They handed over the formula so it wasn't a recall test, more about whether you could translate math into clean code.
Start by writing the naive softmax implementation directly from the formula, then immediately address numerical stability by subtracting the maximum logit. Discuss the computational complexity and potential optimizations like vectorization or using log-sum-exp. Finally, mention edge cases such as large inputs and how to handle them.
Pro tip: Always mention the max-subtraction trick for numerical stability—it's a common interview filter. Also, briefly note that in practice, frameworks like PyTorch combine softmax with cross-entropy loss for better stability and efficiency.
Implement softmax as exp(x_i) / sum(exp(x_j)) for each element. This shows you understand the basic formula.
Explain that exponentiating large numbers can overflow, so subtract the maximum value from all inputs before exponentiating. This keeps the values in a safe range without changing the result.
State that the time complexity is O(n) for n inputs, and discuss how to vectorize the operation using NumPy or similar libraries for efficiency.
Mention handling of very large or small inputs, and note that in real systems, softmax is often fused with cross-entropy loss for stability and speed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.