Anthropic·Machine Learning Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say

Jun 2026Remote

Summary

Anthropic ML interview, one meaty coding/theory question that took up basically the whole session. They wanted you to actually derive things, not just recite formulas, which I was not fully prepared for.

Questions Asked (1)

Implement backpropagation from scratch for a small feed-forward neural network, including the forward pass, chain-rule gradient derivations for each layer's weights and biases, and the parameter update step using SGD. Also discuss vectorization, numerical stability considerations like softmax with cross-entropy, and how the approach scales with network depth.

Algorithms & Data StructuresTechnical Trade-offsSystem Design

Author's notes

This wrecked me a little.

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AI HintsAI Generated

Suggested Approach

Start by clearly defining the network architecture and notation, then derive the forward and backward passes layer by layer using the chain rule, emphasizing vectorized matrix operations. After presenting the gradient computations, explain the SGD update and discuss numerical stability tricks like the log-sum-exp for softmax cross-entropy. Finally, address how the approach scales with depth, mentioning vanishing/exploding gradients and potential mitigations.

Pro tip: Demonstrate practical awareness by mentioning that in real implementations, you'd use automatic differentiation (e.g., PyTorch) but understanding the manual derivation is crucial for debugging and custom layers. Also, highlight that numerically stable softmax with cross-entropy avoids overflow and underflow, which is often overlooked.

1. Define architecture and notation

Specify the network: number of layers, activation functions, loss function. Establish consistent notation for weights, biases, pre-activations, and activations.

2. Forward pass derivation

Write the equations for each layer's linear transformation and activation, culminating in the output and loss computation. Emphasize vectorized matrix operations.

3. Backward pass derivation

Derive gradients for each layer's weights and biases using the chain rule, starting from the loss and propagating backwards. Show how to compute the error term (delta) for each layer.

4. Parameter update with SGD

Explain the SGD update rule: for each parameter, subtract learning rate times gradient. Mention variants like momentum or Adam if relevant.

5. Numerical stability and scaling

Discuss softmax with cross-entropy stability (log-sum-exp trick), and how depth affects training (vanishing/exploding gradients, need for normalization or residual connections).

Key Points to Mention

Vectorization: using matrix operations to compute gradients for all examples in a batch efficiently, avoiding loops.
Chain rule: the recursive application of derivatives from loss to each parameter, often expressed via the delta rule.
Softmax with cross-entropy: combining these operations simplifies the gradient to (y_pred - y_true) and avoids numerical issues by using log-sum-exp.
SGD update: θ = θ - η * ∇θ J(θ), and the importance of learning rate selection.
Scaling with depth: vanishing/exploding gradients, and techniques like careful initialization (Xavier/He), batch normalization, or residual connections.
Computational graph: conceptualizing the network as a graph to systematically apply backpropagation.

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