Compute the Gradient $[1]$

y$=\backslash$sigma $($wx $+$ b$)=\backslash$sigma $(2\mathrm{.}03\mathrm{.}52\mathrm{.}0)0\mathrm{.}0180$

$$wL $=($y $$ y$)$ x $=(0\mathrm{.}01800\mathrm{.}5)3\mathrm{.}50\mathrm{.}493$

$$bL $=$y $$ y $=0\mathrm{.}01800\mathrm{.}50\mathrm{.}482$

$$ Update Moving Averages $[2]$

sW $=\backslash$beta $$ sW $+(1\backslash$beta $)($wL$)$

$2=0\mathrm{.}900+0\mathrm{.}10(0\mathrm{.}493)20\mathrm{.}0243$

sB $=\backslash$beta $$ sB $+(1\backslash$beta $)($bL$)$

$2=0\mathrm{.}900+0\mathrm{.}10(0\mathrm{.}482)20\mathrm{.}0233$

$$ Update Weights and Biases $[2]$

w $=$ w $+$

$\backslash$eta

$$

sW $+$

$$wL $=2\mathrm{.}0+$

$0\mathrm{.}10$

$$

$0\mathrm{.}0243+1$e $8$

$(0\mathrm{.}493)2\mathrm{.}0482$

b $=$ b $+$

$\backslash$eta

$$

sB $+$

$$bL $=2\mathrm{.}0+$

$0\mathrm{.}10$

$$

$0\mathrm{.}0233+1$e $8$

$(0\mathrm{.}482)2\mathrm{.}0471$

$($b$)$ No marks for equations

$$ Forward Pass $[1]$

h $=\backslash$sigma $($w$1$x$1+$ w$2$x$2+$ b$)=\backslash$sigma $(0\mathrm{.}73\mathrm{.}5+0\mathrm{.}20\mathrm{.}5+0)0\mathrm{.}927$

$$ Compute the reconstructed outputs $[1]$

x$1=$ h $$ w$3+$ b $=0\mathrm{.}927(0\mathrm{.}2)=(0\mathrm{.}1854)$

x$2=$ h $$ w$4+$ b $=0\mathrm{.}9270\mathrm{.}5=0\mathrm{.}4635$