Modularity and Sparsity: Evolution of Neural Net Controllers in Physically Embodied Robots

Abstract

While modularity is thought to be central for the evolution of complexity and evolvability, it remains unclear how systems boot-strap themselves into modularity from random or fully integrated starting conditions. Clune et al. (2013) suggested that a positive correlation between sparsity and modularity is the prime cause of this transition. We sought to test the generality of this modularity-sparsity hypothesis by testing it for the first time in physically embodied robots. A population of ten Tadros — autonomous, surface-swimming robots propelled by a flapping tail — was used. Individuals varied only in the structure of their neural net control, a 2 x 6 x 2 network with recurrence in the hidden layer. Each of the 60 possible connections was coded in the genome, and could achieve one of three states: -1, 0, 1. Inputs were two light-dependent resistors and outputs were two motor control variables to the flapping tail, one for the frequency of the flapping and the other for the turning offset. Each Tadro was tested separately in a circular tank lit by a single overhead light source. Fitness was the amount of light gathered by a vertically oriented sensor that was disconnected from the controller net. Reproduction was asexual, with the top performer cloned and then all individuals entered into a roulette wheel selection process, with genomes mutated to create the offspring. The starting population of networks was randomly generated. Over ten generations, the population’s mean fitness increased two-fold. This evolution occurred in spite of an unintentional integer overflow problem in recurrent nodes in the hidden layer that caused outputs to oscillate. Our investigation of the oscillatory behavior showed that the mutual information of inputs and outputs was sufficient for the reactive behaviors observed. While we had predicted that both modularity and sparsity would follow the same trend as fitness, neither did so. Instead, selection gradients within each generation showed that selection directly targeted sparsity of the connections to the motor outputs. Modularity, while not directly targeted, was correlated with sparsity, and hence was an indirect target of selection, its evolution a “by-product” of its correlation with sparsity.