[choxi]

You're correct in a way, you can think of neural nets "remembering" the data set they're trained on. Recurrent neural nets even explicitly have a "feedback loop" like you're referring to that allows them to "remember" previous samples. An example of that is in natural language processing where you want to be able to remember the previous words in a sentence to interpret the current word.

Remembering the previous words in a sentence you're currently reading is more like short term memory though, and this paper is talking about long term memories stored as data structures outside of the neural net itself. This graphic from the DeepMind blog post might be helpful: https://i.imgur.com/KwXXCge.png.

The blog post from DeepMind is a bit more accessible than the Nature paper: https://deepmind.com/blog/differentiable-neural-computers/