If , then for every , replacing by and by leaves each exponent unchanged. The same choices therefore cannot identify both an unrestricted value scale and inverse temperature. Fixing a value scale or adding independent measurements is needed to break this equivalence.
Adding the same scalar-valued function of the input to every class logit leaves all softmax probabilities unchanged. A reference-class constraint removes this common-shift non-identifiability.
For one-hot label and predicted class probabilities , categorical cross-entropy is , the negative categorical log-likelihood.
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The Softmax function is a mathematical function that converts a vector of real numbers into a probability distribution. It is commonly used in machine learning and statistics, particularly in the context of multiclass classification problems. The Softmax function is often applied to the output layer of a neural network when the task is to classify inputs into one of several distinct classes.