Fully Connected Neural Network

Fully Connected Neural Network

The Network Instrument – a work in progress

This post summarizes my current thinking on the Network Instrument, a lot of which is in flux. It is derived from a document I’ve been writing where I have outlined these ideas and have been more or less working them out in practice.  As I continue to explore these ideas expect a lot of the material here to change and develop. I haven’t really done any sort of systematic analysis of other electronic setups (beyond what I reference below of David Tudors), this really is more of an attempt to generalize what I’ve been doing then an attempt to create a pedagogy of Live Electronics (as much as I think this needs to be done).  I think it would take real research to do that, something that would require the ability to work on it near full time. Alas not something I can do what with a demanding day job, musical practice and a wide amount of interests. I’ll keeping work on this  document as I go and perhaps occasionally updating this post or adding new ones.

There were really three major developments that led toward this conception of an electronic instrument. The first would of course be the musical practice I’ve been involved with for the past ten years or so. When I worked with electronics I almost always worked intuitively, connecting things together, experimenting basically until I would get a configuration that I found interesting.  I ‘ve long referred to this as state exploration which is more or less referencing finite state machines, which are also networks (see directed graphs for the mathematics behind a lot of these notions).   In that context a state was a particular network configuration and the exploration aspect was permuting it until it shifted states.  The electronics of David Tudor would be the next major influence on this way of thinking. His large tangles of devices, layers of feedback and cascading amplification would certainly be a form of network though without really getting a chance to examine particular setups it is hard to really classify them. But looking at the existing diagrams of his networks a number of them would fall into my category of a Feedforward Network. Of his work most importantly conceptually though was the Neural Network Synthesizer which would be an example of a highly connected network though a bit more literal then what I’m describing here.  When I was in college Artificial Intelligence was what I spent the bulk of my time studying and at that point in time Neural Networks were all the rage.  I’ve programmed more than my fair share of them, exploring the wide variety of networks and their various features and behaviors (of interest to perhaps some, I was actually studying these during the time the Neural Network Synthesizer was developed and while I didn’t end up stumbling onto Tudor at that time I do remember interest in those chips and hardware being made from them).   It was this experience combined with the above that really got me thinking of the electronics configurations in ways that I hadn’t before.

Neural Synthesis Nos. 6-9Tudor’s Neural Network Synthesizer is a direct application of neural networks to music making which is quite interesting and is something that should perhaps be explored further (see this) but the Network Instrument is more of an attempt to understand something, a metaphor a certain practice. Live Electronics really is almost folklore and there has been little attempt to codify concepts and ideas and what has been done is in scattered journals and often out of print books. A lot of wheels are being reinvented due to an increased interest in live electronics from a handmade/diy/maker/hacker perspective.  The noise, eai, underground comp and new live electronics scenes are rediscovering much of what has been done and thanks to the web it is at least being somewhat documented. Most of this is from the technological standpoint, how to make the tools (for instance, this great book) but the ideas behind it all have been rather neglected. So this is an attempt to put out there some of my thinking on this, though of course it is only my perspective and relatively narrow. It comes from as I said above both experience and paying attention to other sources, but aspects of it are certainly theoretical due to only working with a subset of what is out there. Furthermore there are notions here that arose out of my attempt to codify these ideas which are rather unexplored but will point out aspects of my own current endeavors.

The Network Instrument

The basic concept behind the network instrument is of a number of complete (or near complete) instruments that are networked together to form a greater whole. Beyond mere summing of inputs the network is interconnected and utilizes feedback (in a networking sense) to create instabilities and variation. The notion of the Network Instrument is not necessarily new, it is more of an attempt to codify existing practices.  Within the conceptual framework there is certainly avenues for exploration that could be considered new and there are a few notions here that I’ve rarely, if ever seen, employed.  Note that I’ve appropriated a lot of the notions and terminology from neural networks but the way in which they are applied to this notion of an electronic instrument is not meant to imply any sort of direct correlation.

Network Components

A network has three components:  nodes, connections and interfaces.

Nodes
These are the sound sources which in most cases are a mini-network in and of themselves. That is they can be sound source(s) and various effectors setup in various formats (series, parallel, summed, etc.).  They can be electronic, acoustic or electro-acoustic as long as they can be integrated into the network.

Connections
These are the connections between the nodes. At the most simple this could be seen as the audio out from each node connected via a single mixer whose output is then made audible. Other setups though can include multiple sound outputs, connects between nodes, the lack of a central summing component and so on.

