Mathematically, it is literally a probability distribution, because it fits the definition of a measure whose total mass is one, so I think the language is just imprecise. What they may be trying to say is that semantically it doesn't arise in a principled way from an uncertainty model, such as from Bayesian or frequentist statistics.
replyThe comment in parenthesis mentions "they're not derived from a probability space" [1]. I don't know about probability spaces nor softmax to know what part of a probability space this is missing compared to other probability distributions, nor how other probability distributions satisfy probability spaces.
replySounds like they're saying that since the distribution doesn't come from measuring or calculating the probability of something, it has the form of a probability distribution but isn't really one. Like saying 5 feet is a height that a person can have, but since I just made up that number it's not actually a person's height.
replyiirc, there is a bunch of formal
machinery you need to define probability distributions for situations such as infinite outcomes (eg what is the probability that a random real number between 0 and 10 is less than 3?)
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