocessing, O(log N) per sample.

4. Discuss optimized alternatives

For O(1) sampling, use the alias method (requires O(N) preprocessing and O(N) memory). For dynamic probabilities, consider Fenwick tree for O(log N) updates and sampling.

5. Analyze trade-offs and choose

Compare time/space complexity, preprocessing cost, and suitability for different scenarios (e.g., many samples vs. few, static vs. dynamic probabilities).

Key Points to Mention

Softmax numerical stability: subtract max logit before exponentiation to avoid overflow.
Prefix sum (CDF) + binary search: O(N) preprocessing, O(log N) per sample, simple and effective.
Alias method: O(N) preprocessing, O(1) per sample, but requires O(N) memory and is more complex.
Fenwick tree (Binary Indexed Tree) for dynamic probabilities: supports O(log N) updates and sampling.
Trade-offs: preprocessing time vs. sampling speed, memory usage, and whether probabilities change.
Edge cases: handling zero probabilities, floating-point precision, and ensuring the random number falls within the CDF range.

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