Categorical cross-entropy is the standard loss function for classifying into several mutually exclusive classes. It compares the distribution the network predicts, usually after a softmax, with the true label written in one-hot format, and it penalises heavily any low probability assigned to the correct class.
The Softmax function converts a vector of logits (arbitrary values) into a probability distribution where every value is positive and the values sum to exactly 1. It is the standard output-layer activation for multi-class classification, and the final operation language models use to predict the next token.
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