From the paper [To understand deep learning we need to understand kernel learning][1], two questions:

In section 2 "Setup" there appears a definition of *interpolated classifier* as an algo that has zero or close to zero training error and *overfitted* as an algo "if the same holds for classification loss". 

Question 1: what is the mathematical definition of these two types of classifiers? Was thinking that an overfitting algo here could mean an algo that has zero or near zero *test* error (i.e. generalization error). 

The authors then go on to state that in their definitions an interpolated classifier is necessarily an overfit classifier.

Question 2. In section 4, does the *t-overfits the data* definition depend on a fixed training set? I.e. do they mean t-overfit a *fixed* but arbitrary training dataset?


  [1]: https://arxiv.org/abs/1802.01396