Multi-class loss functions, such as logistic loss, only apply to binary classification problems and are not suitable for multi-class classification tasks.

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Seekh · Accepted Answer

The claim is incorrect: logistic loss, also known as binary cross‑entropy, is designed for two classes, but it can be extended to many classes by using the softmax function and the categorical cross‑entropy loss. In a multi‑class setting each example gets a probability vector over all classes, and the loss sums the negative log of the correct class probability, which is exactly the same idea as binary logistic loss applied to each class separately. For instance, if an image belongs to class “cat,” the model outputs probabilities for cat, dog, and rabbit; the loss penalizes the probability assigned to cat and rewards higher values. This extension, called cross‑entropy or softmax loss, is widely used for tasks like digit recognition or language modeling. Thus, logistic loss is not limited to binary problems; it is the foundation for multi‑class loss functions.

Multi-class loss functions, such as logistic loss, only apply to binary classification problems and are not suitable for multi-class classification tasks.

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