It was your second example:
8,6
9,8
13,9
11,13
10,11
And I can choose to use between 100 and 3000 training samples
Ok, without thinking much about it, I see a few issues.
First, your belief that the order of the samples matters--for your setup.
I've stated before that my thinking on machine learning is not based upon only academic papers and education. I think outside of the box.
That said, I believe I've read where order will always matter. My opinion is that order
should only matter when the NN is designed in a way such that the order matters. I don't offer papers or formulas etc. to support this, only a simple thought experiment.
(The purported fact that order matters
when it shouldn't, imo, is a flaw with NN's in general, imo; or a flaw in the particular platform, imo; or a flaw in design, imo.)
Suppose you are a NN. I give you the following samples to learn:
3,9
4,16
5,25
6,36
7,49
Then, I ask you, what is the output when the input is 8?
Then, I reverse the order, and have you relearn:
7,49
6,36
5,25
4,16
3,9
Then, I ask you, what is the output when the input is 8?
Then, I ask you, did your answer change because the order was reversed.
Then, I ask, why would someone even expect it to change? Why didn't it change?