What we would like to describe is a method by which we can use a neural cellular automaton with added structure in the pattern displayed as it fires.
A neural cellular automata is a single neural network that contains the update rule for a grid of cells that could be represented as pixels or simply as generic cells.
Firstly our agent will take in the state from the environment and feed it to the NCA which then computes actions.
We will seek to impose added structure to the firing of the cellular automaton by grouping the cells in 12’s as in a chromatic scale and then assigning a frequency to each cell.
At time step t, all the frequencies of the cells that fire are combined and a reward for the NCA is calculated by considering the amount of consonance in this “chord”.
This is interesting because we expect that certain features will be associated with certain types of chords, and inversions of that chord will be related features related by some transformation. Similarly too for chord extensions and transpositions.
If we limit the part of the NCA directly responsible for outputs then the rest of it represents some sort of processing.
This is where the system starts to represent a type of TEM, tollum echeinbaum machine. These systems arrange features found in reality on a graph and predict the next feature based on the graph.
Our music group NCA possesses these features In a decoupled way because previously active cells determine the next as we move along the graph.
Another interesting exercise would be to have a NCA receive frames from videos of humans acting naturally or performing tasks from industry.
The NCA system will receive just the reward from consonance levels of chords and not from the environment.
Simultaneously, frames from videos of the untrained simulated agent will be shown to the same NCA but instead disharmony is rewarded.
This system resembles a GAN.
Finally we may now train a simulated agent by exposing the trained NCA to frames from the simulation and generating a reward conditioned on how consonant the cells in the NCA fire with.
It would seem that there would be a correspondence between frames that display correct behaviour firing with high consonance (like that of the human actors) and so we will be training the simulated agent to behave like them by rewarding it when it produces high consonance.
Another advantage to this is that we could use a suite of music generation algorithms, to encourage diversity in the NCA and generality.