Checklist USA-NA-AIO 2026 Round 1 · Task 4
Derivative of tanh and a Vectorised MSE Gradient
Differentiate tanh by hand and implement the gradient of a mean-squared-error loss in NumPy without loops.
The task
Problem 4 (20 points). Part 4.1 (5 points) asks for d tanh(x)/dx with reasoning. Part 4.2 (15 points) asks for a function my_fun_derivative(X, y, theta) that returns the gradient with respect to theta of (1/N) Σ_n (y[n] − theta^T X[n])^2 as an array of shape (d,).
Abridged by SOTA from the official materials. The official statement has the exact rules, and it wins wherever this summary differs.
At a glance
- You get
- NumPy arrays X (N, d), y (N,), theta (d,).
- You submit
- A NumPy array of shape (d,).
- Rules
- No additional imports; no PyTorch autograd; no np.linalg methods, @ or .T; no loops. Violations score 0.
- Format
- 2026 USA-NA-AIO Round 1, 30 January 2026 (date printed on the problem set). Individual, proctored.