[uuwp]

The same way we feed the variable size sequence of characters or sound samples into this RNN. Instead of raw samples at the 16 kHz rate, we'll have one sequence of 1 sample per second, another sequence of 1 sample per 0.5 seconds and so on. We can go as far as 1 sample per 1/48000 sec, but I don't think it's practical (but this is what these music generators do).

[p1esk]

What do you mean by “sample” when you say “sequence of 1 sample per second”?

[pdxww]

We can think of a ML model that takes 1 second of sound as input and produces a vector of fixed length that describes this sound:

S[0..n] = the raw input, 48000 bytes per second of sound F[1][k..k+48000] -> [0..255], maps 1 second of sound to a "sound vector". F[2][k..k+96000] -> ..., same, but takes 2 seconds of sound as input

Now instead of the raw input S, we can use the sequences F[1], F[2], etc. Supposedly, F[10] would detect patterns that change every 10 seconds. It's common in soundtracks to have some background "mood" melody that changes a bit every 10-15 seconds, then a more loud and faster melody that changes every 5 seconds and so on, up to some very frequent patterns like F[0.2] that's used in drum'n'bass or electronic music in general.

This is how music is composed by people, I guess. Most of the electronic music can be decomposed into 5-6 patterns that repeat with almost mathematical precision. The artist only randomly changes params of each layer during the soundtrack, e.g. layer #3 with a period of 7 seconds slightly changes frequency for the next 20 seconds, etc.

Masterpieces have the same multilayered structure, except that those subpatterns are more complex.

[p1esk]

We can think of a ML model that takes 1 second of sound as input and produces a vector of fixed length that describes this sound

You mean like an autoencoder?

Ok, assuming we have those sequences (F1, F2, F10, etc), how would you combine them to train the model?

[pdxww]

I'm not an ML guy, so can't say if this is an autoencoder.

We can combine multiple sequences in any way we want. Obviously, we can come up with some nice looking "tower of lstms" where each level of that tower processes the corresponding F[i] sequence: sequence F1 goes to level T1 which is a bunch of LSTMs; then F2 and the output of T1 go to T2 and so on. The only thing that I think matters is (1) feed all these sequences to the model and (2) have enough weights in the model. And obviously a big GPU farm to run experiments.

[p1esk]

Ok, but if we are using a hierarchical model like multilayer lstm, shouldn’t we expect it to learn to extract the relevant info at multiple time scales? I mean, shouldn’t the output of T1 already contain all the important info in F2? If not, what extra information do you hope to supply there via F2?

[pdxww]

T1 indeed contains all the info needed, but T1 also has limited capacity and can't capture long patterns. T1 would need to have 100s of billions weights to capture minute long patterns. I think this idea is similar to the often used skip connections.