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.

I would add, the quote actually contains the definition, "fitting all the training examples... including noisy ones". So the training loss is zero. The comment "including noisy ones" implies the the data is generated by a process say
$y= f(x) + \epsilon$
Where $\epsilon$ represents noise. By fitting the model such that $y=f(x)$ for every training example even when $\epsilon$ is non-zero you are interpolating.
