I have very similar experiences to the ones described by @
sweetgingerpeach and @
Absurd. Once I learned about Si, I kind of associated my memory with that function... (don't know if correctly, but the idea seems to work).
I'm like a sponge, people sometimes get surprised or joke around with me and "test" me - how do you remember that? I just do. I need to pay attention to what is going on around me or what someone is saying or what I'm reading and that's it. In high school I just needed to be present in class and then maybe quickly browse through the notes to get top scores in the test the next day.
Long term is a bit tricky though. I can accumulate lots & lots of info I consider bs and still score well in a test, but like @
sweetgingerpeach said, it kind of washes out of my memory quite soon later on (although "refreshing" does bring it back after some time). When it comes to stuff that interests me, I tend to remember it long term fairly easily, and if it's a long time between the events of me using it, then I don't need to "refresh" it as much, it's more like a trigger or dragging out a spaghetti, the longer I drag, the more I remember, lol.
That being said, while it helped tremendously at high school/academia, this kind of memory is a bitch irl sometimes. I remember a ton of trivia about people (it proved useful for gift-giving) as people are my "interest" I guess... But when something bad happens and scars me emotionally, I remember it all too well for the longest time and need to make a conscious effort not to replay it in my head. Let's say smn I value was nasty to me. I'll probably remember it for the rest of my life and be able to recall it with all the facial expressions, exact words, tone of the voice, time of the day, lighting in the room, blah blah blah. I might forgive from the depth of my heart and/or I actually might not care about the person anymore, but despite wanting to - I won't forget. This makes finding ways to make good memories quite vital, cause then I can consciously push the bad memory out of my focus and concentrate on some good memory. It's pointless clinging to old bad memories, but the void after pushing one out of the picture needs to be filled with sth good, otherwise the bad one just comes back like a boomerang and steals attention.
Also, I've been told by an ILE that sometimes smells trigger his memory, same happens with me, but it seems that while our memory works similar sometimes, his "sponge-like" capabilities are much weaker and I guess it's consistent with Si being his 4th function and my 1st... hm. He needs to understand in order to remember (so maybe more of Ti usage for memorising? or Si-Ti combo?) and I can memorize without understanding. Although when it comes to maths etc. obviously I need to understand too if the memory's supposed to turn into knowledge to build on (so I guess then I employ Ti, too).
TL;DR - imho Si is probably the function associated with the sponge-like memory. Si-Ti combo would be responsible for learning via remembering & understanding (so logical subjects when recalling data is not enough). Hmm?