Whenever we have a multiclass prediction the classifier generates a vector output. Per the definition of a Jacobian we are actually taking Jacobian steps towards a local minimum - so should it technically be called Jacobian Descent?
Although it is a multi-class classification problem, the loss is still a single number, not a vector.
We use cross entropy to convert a vector output to a single number.
This is a very good tutorial I suggest to read.
Here is an example from this tutorial: suppose we have 3 classes and 4 data points. The model output is
And the ground truth is
Cross entropy is
And final loss is sum of this length 4 cross entropy vector.