Transformations

One of the functions the music AI needs is the ability to compose new phrases. How would it go about this?

One strategy would be completely “de novo” composition, just randomly generating a sequence of notes. However, this is very unlikely to yield beautiful music. So we will eschew this strategy.

Another strategy would be “de novo” synthesis from concepts. We take an existing phrase concept, and randomly synthesize a phrase which satisfies that concept. This strategy is likely to do reasonably well.

A third strategy would be mutation of existing phrases. We take a good phrase, and modify it slightly. There are two obvious ways we could do phrase mutation: preserving concepts, and mutating concepts. In the first case, we mutate the phrase while keeping its concepts the same. In the second case, we mutate the concepts along with the phrase. (First we mutate the concepts, then we mutate the phrase.)

Are these all of the possible mutation strategies? No. In AI, a good rule is: never say, “the only options.” There is always another way to do something. Only the closest other way may be a large inferential distance away from the ideas we already have. In that case we can say, “the only obvious options.” And I think that these phrase mutation strategies are the only obvious options.

Besides phrase mutations, we also need concept mutations — because concepts are supposed to evolve. So we can ask the general question, “how do we mutate these data structures?”

An open-ended strategy would be as follows. For a data structure we wish to mutate, we define a set of transformations: i.e., functions over the data structure. Then to mutate a data structure, we simply apply a series of transformations. When a transformation takes more than one data structure as an argument, we can call it a “combination.” An example of a phrase combination would be, “sequentially concatenate these phrases.”

We have the option to evolve the set of transformations. This process would use the same fitness metrics as concept evolution: simplicity, usefulness, distinctiveness. (“Usefulness” is how likely the transformation is to yield a good data structure, when it is applied.)

Of course, to do that, we need to define a set of transformations over transformations. So at some point, the obvious option is to have a fixed set of transformations for the more “meta” data structures.

We need transformations over all of the things that we want to evolve. The things that we want to evolve include:

* Phrases.
* Phrase concepts.
* Phrase transformations.

So we have an evolved set of phrase transformations, and fixed sets of transformations for concepts and phrase transformations.

A fixed set of transformations seems potentially limiting. But I think the only thing it affects is how quickly the AI comes up with good new ideas; it couldn’t absolutely prevent the AI from coming up with any given idea.

At least, that is true if the set of transformations is “complete.” A set of transformations over a data structure A is “complete” if, for every a and b in A, there is some sequence of transformations which turns a into b. When we have fixed sets of transformations over data structures, we will want those transformation sets to be provably complete.

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