Bad train, good test.

We start with very simple models, and we try to fit them. Turns out we don’t fit very well. The training data has bad error, and the test data also has bad error. That’s called underfitting. Now, as we get more complex models, things get better. The training error goes down, and the test error also goes down. And there’s a sweet spot, a Goldilocks regime in between, in which we have good fit. Now, if we keep going and make the model more complex, the traditional story is, what happens is the training error keeps going down, but the test error starts going up. And that’s called overfitting. And we’ve just talked through three regions: underfitting, overfitting, and good fitting. But it leads to a natural question: two times two is four, so what’s here? What our paper does is it gives it a name, calls it misfitting, a regime in which training error is bad and test error is good. And it turns out it’s not empty. In fact, this can happen, and sometimes it has to happen to generalize well.