Frequently I see artificial neural networks compared by their "classification error rates" or "error rates", particularly for multi-class problems like CIFAR-10. What does this error rate actually refer to? Hamming loss? How is it calculated?
The error rate of any classifier is typically the proportion of classifications it gets wrong, i.e., the input is class A and the classifier determines that it's class B, B != A.
You count the number of datums where the output neuron corresponding to the true class is highest of all outputs of the softmax activation function. The proportion of that number to the total number of data is the classification rate. $100\%$ minus the value results in the error rate.