Despite the whole "ineligible for an Oscar due to use of unoriginal classical music " thing, the score for Birdman made a lot of waves when people first heard it rumbling through the theater hallways.
Mexican jazz drummer Antonio Sanchez composed the score for his old friend Alejandro Iñárritu (you can watch an interview with Sanchez where he talks about their relationship and more here) first in New York and then in Los Angeles. The first time Sanchez recorded he didn't even have any visuals to go off of. Iñárritu wanted something raw and improvised, so he would describe a scene to Sanchez and then sit with his eyes closed and raise his hand when something in the scene would change (e.g. Riggan would open a door, turn a corner, greet someone, etc.).
Though the score was completely redone after the film was shot, those initial takes served as the basis of the sort of chaotic, staccato beats Iñárritu was looking for. In fact, Iñárritu thought the drums sounded too clean on the first take and had Sanchez dirty things up a bit so they sounded even more haphazard and disheveled.
Of course, the point of this sound is to mirror the state of Riggan's mind. The camera follows Riggan around for most of the film, giving us a window into his experience, and like the cinematography, the score also serves to give us a taste of the chaos Riggan endures as he wanders what Sanchez calls the "bowels of the theater," stuck in its claustrophobic hallways.
Sometimes, the drums themselves actually make an appearance in the movie. The first time is when Riggan and Mike take a walk on the street outside the theater. We hear the drums in the background but they slowly grow louder as the characters walk towards the drummer on the street before fading away when they enter the bar.
The second time is a bit odder—Riggan walks through the halls on his way to the opening night second act and sees the same drummer playing in some random room he passes. It's unlikely that this street drummer is actually hanging out in a theater—he's probably just a manifestation of Riggan's inner-turmoil. Although with this movie, nothing's certain.
Okay, maybe one thing's for certain: the next time we're super-stressed out, we're probably going to turn on the Birdman soundtrack.