Sebastian Risi, Joel Lehman, and Kenneth O. Stanley (2010)
Evolving the Placement and Density of Neurons in the HyperNEAT Substrate
In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2010). New York, NY:ACM (8 pages)

Winner of the Best Paper Award in Generative and Developmental Systems at GECCO-2010


The Hypercube-based NeuroEvolution of Augmenting Topologies (HyperNEAT) approach demonstrated that the pattern of weights across the connectivity of an artificial neural network (ANN) can be generated as a function of its geometry, thereby allowing large ANNs to be evolved for high-dimensional problems. Yet it left to the user the question of where hidden nodes should be placed in a geometry that is potentially infinitely dense. To relieve the user from this decision, this paper introduces an extension called evolvable-substrate HyperNEAT (ES-HyperNEAT) that determines the placement and density of the hidden nodes based on a quadtree-like decomposition of the hypercube of weights and a novel insight about the relationship between connectivity and node placement. The idea is that the representation in HyperNEAT that encodes the pattern of connectivity across the ANN contains implicit information on where the nodes should be placed and can therefore be exploited to avoid the need to evolve explicit placement. In this paper, as a proof of concept, ES-HyperNEAT discovers working placements of hidden nodes for a simple navigation domain on its own, thereby eliminating the need to configure the HyperNEAT substrate by hand and  suggesting the potential power of the new approach.