What would it mean to ask what is societies loss function?
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A loss function is to determine how far off you were from the correct answer and use that to train the model by adjusting the weights.
A society does not have a loss function, it does not even have a correct outcome or numerical value.
When a neural network makes a mistake, or even when it guesses mostly correctly but is less confident than it should have been, the loss function is a fancy way of figuring out which parts of it were responsible for the error, and which were not, and then changing them slightly so that it will be less wrong the next time it sees that problem or similar ones. Neurons and connections which contributed to the mistake become weaker and less influential in the future, while neurons and connections which pushed towards the correct answer get strengthened.
It is a technical term in machine learning, it doesn’t formally apply to things outside of that context. But maybe if we’re being creative you could sort of think of it as a blame assignment mechanism and treat humans in society, at least people in authoritative positions who make decisions, as being analogous to neurons. Then a “loss function for society” would be the mechanisms by which we assign blame to people when things go wrong and, more importantly, update to make fewer in the future: ie firing people for messing things up and hiring/promoting people who do things well.
I don’t think this is standard language that people use to describe this process, and the parallels only go so far, but it is a kind of interesting analogy.
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