Is there a study of "smooth"/"stable" "AI" algorithms - i.e. if you feed them input that is "close" then then the output is also "close"? (smooth as in smoothly

Is there a study of "smooth"/"stable" "AI" algorithms - i.e. if you feed them input that is "close" then then the output is also "close"? (smooth as in smoothly differentiable/stable as in stable sorted)