/m154: Yes, Viterbi assumes the weights are given. However, these weights are updated by each step of the perceptron. In each epoch through the training data, when you run Viterbi on example i+1, you need to use the weights updated based on example i.

Running Viterbi on every example only at the beginning of each epoch might conceivably work. This would be an interesting experiment to try. To get a useful answer, you would have to adjust the learning rate separately for each method.