#binary-cross-entropy

The output unit of a pass/fail network computes $z^2 = W^2a^1 + b^2$ and $\hat y = \sigma(z^2)$, and it is trained with binary cross-entropy. For one student the hidden activations are $a^1 = (2, 0)^\top$ and the current parameters are $W^2 = (0.4,\ -0.6)$ and $b^2 = -0.8$, so $z^2 = 0$ and $\hat y = 0.5$. The student failed ($y = 0$). After one gradient-descent step with $\eta = 0.1$, the first weight is , the second weight is and the bias is .