This makes me think of what a probabilistic version of defining this extrapolation procedure would look like. It seems like you could very easily give something a bunch of labeled data in a region with high confidence, and it could extend this with progressively lower confidence as you extrapolate more, with no paradoxes. The problem entirely seems to come from the fact that the generalizer’s guesses are treated as just as good as the original examples in every way.
This makes me think of what a probabilistic version of defining this extrapolation procedure would look like. It seems like you could very easily give something a bunch of labeled data in a region with high confidence, and it could extend this with progressively lower confidence as you extrapolate more, with no paradoxes. The problem entirely seems to come from the fact that the generalizer’s guesses are treated as just as good as the original examples in every way.