Softmax

The softmax function is a mathematical function that transforms a vector of raw scores, known as logits, into a probability distribution. Given a vector z of logits, the softmax function is defined as: softmax(z_i) = exp(z_i) / Σ(exp(z_j)), where the summation is over all elements in the vector z. This function is particularly useful in multi-class classification problems, where it ensures that the output probabilities sum to one, thus allowing for interpretation as probabilities. The softmax function is commonly employed in neural networks, especially in the final layer of models designed for classification tasks and in language models (LMs). It is closely related to concepts in statistical mechanics and information theory, as it can be viewed as a form of the Gibbs distribution. The differentiability of the softmax function also allows for the application of gradient descent optimization techniques, facilitating the training of deep learning models.