I really wish people would define terms when using math. What is y? What is LLM(x)? Presumably it evaluates to some real number so that it can be fed to the logistic sigmoid function. If it is the logistic function, then why does beta going to infinity matter? It seems to just collapse the output of the sigmoid function to 1 and make the value of LLM(x) meaningless instead of their claim that it recovers the LLM classifier. What is the function I()?

Maybe these are well understood terms in some field? Maybe I'm just lost?