Checklist ROAI 2024 County Stage · Task 1
Problem 1
Romanian title: Problema 1
Show, theoretically or empirically, which functions small ReLU multilayer perceptrons can and cannot represent relative to each other.
The task
The problem studies what ReLU multilayer perceptrons can represent. Question 1.1 asks whether MLP1 (Linear(2,4) → ReLU → Linear(4,1) without bias) can represent every function learned by MLP2 (Linear(2,3) → ReLU → Linear(3,1)), to be shown either theoretically or through experiments on a chosen dataset.
Question 1.2 asks for the opposite direction and then whether the single-hidden-layer MLP4 (Linear(1,5) → ReLU → Linear(5,1)) can express every function implemented by the two-hidden-layer MLP3 (Linear(1,3) → ReLU → Linear(3,2) → ReLU → Linear(2,1)), with hints based on the geometric view of ReLU units and linear layers.
Abridged and translated by SOTA from the official Romanian materials. The official statement has the exact rules, and it wins wherever this summary differs.
At a glance
- You get
- The problem document only (PyTorch model definitions and diagrams).
- You submit
- Answers justified theoretically or empirically; the document does not specify a submission format.
- Scoring
- Not stated in the document.
- Rules
- 4-hour test, common paper for all grades (per the stage page)
- Format
- ROAI 2024 county stage, 28 June 2024, held at UB, UBB, UAIC and UVT; the top 20 overall qualified for the national stage.