Patching up an artificial neuron in Pure Data Vanilla for some nonlinear mixing. There’s no talking on this one, just building the patch, and listening to it go.
An artificial neuron is basically just a mixer: inputs come in, and are weighted differently, modelling the dendrites of a biological neuron; then the mixed signal is transformed by an “activation function”, usually nonlinear, and output, modelling the axon.
Now, we can say that “learning” occurs when we adjust the weights (levels) of the inputs based on the output, but let’s not do that here, let’s just revel in our our nonlinear mix.
Recently, I’ve been hooked on the idea of neurons and electronic and digital models of them. As always, this interest is focused on how these models can help us make interesting music and sound design.
It all started with my explorations into modular synths, especially focusing on the weirdest modules that I could find. I’d already spent decades doing digital synthesis, so I wanted to know what the furthest reaches of analog synthesis had to offer, and one of the modules that I came across was the nonlinearcircuits “neuron” (which had the additional benefit that it was simple enough for me to solder together on my own for cheap).
Anyway, today, I don’t want to talk about this module in particular, but rather more generally about what an artificial neuron is and what it can do with audio.
I wouldn’t want to learn biology from a composer, so I’ll keep this in the most simple terms possible (so I don’t mess up). The concept here is that neuron is receives a bunch of signals into its dendrites, and, based off of these signals, send out its own signal through its axon.
Are you with me so far?
In the case of biological neurons these “signals” are chemical or electrical, and in these sonic explorations the signals are the continuous changing voltages of an analog audio signal.
So, in audio, the way we combine multiple audio source is a mixer:
Now, the interesting thing here is that a neuron doesn’t just sum the signals from its dendrites and send them to the output. It gives these inputs different weights (levels), and combines them in a nonlinear way.
In our sonic models of neurons, this “nonlinearity” could be a number of things: waveshapers, rectifiers, etc.
In the case of our sonic explorations, different nonlinear transformations will lead to different sonic results, but there’s no real “better” or “worse” choices (except driven by your aesthetic goals). Now, if I wanted to train an artificial neural net to identify pictures or compose algorithmic music, I’d think more about it (and there’s lots of literature about these activation function choices).
But, OK! A mixer with the ability to control the input levels and a nonlinear transformation! That’s our neuron! That’s it!
In this patch, our mixer receives three inputs: a sequenced sine wave, a chaotically-modulated triangle wave, and one more thing I’ll get back to in a sec. That output is put through a hyperbolic tan function (soft-clipping, basically), then run into a comparator (if the input is high enough, fire the synapse!), then comparator is filtered, run to a spring reverb, and then the reverb is fed back into that third input of the mixer.
Now, as it stands, this neuron doesn’t learn anything. That would require the neuron getting some feedback from it’s output (it feeds back from the spring reverb, but that’s a little different) Is the neuron delivering the result we want based on the inputs? If not, how can it change the weights of these inputs so that it does?