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This is a medium difficulty Machine Learning question, commonly asked during Onsite rounds at Anthropic.

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This question is commonly asked for Software Engineer candidates at Anthropic during technical interviews.

Implement and derive backprop from scratch | Anthropic Interview Question

Quick Overview

This question evaluates understanding and practical implementation of neural network fundamentals, specifically analytic backpropagation and gradient derivation, numerically stable binary cross-entropy computation, parameter initialization, gradient descent updates, and gradient checking.

Tiny Neural Network (From First Principles): Binary Classification

Context

You will implement and analyze a minimal neural network for binary classification with one hidden layer. Assume a dataset with features X ∈ R^{N×D} and labels y ∈ {0,1}^N. The network has:

Hidden layer: H units with an activation (ReLU or tanh).
Output layer: 1 unit with a sigmoid for P(y=1|x).

Use vectorized NumPy (or similar) without autograd.

Tasks

Forward pass
- Define shapes: W1 ∈ R^{D×H}, b1 ∈ R^{H}, W2 ∈ R^{H×1}, b2 ∈ R^{1}.
- Compute z1 = XW1 + b1, a1 = f(z1), z2 = a1W2 + b2, p = σ(z2).
Loss (numerically stable)
- Implement binary cross-entropy. Use a stable formulation (e.g., softplus: log(1+exp(x)) or log-sum-exp) to avoid overflow/underflow.
Backward pass (analytic gradients; no autograd)
- Derive and implement gradients for W1, b1, W2, b2.
Optimization
- Implement gradient descent updates for all parameters.
Gradient checking
- Verify gradients by finite differences: g_num ≈ (L(θ+ε) − L(θ−ε)) / (2ε). Report relative errors.
Discussion
- Numerical stability (sigmoid/logistic loss, softplus/log-sum-exp, log1p, expm1, clipping).
- Initialization (He vs Xavier; biases).
- Activation choices (ReLU, tanh, sigmoid; pros/cons).
- Batch size and gradient variance; learning-rate scaling.

Deliverables

Clean, vectorized code for forward, loss, backward, training loop, and gradient check.
Short written derivations and notes on the topics above.

Quick Overview

Context

You will implement and analyze a minimal neural network for binary classification with one hidden layer. Assume a dataset with features X ∈ R^{N×D} and labels y ∈ {0,1}^N. The network has:

Hidden layer: H units with an activation (ReLU or tanh).

Output layer: 1 unit with a sigmoid for P(y=1|x).

Use vectorized NumPy (or similar) without autograd.

Tasks

Forward pass

Define shapes: W1 ∈ R^{D×H}, b1 ∈ R^{H}, W2 ∈ R^{H×1}, b2 ∈ R^{1}.
Compute z1 = XW1 + b1, a1 = f(z1), z2 = a1W2 + b2, p = σ(z2).

Loss (numerically stable)

Implement binary cross-entropy. Use a stable formulation (e.g., softplus: log(1+exp(x)) or log-sum-exp) to avoid overflow/underflow.

Backward pass (analytic gradients; no autograd)

Derive and implement gradients for W1, b1, W2, b2.

Optimization

Implement gradient descent updates for all parameters.

Gradient checking

Verify gradients by finite differences: g_num ≈ (L(θ+ε) − L(θ−ε)) / (2ε). Report relative errors.

Discussion

Numerical stability (sigmoid/logistic loss, softplus/log-sum-exp, log1p, expm1, clipping).
Initialization (He vs Xavier; biases).
Activation choices (ReLU, tanh, sigmoid; pros/cons).
Batch size and gradient variance; learning-rate scaling.

Implement and derive backprop from scratch

Quick Overview

Tiny Neural Network (From First Principles): Binary Classification

Context

Tasks

Deliverables

Solution

Comments (0)

Implement and derive backprop from scratch

Quick Overview

Tiny Neural Network (From First Principles): Binary Classification

Context

Tasks

Deliverables

Solution

Comments (0)