A Hypercube-Based Encoding for Evolving Large-Scale Neural Networks

Abstract

Research in neuroevolution-that is, evolving artificial neural networks (ANNs) through evolutionary algorithms-is inspired by the evolution of biological brains, which can contain trillions of connections. Yet while neuroevolution has produced successful results, the scale of natural brains remains far beyond reach. This article presents a method called hypercube-based NeuroEvolution of Augmenting Topologies (HyperNEAT) that aims to narrow this gap. HyperNEAT employs an indirect encoding called connective compositional pattern-producing networks (CPPNs) that can produce connectivity patterns with symmetries and repeating motifs by interpreting spatial patterns generated within a hypercube as connectivity patterns in a lower-dimensional space. This approach can exploit the geometry of the task by mapping its regularities onto the topology of the network, thereby shifting problem difficulty away from dimensionality to the underlying problem structure. Furthermore, connective CPPNs can represent the same connectivity pattern at any resolution, allowing ANNs to scale to new numbers of inputs and outputs without further evolution. HyperNEAT is demonstrated through visual discrimination and food-gathering tasks, including successful visual discrimination networks containing over eight million connections. The main conclusion is that the ability to explore the space of regular connectivity patterns opens up a new class of complex high-dimensional tasks to neuroevolution.

Evolving neural fields for problems with large input and output spaces

“…In HyperNEAT (D'Ambrosio and Stanley, 2007;Gauci and Stanley, 2007;Stanley et al, 2009), neurons are embedded into a substrate that has an externally specified topology. For example, the substrate can be a two-dimensional plane.…”

“…HyperNEAT (Gauci and Stanley, 2007;D'Ambrosio and Stanley, 2007;Stanley et al, 2009) is the most well known recent method to evolve large neural networks. In HyperNEAT, the number and position of neurons on a substrate is prespecified, while a NEAT-like compositional pattern producing network (CPPN) that gets the neuron coordinates as inputs specifies whether neurons are connected and what the weight of their connection is.…”

Evolving Gaits for Physical Robots with the HyperNEAT Generative Encoding: The Benefits of Simulation

“…Such manual intervention is time consuming, requires expert knowledge, and adds constraints that may hurt performance. Previous work has shown that the Hypercube-based NeuroEvolution of Augmenting Topologies (HyperNEAT) generative encoding [20] can automatically generate a variety of regular gaits that outperform gaits evolved with direct encodings [4,7]. However, that work only verified these claims in simulation.…”

Comparing the Evolvability of Generative Encoding Schemes

“…The first generative encoding scheme evaluated is a simplified version of HyperNEAT indirect encoding 2 (Stanley et al, 2009;Clune et al, 2011;Yosinski et al, 2011). The CPPNs encode the weights of a fixed topology, single-layer feedforward ANN, featuring 2-D cartesian grids of inputs, hidden and output neurons (Fig.…”

“…Evolvability is analyzed for a parametrized direct encoding, and the generative encoding of artificial neural networks (similar to HyperNEAT, Stanley et al (2009)) and single-unit pattern generators (Morse et al, 2013), in three independent experiments. The significance of our measure of evolvability is analyzed by the ability of the robot to adapt to previously unencountered changes in its morphology.…”