In a multi-class classification problem, given a model that outputs the probabilities of each class using softmax, how is the cross-entropy loss calculated when using one-hot encoding for the true labels, and how does this relate to precision and recall in evaluating the model's performance?

Cross-entropy loss measures the difference between predicted probabilities and actual classes, where one-hot encoding assigns a probability of 1 to the true class and 0 to others. Precision and recall are metrics used to evaluate binary classification only.

Cross-entropy loss is calculated by averaging the log probabilities of the predicted classes corresponding to one-hot encoded labels, and it directly influences precision and recall as they indicate the true positive rate and the accuracy of positive predictions.

Cross-entropy loss is irrelevant in multi-class settings as precision and recall are solely based on the confusion matrix, which ignores the predicted probabilities.

Cross-entropy loss provides no insight into model performance; precision and recall are sufficient to measure the model's effectiveness in a multi-class scenario.