loubbrad

The author does define these terms implicitly at the beginning of §1, where they define standard MHA in this notation. From the formula, (q_t) is the query generated from the hidden state at the (t)-th position (e.g. the token at position (t)), (k_i) is the key for the token at the (i)-th position, (o_t) is the (vector) attention output for the (t)-th position, etc. (S) is then defined later as the sum of the outer products of (k_i) and (v_i) over all positions up to (t). However, I do agree with you that it would not hurt to make this more explicit.

> I think there is a section of programmer who actually do like the actual typing of letters, numbers and special characters into a computer...

Reminds me of this excerpt from Richard Hamming's book:

> Finally, a more complete, and more useful, Symbolic Assembly Program (SAP) was devised—after more years than you are apt to believe during which most programmers continued their heroic absolute binary programming. At the time SAP first appeared I would guess about 1% of the older programmers were interested in it—using SAP was “sissy stuff”, and a real programmer would not stoop to wasting machine capacity to do the assembly. Yes! Programmers wanted no part of it, though when pressed they had to admit their old methods used more machine time in locating and fixing up errors than the SAP program ever used. One of the main complaints was when using a symbolic system you do not know where anything was in storage—though in the early days we supplied a mapping of symbolic to actual storage, and believe it or not they later lovingly pored over such sheets rather than realize they did not need to know that information if they stuck to operating within the system—no! When correcting errors they preferred to do it in absolute binary addresses.

Multi-track transcription has a long way to go before it seriously useful for real-world applications. Ultimately I think that converting audio into MIDI makes a lot more sense for piano/guitar transcription than it does for complex multi-instrument works with sound effects ect...

Luckily for me, audio-to-seq approaches do work very well for piano, which turns out to be an amazing way of getting expressive MIDI data for training generative models.

I agree that the audio->score and MIDI->score problems are quite hard. There has been research in this area too, however it is far less developed than audio->MIDI.

When I was studying Mathematics I initially thought TDA was magic. I remember seeing MATLAB correctly compute the Homology groups of a Torus from a randomly sampled point cloud. As I veer farther into the CS/ML world I've come to appreciate that most of the advertised practical applications of higher Mathematics are quite niche. Having said that, Algebraic Topology is still one of my favorite areas of Mathematics from a purely mathematical viewpoint.