[velcroscientist]

You're correct. As long as your test set remains within the training distribution, you can expect the NN to be well behaved. However, its behavior is undefined for testing data out of training distribution. There is a lot of work on detecting out of distribution inputs, regularizing NNs to follow a simple prior, etc. but the core problem remains because NNs learn from data. Extrapolation is something that symbolic systems do well, and NNs do not.

[killjoywashere]

Let's say I have an interesting problem, like classifying cancer from images. What are some classes of symbolic systems that can reason about types of cancer the system wasn't trained on? Even humans don't know what to do until they've seen it. And then, the grown up answer is "variance is infinite when N=1"