CPPNs

Compositional Pattern Producing Networks (CPPNs) are a form of artificial neural network used as a generative encoding in neuroevolution. Instead of directly encoding a fixed network, a CPPN acts as a compact program that, when queried with input coordinates, outputs parameters for another network or for a pattern.

CPPNs are typically feedforward networks whose nodes apply a variety of activation functions, such as sigmoid, gaussian, sine, or polynomial functions. The network itself is evolved, and its outputs are interpreted as connection weights, biases, or even the existence of connections in a target network, or as color intensities or spatial attributes for generated patterns.

A central application is the indirect encoding of large patterned networks through geometry. In HyperNEAT, for example, a CPPN is evolved and then queried with coordinates corresponding to neuron positions in a substrate. For any pair of coordinates, the CPPN outputs the weight of the connection (or zero if no connection). Repeating this across a grid or mesh yields a large, regular network.

Uses include evolving neural networks for robotics and control tasks, as well as generating procedural content such as images, textures, 3D shapes, or game levels. CPPNs can capture symmetry, repetition, and other regularities from their activation functions and input coordinates.

Advantages include compact, scalable encodings and the ability to exploit geometric regularities; limitations involve bias toward regular structures and potential difficulties encoding highly irregular or non-geometric patterns, as well as computational overhead from evaluating many coordinates.