Compositional pattern-producing network
Encyclopedia
Compositional pattern-producing networks (CPPNs), are a variation of artificial neural network
s (ANNs) which differ in their set of activation functions and how they are applied.
While ANNs often contain only sigmoid function
s (and sometimes Gaussian functions), 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
produce segmented patterns with repetitions, while symmetric functions such as Gaussian produce symmetric patterns. Linear functions can be employed to produce linear or fractal
-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
techniques such as NeuroEvolution of Augmenting Topologies (called CPPN-NEAT).
CPPNs been shown to be a very powerful encoding when evolving the following:
Artificial neural network
An artificial neural network , usually called neural network , is a mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes...
s (ANNs) which differ in their set of activation functions and how they are applied.
While ANNs often contain only sigmoid function
Sigmoid function
Many natural processes, including those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. When a detailed description is lacking, a sigmoid function is often used. A sigmoid curve is produced by a mathematical...
s (and sometimes Gaussian functions), 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
Sine
In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....
produce segmented patterns with repetitions, while symmetric functions such as Gaussian produce symmetric patterns. Linear functions can be employed to produce linear or fractal
Fractal
A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...
-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
Neuroevolution, or neuro-evolution, is a form of machine learning that uses evolutionary algorithms to train artificial neural networks. It is useful for applications such as games and robot motor control, where it is easy to measure a network's performance at a task but difficult or impossible to...
techniques such as NeuroEvolution of Augmenting Topologies (called CPPN-NEAT).
CPPNs been shown to be a very powerful encoding when evolving the following:
- Neural Networks, via the HyperNEATHyperNEATHypercube-based NEAT, or HyperNEAT, is a generative encoding that evolves artificial neural networks with the principles of the widely used NeuroEvolution of Augmented Topologies algorithm. It is a novel technique for evolving large-scale neural networks utilizing the geometric regularities of...
algorithm - 2D images, on "PicBreeder.org"
- 3D objects, on "EndlessForms.com"
See also
- Artificial neural networkArtificial neural networkAn artificial neural network , usually called neural network , is a mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes...
- NeuroEvolution of Augmenting Topologies
- Interactive evolutionary computationInteractive evolutionary computationInteractive evolutionary computation or aesthetic selection is a general term for methods of evolutionary computation that use human evaluation...
- Evolutionary artEvolutionary artEvolutionary art is created using a computer. The process starts by having a population of many randomly generated individual representations of artworks. Each representation is evaluated for its aesthetic value and given a fitness score...
External links
- "PicBreeder.org" - Online, collaborative art generated by CPPNs evolved with NeuroEvolution of Augmenting Topologies.
- "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.