An Enhanced Hypercube-Based Encoding for Evolving the Placement, Density, and Connectivity of Neurons

Abstract

Intelligence in nature is the product of living brains, which are themselves the product of natural evolution. Although researchers in the field of neuroevolution (NE) attempt to recapitulate this process, artificial neural networks (ANNs) so far evolved through NE algorithms do not match the distinctive capabilities of biological brains. The recently introduced hypercube-based neuroevolution of augmenting topologies (HyperNEAT) approach narrowed this gap by demonstrating that the pattern of weights across the connectivity of an ANN can be generated as a function of its geometry, thereby allowing large ANNs to be evolved for high-dimensional problems. Yet the positions and number of the neurons connected through this approach must be decided a priori by the user and, unlike in living brains, cannot change during evolution. Evolvable-substrate HyperNEAT (ES-HyperNEAT), introduced in this article, addresses this limitation by automatically deducing the node geometry from implicit information in the pattern of weights encoded by HyperNEAT, thereby avoiding the need to evolve explicit placement. This approach not only can evolve the location of every neuron in the network, but also can represent regions of varying density, which means resolution can increase holistically over evolution. ES-HyperNEAT is demonstrated through multi-task, maze navigation, and modular retina domains, revealing that the ANNs generated by this new approach assume natural properties such as neural topography and geometric regularity. Also importantly, ES-HyperNEAT's compact indirect encoding can be seeded to begin with a bias toward a desired class of ANN topographies, which facilitates the evolutionary search. The main conclusion is that ES-HyperNEAT significantly expands the scope of neural structures that evolution can discover.

Guided self-organization in indirectly encoded and evolving topographic maps

“…Similar results indicating that discovering particular kinds of structures is deceptive were also observed by Verbancsics and Stanley [32] and Risi and Stanley [17] on seeding HyperNEAT with the concept of locality. This growing body of evidence suggests that such deception might be common when geometric principles such as lateral connectivity or locality are essential to achieving the desired behavior but fitness does not reward the intermediate stepping stones that lead to that final objective.…”

“…In the future it might be possible to combine a SOM-generating seed with a recent HyperNEAT extension called adaptive evolvablesubstrate HyperNEAT [17,18]. Adaptive ES-HyperNEAT can au- tomatically determine the placement, density and plasticity of neurons in the HyperNEAT substrate.…”

Evolving multimodal controllers with HyperNEAT

“…For example, in some cases modalities that consist of a single boolean value should be treated in a similar way that is different from the way that continuous rangefinder arrays should be treated. However, current applications of HyperNEAT feature relatively few sensory modalities [3,5,6,8,16,24]. For example, Stanley et al [24] evolve agents with HyperNEAT for a food gathering task.…”

“…In this application, agents only have a single array of eight rangefinders (corresponding to a single sensory modality). Similarly, the agents featured in Risi and Stanley [16] have only two sensory modalities: wall sensors and target sensors. Although multiagent domains often necessitate the addition of extra sensory information to facilitate communication and the detection of friendly agent locations or status, multiagent HyperNEAT has so far only been used to evolve agents with one [5] or two [6] sensory modalities.…”

Experiments on Neuroevolution and Online Weight Adaptation in Complex Environments

“…This means that further research on online learning and adaptation for ANNs is required, to let us develop systems able to perform well on changing domains. In this sense, adaptive Evolving-Substrate HyperNEAT (Adaptive ESHyperNEAT) [6][5] has done a first step by adding Hebbian ABC Plasticity [3] as patterns of local rules to ANNs, and also using CPPNs to continuously adapt weights over time. Nevertheless, there is no theoretical or empirical evidence about the performance of these approaches in complex environments.…”