Openai·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

OpenAI MLP engineer interview where they had me implement backprop entirely from scratch, no autograd crutch. Pretty intense for a technical screen but felt very on-brand for them.

Questions Asked (1)

Implement backpropagation from scratch for a small multi-layer neural network, manually computing gradients for each layer using the chain rule, without using any automatic differentiation library.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

This one took me a minute to settle into.

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AI HintsAI Generated

Suggested Approach

Start by defining a simple feedforward network architecture (e.g., 2-layer MLP) with sigmoid/ReLU activations and MSE loss. Then, implement forward pass, manually derive gradients using chain rule for each layer, and update weights via gradient descent. Emphasize modularity and verification against numerical gradients.

Pro tip: Use numerical gradient checking to validate your manual gradients—this demonstrates rigor and catches subtle errors, which is highly valued at OpenAI.

1. Define Network Architecture and Forward Pass

Specify layer sizes, activation functions, and loss function. Implement forward propagation storing intermediate values (pre-activations, activations) needed for backward pass.

2. Derive Gradients via Chain Rule

For each layer, compute local gradients (e.g., dL/dz, dL/dW, dL/db) by applying chain rule from output to input. Write down the equations explicitly.

3. Implement Backward Pass

Code the backward propagation using the derived equations, ensuring correct shapes and matrix operations. Propagate error term delta layer by layer.

4. Update Parameters and Train

Apply gradient descent updates to weights and biases. Iterate over epochs, monitoring loss to ensure convergence.

5. Validate with Gradient Checking

Implement numerical gradient approximation and compare with analytical gradients to verify correctness. Debug any discrepancies.

Key Points to Mention

Chain rule application: local gradient of loss w.r.t. pre-activation, then w.r.t. weights and biases.
Importance of caching forward pass values (e.g., activations) for efficient backward computation.
Matrix calculus: using Jacobians and understanding dimensions to avoid shape mismatches.
Choice of activation functions and their derivatives (e.g., sigmoid, ReLU) and impact on vanishing gradients.
Gradient checking: finite difference approximation to validate analytical gradients.
Modular design: separating forward/backward for each layer to enable easy extension and debugging.

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