ReLU forward pass

Tutor me on https://mlprep.iwase.dev/item/ml-screen-neural-networks-foundation-forward/. This is a screening item. If window.mlPrepAgent is available, read attempts for item ml-screen-neural-networks-foundation-forward before tutoring. Inspect my attempt, keep the item ID, and do not reveal the full answer first. After a real attempt, append its record with recorded_by agent, include agent_session_id when available, and read it back.

Problem

Let

z=Wx+b,\qquad h=\operatorname{ReLU}(z),\qquad \hat{y}=v^{\mathsf T}h+c,

with

W=\begin{bmatrix}1&-1\\-2&1\end{bmatrix},\quad b=(0,1),\quad x=(2,-1),\quad v=(2,-1),\quad c=\frac{1}{2}.

Compute $z$ , $h$ , and $\hat{y}$ .

Reveal answer or reference solution

The preactivation is

z=Wx+b=(3,-4).

Applying ReLU gives $h=(3,0)$ . Therefore,

\hat{y}=2(3)-1(0)+\frac{1}{2}=\frac{13}{2}=6.5.

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ReLU forward pass

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