#backpropagation

Continue with the pass/fail network $z^1 = W^1 x + b^1$, $a^1 = \mathrm{ReLU}(z^1)$, $\hat y = \sigma(W^2 a^1 + b^2)$, where

$W^1 = \begin{bmatrix} 0.5 & -1 \\ 1 & 0.5 \end{bmatrix},\quad b^1 = \begin{bmatrix} -1 \\ -1 \end{bmatrix},\quad W^2 = \begin{bmatrix} 1 & 2 \end{bmatrix},\quad b^2 = -1,$

$x = (2, 1)^\top$, $y = 1$, binary cross-entropy loss, so $z^1 = (-1, 1.5)$ and $\hat y = \sigma(2) \approx 0.8808$. After one gradient-descent step with $\eta = 0.5$, what is the new value of $W^1_{21}$ (row 2, column 1: the weight from input $x_1$ to hidden unit 2)? Give 4 decimals.