Amazon·Software Engineer·Online Assessment (OA)·Intermediate

Intermediate

Jun 2026

Summary

Amazon SWE online assessment, one coding problem that looked like a standard ML implementation task but had enough edge cases to slow me down.

Questions Asked (1)

Implement a linear regression model from scratch using backpropagation to iteratively update weights and bias. Given a 2D feature matrix X, a label array y, a learning rate, and an epoch count, return the final predictions along with the trained weights and bias.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I knew the math going in but writing it cleanly under time pressure was a different story.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and assumptions (e.g., loss function, initialization, convergence criteria). Then outline the forward pass, loss computation, and gradient derivation for weights and bias, followed by the update rule. Finally, discuss implementation details, complexity, and potential optimizations or trade-offs.

Pro tip: Demonstrate production awareness by mentioning vectorization for efficiency and numerical stability techniques like feature scaling or gradient clipping, which are crucial for large-scale systems at Amazon.

1. Clarify Requirements and Assumptions

Confirm the loss function (MSE), initialization (zeros or small random), and stopping criteria (fixed epochs). Ask about data size and performance expectations.

2. Derive Gradients and Update Rule

Compute gradients of MSE with respect to weights and bias: dW = (2/n) * X^T * (y_pred - y), db = (2/n) * sum(y_pred - y). Update using W = W - lr * dW, b = b - lr * db.

3. Implement Efficiently with Vectorization

Use NumPy for vectorized operations to avoid loops. Precompute X^T or use efficient matrix multiplications. Handle bias by augmenting X with a column of ones or separately.

4. Train and Return Predictions

Iterate for the given epochs, updating weights and bias. After training, compute final predictions as X @ W + b. Return predictions, weights, and bias.

5. Analyze Complexity and Trade-offs

Discuss time complexity O(epochs * n * d) and space complexity O(n*d). Mention trade-offs: batch vs stochastic gradient descent, learning rate tuning, and convergence.

Key Points to Mention

Mean Squared Error (MSE) as the loss function and its gradient derivation.
Vectorized implementation using NumPy for efficiency.
Learning rate selection and its impact on convergence.
Handling bias term (e.g., augmenting feature matrix).
Time and space complexity analysis.
Potential improvements: regularization, early stopping, or adaptive learning rates.

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