[ghkbrew]

Sounds 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.

[jmalicki]

The soft max is the probability of the next token being whatever in the training data conditioned on the inputs. The author just doesn't know that apparently and thinks it was an arbitrary choice.

The author's essay on the sigmoid similarly lacks the deep understanding that it comes from somewhere and isn't an arbitrary choice.

[canjobear]

The softmax, after the network has been trained, yields an estimate of the probability in the training data, but it is not that probability itself.

[jmalicki]

Which models are not trained with the log softmax as the loss function?

[canjobear]

Softmax isn't a loss function. It is used to transform model outputs into positive numbers that sum to 1, so that they can be interpreted as probabilities, and then those numbers are passed into (typically) the cross entropy loss function. I think you mean, which models are trained using some function other than softmax to transform the model outputs. There are a number of alternatives to softmax, such as the ones described here https://www.emergentmind.com/topics/sparsemax

[jmalicki]

The cross entropy loss function is softmax. They are one and the same.

[canjobear]

They’re not. Cross entropy loss is E[-log q] where q is a probability. You could convert the model outputs x into probabilities using some other function like q = 1/Z x^2, and compute cross entropy loss just fine.

[mojosmojo]

iirc, 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?)