2025 USA-NA-AIO Round 2, Problem 1, Part 3

AI Olympiads 2025 USA-NA-AIO Round 2
1

Part 3 (5 points, coding task)

Do the following tasks:

Let x be a tensor with shape (N,2).

  1. What is the number of dimensions of model(x)?

  2. What is the shape of model(x)?

  3. Explain the reasoning of your answers.

2

\color{green}{\text{### WRITE YOUR SOLUTION HERE ###}}

  1. The dimension of model(x) is 2.

  2. The shape of model(x) is (N,1).

  3. For each sample, the output is a 1-dim tensor with shape (1,). Therefore, by having N samples, we get the answers above.

\color{red}{\text{""" END OF THIS PART """}}

3

The model takes in 2 input features to produce an output feature, so with a batch of size N, the shape of model(x) will be (N,1), making the number of dimensions 2.