The update rule of the perceptron learning algorithm is:

if $y^{(i)}$sign$(w_t^T{x}^{(i)}),$

then $w_{t+1}larr{w}_t+y^{(i)}{x}^{(i)}$

where is the coefficients at time step $t.$

Which of the following formulas is correct?

$y^{(i)}=w_{t+1}^T{x}^{(i)}$

$y^{(i)}=$sign$(w_{t+1}^T{x}^{(i)})$

$w_{t+1}^T{x}^{(i)}{y}^{(i)}{w}_t^T{x}^{(i)}{y}^{(i)}$

$w_{t+1}^T{x}^{(i)}{y}^{(i)}$