Cyclic Incrementality in Competitive Coevolution: Evolvability through Pseudo-Baldwinian Switching-Genes.

Coevolving systems are notoriously difficult to understand. This is largely due to the Red Queen effect that dictates heterospecific fitness interdependence. In simulation studies of coevolving systems, master tournaments are often used to obtain more informed fitness measures by testing evolved individuals against past and future opponents. However, such tournaments still contain certain ambiguities. We introduce the use of a phenotypic cluster analysis to examine the distribution of opponent categories throughout an evolutionary sequence. This analysis, adopted from widespread usage in the bioinformatics community, can be applied to master tournament data. This allows us to construct behavior-based category trees, obtaining a hierarchical classification of phenotypes that are suspected to interleave during cyclic evolution. We use the cluster data to establish the existence of switching-genes that control opponent specialization, suggesting the retention of dormant genetic adaptations, that is, genetic memory. Our overarching goal is to reiterate how computer simulations may have importance to the broader understanding of evolutionary dynamics in general. We emphasize a further shift from a component-driven to an interaction-driven perspective in understanding coevolving systems. As yet, it is unclear how the sudden development of switching-genes relates to the gradual emergence of genetic adaptability. Likely, context genes gradually provide the appropriate genetic environment wherein the switching-gene effect can be exploited.

The error surface of the 2-2-1 XOR network: The finite stationary points.

We investigate the error surface of the XOR problem for a 2-2-1 network with sigmoid transfer functions. It is proved that all stationary points with finite weights are saddle points with positive error or absolute minima with error zero. So, for finite weights no local minima occur. The proof results from a careful analysis of the Taylor series expansion around the stationary points. For some points coefficients of third or even fourth order in the Taylor series expansion are used to complete the proof. The proofs give a deeper insight into the complexity of the error surface in the neighbourhood of saddle points. These results can guide the research in finding learning algorithms that can handle these kinds of saddle points.