K is a placeholder for the number of additional dimensions your output and target have.
In a simple classification use case, K would be 0, which means:
-
output = [batch_size, nb_classes],target = [batch_size]
In the case of K=1, e.g. for a temporal signal, where each sample belongs to a specific class:
-
output = [batch_size, nb_classes, seq_len],target = [batch_size, seq_len]
For a segmentation use case:
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output = [batch_size, nb_classes, height width],target = [batch_size, height width]
…
As you can see, K simply indicates the dimensionality of your current use case and how the output and target should look like.