Interfaces
Interfaces are manner in which connections are made. These are generally either direct, indirect or a hybrid of these two. Direct interfaces are simply wires going from an output to an input.  Very simple but these are the backbone of the bulk of the connections.  Indirect interfaces, on the other hand, can be highly diverse but can be primarily thought of as an external input/output interface. That is a node has its own audio-output which is then connected to the network via sound capturing device. Indirect interfaces can be thought of as a layer of processing applied upon a node but done via its connection as opposed to an external device.  The use of a device between the output of a node and the input of another node could be thought of as a hybrid interface. That is to say a form of processing is applied upon the signal but the connections themselves utilize a direct interface.

Network Configurations

Determinate Configuration
A configuration that is more predictable, namely with a decreased amount of interconnections. You could think of a standard chain of guitar pedals as an example of this: the guitarist expects something played on the guitar to be modified in an expected way.

Indeterminate Configuration
A configuration that maximizes the unpredictability of the instrument, primarily though degree of interconnection. To continue with the guitar pedal example above, if you increase the the inter-connectivity, so as to not be in a standard linear configuration the transformation of that sound becomes increasing difficult to predict at least from a given input.

Note that Determinate/Indeterminate denotes a continuum upon which any given configuration lies

Network Types

Fully Connected Network
A configuration where every node is connected to every other node.

Partially Connected Network
A configuration where every node is not connected to every other node. This is the typical network case as a fully connected network is impracticable beyond a certain limited size.

Note that while the degree of connectivity lies upon a continuum a network is either fully connected or not.

Feedforward Network
A type of network where multiple elements are chained together and summed together prior to output. This configuration may contain loops in its various sub-elements but these too are always fed into the next element. The modular parts that make up a Fully or Partially Connected Network are almost always feedforward chains but it is the interconnections between those chains that create the distinction.

Interconnections

Electro-Acoustic Nodes
Using of an acoustic sound source that is tied into the network via various interfaces.  These can differ from other nodes in that they may allow for only certain types or degrees of interconnections

Electromechanical Interface
These interfaces are used to drive an Electro-Acoustic node in a mechanical method. These may offer limited degree of interconnectivity and may be only one way.  However they often can be extended for higher degrees of connection.

Clouds

Clouds are the myriad states within a network. This is a more nuanced understanding of the State Exploration that I pursued in the early phases of the no-mind project. A given network has a large number of permutations that can be varied by altering inputs, adjusted various values (feedback, volumes, filtering, etc) that in and of themselves can be sufficient for a piece of music. Conceptually if you thought of each possible setting of a component as its own device that could only be connected in isolation you would have a vast array of networks within any given network. In the same way that a cloud is both the signifier of an individual as well as a constantly shifting collective of individuals, a network instrument is a single entity that is made up of myriad of states.

An Example Network Instrument

An Example Network Instrument

Sound Sources

1.1 – Chimera BC16 patchable synthesizer
1.2 – Sinewave/Squarewave generator
1.3 – Realistic Mixer with stereo feedback
1.4 – Berhinger 16 Channel Stereo mixer

Effectors

2.1 – Realistic Reverb
2.2 – Spring Reverb
2.3 – Parallel Universe Oscillating Fuzz

Interfaces

3.1 – Berhinger 16 Channel Stereo mixer
3.2 – Direct connection from node 1.1
3.3 – Direct connection from node 1.2
3.4 – Indirect connection from Node 1.3
3.5 – Indirect connection from Node 1.3
3.6 – Indirect connection from Node 1.4

Output

4.1 – Primary Output
4.2 – Secondary Output
4.3 – Mini-Speaker for Node 1.3
4.4 – Mini-Speaker for Node 1.3

This was an actual setup I used for a bit as I explored some of these notions, but I don’t think I ever recorded anything with it. I’ve listed the specific instruments, effects, etc used here but obviously they aren’t particularly essential.

In some sort of conclusion

While it was my own electronics work that got me started on this path and David Tudor’s that really got me thinking, these notions are like I said a metaphor and not really describing specifics.  You could use this terminology to describe any electronics setup, I’m sure discovering that there are gaps in the terminology perhaps even discovering a form of electronics that is not network based.  This document is certainly incomplete, my descriptions insufficient, probably even downright incoherent at time. But its a start and I’ll keep working on it. Feel free to start a dialog in the comments about any aspect of this. I would definitely like to flesh out a lot of these ideas and could certainly use feedback.

Read more on the Network Instrument: Subnetworks

References
1) David Tudor Pages at EMF
2) Neural Synthesis Nos. 6-9, Lovely Music
3) Neural Network Synthesizer 1 by  Forrest Warthman
4) Neural Network Synthesizer 2 by Mark Holler
5) Neural Networks on Wikipedia