In this paper we introduce the Developmental Symbolic Encoding (DSE), a new generative encoding for evolving networks (e.g. neural or boolean). DSE combines elements of two powerful generative encodings, Cellular Encoding and HyperNEAT, in order to evolve networks that are modular, regular, scale-free, and scalable. Generating networks with these properties is important because they can enhance performance and evolvability. We test DSE's ability to generate scale-free and modular networks by explicitly rewarding these properties and seeing whether evolution can produce networks that possess them. We compare the networks DSE evolves to those of HyperNEAT. The results show that both encodings can produce scale-free networks, although DSE performs slightly, but significantly, better on this objective. DSE networks are far more modular than HyperNEAT networks. Both encodings produce regular networks. We further demonstrate that individual DSE genomes during development can scale up a network pattern to accommodate different numbers of inputs. We also compare DSE to Hyper-NEAT on a pattern recognition problem. DSE significantly outperforms HyperNEAT, suggesting that its potential lay not just in the properties of the networks it produces, but also because it can compete with leading encodings at solving challenging problems. These preliminary results imply that DSE is an interesting new encoding worthy of additional study. The results also raise questions about which network properties are more likely to be produced by different types of generative encodings.

Evolutionary neural networks, or neuroevolution, appear to be a promising way to build versatile adaptive systems, combining evolution and learning. One of the most challenging problems of neuroevolution is finding a scalable and robust genetic representation, which would allow to effectively grow increasingly complex networks for increasingly complex tasks. In this paper we propose a novel developmental encoding for networks, featuring scalability, modularity, regularity and hierarchy. The encoding allows to represent structural regularities of networks and build them from encapsulated and possibly reused subnetworks. These capabilities are demonstrated on several test problems. In particular for parity and symmetry problems we evolve solutions, which are fully general with respect to the number of inputs. We also evolve scalable and modular weightless recurrent networks capable of autonomous learning in a simple generic classification task. The encoding is very flexible and we demonstrate this by evolving networks capable of learning via neuromodulation. Finally, we evolve modular solutions to the retina problem, for which another well known neuroevolution method-HyperNEAT-was previously shown to fail. The proposed encoding outperformed HyperNEAT and Cellular Encoding also in another experiment, in which certain connectivity patterns must be discovered between layers. Therefore we conclude the proposed encoding is an interesting and competitive approach to evolve networks.

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