2025 USA-NA-AIO Round 1, Problem 2, Part 7

AI Olympiads 2025 USA-NA-AIO Round 1
1

Part 7 (5 points, non-coding task)

This question follows Part 6.

Denote by \mathbf{W} \in \Bbb R^{hidden\_features \times input\_features} the transformation matrix from the input layer to the hidden layer.

Given input \mathbf{x} \in \Bbb R^{input\_features}, write down the formula of the output \mathbf{y} and its shape.

  • Reasoning is not required.
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\color{green}{\text{### WRITE YOUR SOLUTION HERE ###}}

\begin{align*} \mathbf{y} & = \mathbf{W}^\top \mathbf{W} \mathbf{x} \\ & \in \Bbb R^{input_features} . \end{align*}

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