Bytedance·Machine Learning Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Bytedance ML engineer screen, one meaty coding question that was basically a math implementation with a gotcha baked in. Felt more like a numerical methods quiz than a typical coding round.

Questions Asked (1)

Implement the softmax function in a numerically stable way. Given a 1D array of logits (or a batch), return softmax probabilities. Be prepared to explain why you subtract the max before exponentiating and how this connects to log-sum-exp.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I knew the formula cold but fumbled the first version by just writing exp(x) / sum(exp(x)) and they immediately asked what happens with large values.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by clarifying the input shape (1D or batch) and then present a numerically stable implementation that subtracts the maximum logit along the appropriate axis before exponentiating. Explain the mathematical reasoning behind the max subtraction and its connection to the log-sum-exp trick, emphasizing how it prevents overflow and underflow.

Pro tip: Mention that for batched inputs, you must subtract the max per example (along the class dimension) to maintain numerical stability, and note that using a library function like scipy.special.logsumexp or torch.logsumexp can simplify the implementation while demonstrating awareness of existing optimized solutions.

1. Clarify input and output

Confirm whether the input is a 1D array of logits or a batch (2D array), and specify the expected output shape (same as input, with probabilities summing to 1 along the appropriate axis).

2. Explain the numerical stability issue

Describe how directly exponentiating large logits can cause overflow (inf) and very negative logits can cause underflow (0), leading to NaN or incorrect probabilities.

3. Present the stable softmax algorithm

Outline the steps: subtract the maximum logit (per example if batched), exponentiate, sum, and divide. Provide pseudocode or actual code, ensuring to handle the axis correctly.

4. Connect to log-sum-exp

Explain that softmax(x) = exp(x - logsumexp(x)), and that subtracting the max is a special case of the log-sum-exp trick where the shift is the maximum value, which is optimal for stability.

5. Discuss trade-offs and edge cases

Mention potential trade-offs (e.g., extra computation for max) and edge cases like all logits equal (uniform distribution) or extremely large batches, and how the implementation handles them.

Key Points to Mention

Numerical stability: subtracting max prevents overflow/underflow in exp.
Log-sum-exp trick: softmax(x) = exp(x - logsumexp(x)), and max subtraction is a stable way to compute logsumexp.
Batched implementation: subtract max along the class dimension (axis=1 for batch of examples).
Mathematical equivalence: softmax(x) = softmax(x - c) for any constant c, so subtracting max does not change the result.
Efficiency: using vectorized operations and avoiding loops; leveraging library functions like logsumexp.
Edge cases: handling -inf logits (e.g., masked positions) and ensuring no division by zero.

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