- the instrument
- the room or hall
- their personal experiences
- their personal philosophy of music (e.g., Gould and his anti-hedonistic philosophy)
- cultural norms and explicit respect paid thereof (e.g., in the interpretation of a Chopin mazurka)
- available recording technology and expertise
- available audio engineering technology and expertise
- what emotion they want to invoke or evoke to contextualize the music
- their patience
- their willingness to experiment
- etc.
It is not at all farfetched that a performer is taking most of these into account, directly or indirectly, to render a live or recorded performance.
It's not as if there's just this tradition of unwritten rules about interpreting a score that music students learn from their teachers, rather, it's that an interpretation is an amalgamation of experience, context, and on-the-spot reactive decision-making.
For an AI to successfully achieve this, they'll need the same variety of inputs and contexts to learn from.
This is why the act of playing music by a human is called a "performance", an "interpretation" in some languages. The musician is not just playing a score exactly as it is written, the musician gives a part of his/her into the act and make the music his/her own to make art.