There are so many musical decisions you make while learning a piece, a lot of small ones too, like playing a specific note of the melody a millisecond after the bassnote for instance. How on earth do you remember all of those choices? I feel like I have to practice a piece for at least ten years to make all of those decisions and memorize them. Often I think, oh, that was beautiful, I want to play it like that every time. But if I don't repeat it immediately I just forget what I just did. And it's so much to remember, in every phrase there are ideas to memorize. How do you do that, memorize your own musical interpretation?
Memorize your own interpretation
Josephine As far as interpretation goes, I think there are several parts. Normally one starts with all the markings of the composer and sometimes there are an awful lot of those. I think you are mostly talking about what one does with those marking(because, for example, a composer's marking of forte is not some absolute dynamic level) or what one does that's not written in the score. Part of one's interpretation is intellectual which implies there are reasons for ones choices so those choices shouldn't be that difficult to remember and can also be marked in the score by the pianist. But sometimes, as I think you've said, one more or less accidentally does something without really planning it that seems to be particularly good. So then one has to figure out what one did that made the passage sound good and either remember it or mark it in the score.
Although it's not interpretive, sometimes my hand chooses a fingering that's better than the one I've been using and previously already marked in the score. If that happens I would usually immediately write it in the score because otherwise I might not remember it.
Josephine some of it, definitely write it in the score when it happens! But you can also study the music away from the piano to make decisions and the more you play it in your head, the more these decisions will solidify. Sometimes it takes me months to come to decisions about phrasing or pedaling and I have to think about it quite a lot and it really is a form of practicing your own interpretation away from the piano. If you do it enough, it will become memorized and "yours".
Josephine How on earth do you remember all of those choices?
I try to write those choices in the score, mostly using existing musical notation, but I have also invented my own one, which is this: °. It means that this note needs to be played softer than the note before. I find it more elegant than squeezing in a one-note-hairpin.
Sometimes also, I write those choices down in my notebook.
*
... feeling like the pianist on the Titanic ...
Josephine There are so many musical decisions you make while learning a piece, a lot of small ones too, like playing a specific note of the melody a millisecond after the bassnote for instance. How on earth do you remember all of those choices?
This is a fascinating question, and I think I have a different answer that might provide food for thought.
I find that once my interpretation "makes sense", it almost feels so "obvious" that it's hard to imagine it another way. So that doing it another way seems like more "effort" than doing it the original way. It's like a ball rolling down a hill following a certain trajectory, it goes along the path with a certain velocity according to gravity, and you feel it instinctively to the point where you don't think about it. That's what I find I usually use to remember details of my playing. I wonder if that makes sense, and if others can relate.
I should write things on the sheet music indeed, I never do that. Although I did use a red pencil for a while to add color to important things, until the pencil got lost. It didn't write down what I meant, it was more like 'pay attention here'. I can use different colors for different things maybe.
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pianoloverus or what one does that's not written in the score
Yes, that's what I meant. I like particular notes to sound a bit after the bass for instance, but sometimes so minimal that you almost don't hear it. Because it sounds natural, like singing. Sometimes it happens accidentally or maybe naturally because I have days my playing is suddenly much better, and it's all easier and feels better (only lasts for a moment unfortunately), and then you do something and think, this sounds good. But I'm afraid I will forget about it when my playing is worse the next day.
Maybe that's another question I have. A while ago something strange happened, my playing suddenly improved a lot after playing for an hour or something like that. My hands felt so different, everything was so much easier, the sound was much better. Not a small difference, it was quite a big difference. And the next day it was gone. I felt like it had been some sort of spell, like in a fairytale, that it was some sort of temporary gift that only lasted until midnight, and then my ability to play had dissappeared.
After a while it happened again. And now it happens every now and then, maybe once a week. And I can't replicate it. It just happens or it doesn't.
Is that progress, or not? Is it normal? Will it happen more often? Does someone recognize this, and if so, what happened after?
Josephine I think most people have days where they play better than on an average day. One should try to figure out why this is occurring although it may not be at obvious. It could just be your mental mood on that day. Or you might be doing something different technically but not be that aware of it. One advantage of having a live teacher is to discuss these things. But if one figures something out that makes a passage easier or sound better and is not sure when can remember it, then definitely write it down.
I recently had my first in person lesson with my normally online teacher 
I think that's why it improved. But indeed I have to figure out what it exactly is that I'm doing differently when it goes so much better.
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Josephine So the teacher gave you specific ideas that helped?
Josephine After a while it happened again. And now it happens every now and then, maybe once a week. And I can't replicate it. It just happens or it doesn't.
Is that progress, or not? Is it normal? Will it happen more often? Does someone recognize this, and if so, what happened after?
I think it's progress and the ability to be more free and relaxed when you play. At the initial stages you are so focused on getting the right notes and the details that it's hard to be relaxed. When the piece gets "under your fingers" it's almost like the piece plays itself! You can focus on the phrasing and it all comes naturally
pianoloverus So the teacher gave you specific ideas that helped?
Yes, but I think I also learned from seeing him play.
twocats I think it's progress and the ability to be more free and relaxed when you play. At the initial stages you are so focused on getting the right notes and the details that it's hard to be relaxed. When the piece gets "under your fingers" it's almost like the piece plays itself! You can focus on the phrasing and it all comes naturally
I was thinking about this, and also @ranjit 's post, and I realized that this probably didn't happen often before because I often choose pieces that are a bit too difficult, but it's getting easier now. I also started another piece today, one grade lower, to see what that will be like.