>but that's still far better than a black box ML model that doesn't give you guarantees that similar inputs will lead to similar outputs (there's a mathematical

>but that's still far better than a black box ML model that doesn't give you guarantees that similar inputs will lead to similar outputs (there's a mathematical formalism to this whose name escapes me now). You might be thinking of the K-lipschitz-smoothness or K-lipschitz-continuity of a model for a given norm, i.e. $\Vert f(x)-f(y)\Vert \leq K \Vert x-y\Vert$. A guarantee that K is smaller or equal a certain value is called a Lipschitz certificate . We can by now give this type of guarantee in balls around the training data (coming out of Adversarial example research), but with some limitations and generalization of Lipschitz certificates to test data and/or other norms is pretty bad in general. I personally think that the term "black box ML model" needs to die with respect to neural networks, the theory work being done has pried open that box sufficiently by now that we can start reasoning about them somewhat. People just generally don't like the answers because it unveils limitations or challenges