What does interpolating the training set actually mean? I just read this article: Understanding Deep Learning (Still) Requires Rethinking Generalization
In section 6.1 I stumbled upon the following sentence

Specifically, in the overparameterized regime where the model capacity
greatly exceeds the training set size, fitting all the training
examples (i.e., interpolating the training set), including noisy ones,
is not necessarily at odds with generalization.

I do not fully understand the term "interpolating" in the context of fitting training data. Why do we speak of "interpolation" in this context? What does the term exactly mean here? Is there any other term that can be used instead?
In my understanding interpolation means the prediction within the training domain for some novel input that was not part of the training set.

Apart from literal meaning of interpolation, this is related to  something called deep learning models totally memorize the training data. Hence, both interpolating and memorisation in this paper/context means zero training loss but still not overfitting on the test set. Hence the curious phenomena, that normally we would call an overfitting (overtraining actually), which is not resolved yet.
