Checklist USA-NA-AIO 2026 Round 1 · Task 7
Hand-Built Threshold MLP for a Triangle
Implement threshold and linear modules in PyTorch and set their weights by hand so that an MLP detects points inside a triangle.
The task
Problem 7 (30 points). Part 7.1 builds a threshold activation module My_Threshold. Part 7.2 derives the weight standard deviation σw that preserves variance through a linear transformation. Part 7.3 builds a linear module My_Linear initialised with that σw.
Part 7.4 (15 points) asks for a model My_Triangle, composed only of those two modules, whose weights and biases are set manually so that it outputs 1 for points inside the triangle with vertices (0, 0), (3, 1), (1, 5) and 0 otherwise. No training is performed and all parameters must have requires_grad set to False.
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
- A tensor of shape (B, 2).
- You submit
- A binary tensor of shape (B,).
- Rules
- Only My_Threshold and My_Linear modules may be used in My_Triangle.
- Inference only; no training.
- Format
- 2026 USA-NA-AIO Round 1, 30 January 2026 (date printed on the problem set). Individual, proctored.