this is a homework question that I need some help with. PM me or something if you think I should take this question down
So I have the objective functionand the loss function of a multi-class svm.
I am asked about the gradient descent $\frac{\partial L((\omega_1,....,\omega_k), (x,y))}{\partial \omega_{j,l}}$ in the conditions where
$\hat{y} = argmax_{y'\neq y}\omega_{y'}^T x$
$\omega_{j,l}$ is the lth entry in $\omega_{j}$ and
$x_l$ is the lth entry in x
when
1) $\omega_y^T x < \omega_\hat{y}^T x + 1$
2) $\omega_y^T x < \omega_\hat{y}^T x + 1$ and j = y
3) $\omega_y^T x < \omega_\hat{y}^T x + 1$ and j = $\hat{y}$
4) $\omega_y^T x < \omega_\hat{y}^T x + 1$ and $j \neq y$ and $j \neq \hat{y}$
Just don't understand why these four conditions would matter, and how I should approach this question?