Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 218 / 4 / a / Solution

Encode the two classes by the standard basis vectors of ${\mathbb{R}}^2$. With rectified linear unit $r(t)=\max (t,0)$ applied coordinatewise and softmax function $s_j(z)=e^{z_j}/{\sum }_k{e}^{z_k}$, the fitted feedforward neural network iswhere $W_1\in {\mathbb{R}}^{40\times 40}$, $b_1\in {\mathbb{R}}^{40}$, $W_2\in {\mathbb{R}}^{20\times 40}$, $b_2\in {\mathbb{R}}^{20}$, $W_3\in {\mathbb{R}}^{2\times 20}$, and $b_3\in {\mathbb{R}}^2$. The number of trainable parameters is