Bradley Tonkes

Maximally rugged NK landscapes contain the highest peaks

NK models provide a family of tunably rugged fitness landscapes used in a wide range of evolutionary computation studies. It is well known that the average height of local optima regresses to the mean of the landscape with increasing epistasis, k. This fact has been confirmed using both theoretical studies of landscape structure and empirical studies of evolutionary search. We show that the global optimum behaves quite differently: the expected value of the global maximum is highest in the maximally rugged case. Furthermore, we demonstrate that this expected value increases with K, despite the fact that the average fitness of the local optima decreases. That is, the highest peaks are found in the most rugged landscapes, scattered amongst masses of low-lying peaks. We find the asymptotic value of the global optimum as N approaches infinity for both the smooth and maximally rugged cases. In evolutionary search, the optima that are found reflect the local optima that exist in the landscape, the size of these optima -- which corresponds to the size of their basins of attraction, and the effort expended in the search process. Increasing the level of epistasis in an NK landscape stochastically introduces higher peaks, but renders them exponentially more difficult to find.

Transient Phenomena in Learning and Evolution: Genetic Assimilation and Genetic Redistribution

Deacon has recently proposed that complexes of genes can be integrated into functional groups as a result of environmental changes that mask and unmask selection pressures. For example, many animals endogenously synthesize ascorbic acid (vitamin C), but anthropoid primates have only a nonfunctional version of the crucial gene for this pathway. It is hypothesized that the loss of functionality occurred in the evolutionary past when a diet rich in vitamin C masked the effect of the gene, and its loss effectively trapped the animals in a fruit-eating lifestyle. As a result, the complex of abilities that support this lifestyle were evolutionarily bound together, forming a multilocus complex. In this study we use evolutionary computation simulations to explore the thesis that masking and unmasking can transfer dependence from one set of genes to many sets, and thereby integrate the whole complex of genes. We used a framework based on Hinton and Nowlans 1987 simulation of the Baldwin effect. Additional gene complexes and an environmental parameter were added to their basic model, and the fitness function extended. The simulation clearly demonstrates that the genetic redistribution effect can occur in silico, showing an initial advantage of endogenously synthesized vitamin C, followed by transfer of the fitness contribution to the complex of genes that together allow the acquisition of vitamin C from the environment. As is well known in the modeling community, the Baldwin effect only occurs in simulations when the population of agents is poised on the brink of discovering the genetically specified solution. Similarly, the redistribution effect occurs in simulations under specific initial conditions: too little vitamin C in the environment, and its synthesis it is never fully masked; too much vitamin C, and the abilities required to acquire it are not tightly integrated. The Baldwin effect has been hypothesized as a potential mechanism for developing language-specific adaptations like innate universal grammar and other highly modular capacities. We conclude with a discussion of the relevance of genetic assimilation and genetic redistribution to the evolution of language and other cognitive adaptations.

Hyperspace Geography: Visualizing Fitness Landscapes beyond 4D

Human perception is finely tuned to extract structure about the 4D world of time and space as well as properties such as color and texture. Developing intuitions about spatial structure beyond 4D requires exploiting other perceptual and cognitive abilities. One of the most natural ways to explore complex spaces is for a user to actively navigate through them, using local explorations and global summaries to develop intuitions about structure, and then testing the developing ideas by further exploration. This article provides a brief overview of a technique for visualizing surfaces defined over moderate-dimensional binary spaces, by recursively unfolding them onto a 2D hypergraph. We briefly summarize the uses of a freely available Web-based visualization tool, Hyperspace Graph Paper (HSGP), for exploring fitness landscapes and search algorithms in evolutionary computation. HSGP provides a way for a user to actively explore a landscape, from simple tasks such as mapping the neighborhood structure of different points, to seeing global properties such as the size and distribution of basins of attraction or how different search algorithms interact with landscape structure. It has been most useful for exploring recursive and repetitive landscapes, and its strength is that it allows intuitions to be developed through active navigation by the user, and exploits the visual systems ability to detect pattern and texture. The technique is most effective when applied to continuous functions over Boolean variables using 4 to 16 dimensions.

Mapping the royal road and other hierarchical functions

In this paper we present a technique for visualising hierarchical and symmetric, multi-modal fitness functions that have been investigated in the evolutionary computation literature. The focus of this technique is on landscapes in moderate-dimensional, binary spaces (i.e., fitness functions defined over 0,1n, for n 16). The visualisation approach involves an unfolding of the hyperspace into a two-dimensional graph, whose layout represents the topology of the space using a recursive relationship, and whose shading defines the shape of the cost surface defined on the space. Using this technique we present case-study explorations of three fitness functions: royal road, hierarchical-if-and-only-if (H-IFF), and hierarchically decomposable functions (HDF). The visualisation approach provides an insight into the properties of these functions, particularly with respect to the size and shape of the basins of attraction around each of the local optima.

Decentralised data fusion with exponentials of polynomials

We demonstrate applicability of a general class of multivariate probability density functions of the form e-P(x), where P(x) is an elliptic polynomial, to decentralised data fusion tasks. In particular, we derive an extension to the covariance Intersect algorithm for this class of distributions and demonstrate the necessary operations - diffusion, multiplication and linear transformation - for Bayesian operations. A simulated target tracking application demonstrates the use of these operations in a decentralised scenario, employing range-only sensing to show their generality beyond Gaussian representations.

A Paradox of Neural Encoders and Decoders or Why Don't We Talk Backwards?

We present a framework for studying the biases that recurrent neural networks bring to language processing tasks. A semantic concept represented by a point in Euclidean space is translated into a symbol sequence by an encoder network. This sequence is then presented to a decoder network which attempts to translate it back to the original concept. We show how a pair of recurrent networks acting as encoder and decoder can develop their own symbolic language that is serially transmitted between them either forwards or backwards. The encoder and decoder bring different constraints to the task, and these early results indicate that the conflicting nature of these constraints may be reflected in the language that ultimately emerges, providing clues to the structure of human languages.

Visualisation of hierarchical cost surfaces for evolutionary computing

We present a technique for visualising cost surfaces that are relevant to work in evolutionary computation, particularly genetic algorithms. The focus is on moderate-dimensional, binary cost surfaces (i.e., functions defined over {0, 1}/sup n/, for n/spl les/16) that have a hierarchical, modular structure. The visualisation approach involves an unfolding of the hyperspace into a two-dimensional graph, whose layout represents the topology of the space using a recursive relationship, and whose shading defines the shape of the cost surface defined on the space. Using this technique we present a case-study exploration of the hierarchical-if-and-only-if (H-IFF) function. The visualisation approach provides an insight into the properties of this function, particularly in regards to the size and shape of the basins of attraction around each of the local optima.