Compositional pattern-producing networks (CPPNs) are a variation of
artificial neural network
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains.
An ANN is based on a collection of connected unit ...
s (ANNs) that have an architecture whose evolution is guided by genetic algorithms.
[Stanley, Kenneth O. "Compositional pattern producing networks: A novel abstraction of development." Genetic programming and evolvable machines 8.2 (2007): 131-162.]
While ANNs often contain only
sigmoid function
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve.
A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula:
:S(x) = \frac = \f ...
s and sometimes
Gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real constants , and non-zero . It is n ...
s, CPPNs can include both types of functions and many others. The choice of functions for the canonical set can be biased toward specific types of patterns and regularities. For example, periodic functions such as
sine
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is oppo ...
produce segmented patterns with repetitions, while symmetric functions such as Gaussian produce symmetric patterns. Linear functions can be employed to produce linear or
fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
-like patterns. Thus, the architect of a CPPN-based genetic art system can bias the types of patterns it generates by deciding the set of canonical functions to include.
Furthermore, unlike typical ANNs, CPPNs are applied across the entire space of possible inputs so that they can represent a complete image. Since they are compositions of functions, CPPNs in effect encode images at infinite resolution and can be sampled for a particular display at whatever resolution is optimal.
CPPNs can be evolved through
neuroevolution
Neuroevolution, or neuro-evolution, is a form of artificial intelligence that uses evolutionary algorithms to generate artificial neural networks (ANN), parameters, and rules. It is most commonly applied in artificial life, general game playing ...
techniques such as
neuroevolution of augmenting topologies NeuroEvolution of Augmenting Topologies (NEAT) is a genetic algorithm (GA) for the generation of evolving artificial neural networks (a neuroevolution technique) developed by Kenneth Stanley and Risto Miikkulainen in 2002 while at The University of ...
(called CPPN-NEAT).
CPPNs have been shown to be a very powerful encoding when evolving the following:
* Neural networks, via the
HyperNEAT
Hypercube-based NEAT, or HyperNEAT, is a generative encoding that evolves artificial neural networks
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biolog ...
algorithm,
* 2D images, o
"PicBreeder.org"
* 3D objects, o
"EndlessForms.com"
* Robot morphologie
Rigid RobotsSoft Robots
See also
* Evolutionary art
Evolutionary art is a branch of generative art, in which the artist does not do the work of constructing the artwork, but rather lets a system do the construction. In evolutionary art, initially generated art is put through an iterated process o ...
* Interactive evolutionary computation Interactive evolutionary computation (IEC) or aesthetic selection is a general term for methods of evolutionary computation that use human evaluation. Usually human evaluation is necessary when the form of fitness function is not known (for example, ...
Bibliography
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References
{{Reflist
External links
"PicBreeder.org"
– Online, collaborative art generated by CPPNs evolved with NeuroEvolution of Augmenting Topologies NeuroEvolution of Augmenting Topologies (NEAT) is a genetic algorithm (GA) for the generation of evolving artificial neural networks (a neuroevolution technique) developed by Kenneth Stanley and Risto Miikkulainen in 2002 while at The University of ...
.
"EndlessForms.com"
– A 3D version of Picbreeder, where you interactively evolve 3D objects that are encoded with CPPNs and evolved with NeuroEvolution of Augmenting Topologies NeuroEvolution of Augmenting Topologies (NEAT) is a genetic algorithm (GA) for the generation of evolving artificial neural networks (a neuroevolution technique) developed by Kenneth Stanley and Risto Miikkulainen in 2002 while at The University of ...
.
Artificial neural networks
Classification algorithms