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Per page 7 of this MIT lecture notes, the original single-layer Perceptron uses 0-1 loss function.
Wikipedia uses
$${\displaystyle {\frac {1}{s}}\sum _{j=1}^{s}|d_{j}-y_{j}(t)|} \tag{1}$$
to denote the error.
Is the formula (1) the correct form of 0-1 loss function?
sign) that does not quantify the predictions, but only says whether they were correct or not, so you cannot optimize it using gradient descent. Therefore, it is not a loss function in the usual sense. There is a loss function if your activation is differentiable. For instance, sigmoid. Then, the loss will be binary cross-entropy. $\endgroup$