Imitation Programming Larry Bull University of the West of England

Alan Mathison Turing Further research into intelligence of machinery will probably be very greatly concerned with ‘searches’ …. There is the genetical or evolutionary search by which a combination of genes is looked for, the criterion being survival value …. The remaining form of search is what I should like to call the ‘cultural search’ … the search for new techniques must be regarded as carried out by the human community as a whole. Intelligent Machinery 1948

Culture-inspired Search Artefacts - left between evolutionary generations [Hutchins & Hazelhurst 1990, ALife II procs.] Cultural Algorithms - belief space to store knowledge to guide evolutionary search [Reynolds1994, EP III procs.] Ant Colony Optimization – social insect mechanisms for path finding in graphs [Dorigo et al. 1996, IEEE SMC-B]

(Socio) Cultural Evolution The use of an evolutionary metaphor has being applied to culture since Darwin’s time, e.g., by Herbert “survival of the fittest” Spencer. The most direct use of evolutionary biology to understand culture is based on Edward Wilson’s “sociobiology” [1975], e.g., see [Boyd & Richerson, 1985].

Imitation: Memes Dawkins’ meme [1976] is a unit of cultural ideas, symbols or practices, which can be transmitted from one mind to another through: ◦ Writing ◦ Speech ◦ Gestures ◦ Rituals ◦ Other imitable phenomena. Meme = Cultural gene.

Imitation Computation Supervised Learning - controller design through copying of human movement [e.g., review by Schaal et al. 2003, Phil. Trans.] Reinforcement Learning - value function approximation sharing between multiple agents [e.g., Price & Boutilier 1999, ML 16 procs.] Particle Swarm Optimization – boids inspired model of social behaviour [Kennedy & Eberhart 1995, IEEE NN procs.]

Unorganised Machines: A-Type In the same 1948 paper, Turing presented a general knowledge representation scheme. Parallel, recurrent networks of 2-input NAND gates.

Discrete Dynamical Systems Unorganised machines have a finite number of possible states and they are deterministic. Hence such networks eventually fall into a basin of attraction.

Motivation Discrete dynamical systems are known to (potentially) exhibit an inherent robustness to faults. Unorganised machines are made from uniform components. How to design dynamical circuits from such systems through culture-inspired mechanisms?

Related Work Evolving Cellular Automata ◦ [Packard, 1988][Mitchell et al., 1991][Sipper, 1997] Evolving Random Boolean Networks ◦ [Kauffman, 1993][Lemke et al., 2001] Evolving Graph Representations ◦ [Fogel et al., 1966][Teller & Veloso, 1996][Poli, 1997][Miller, 1999][Teuscher, 2002] …

Imitation Programming Create initial random population Evaluate For each individual ◦ Select individual in population to imitate ◦ Copy a randomly chosen aspect (with error) ◦ Evaluate ◦ Adopt new solution if better (or if smaller but =) Repeat

Imitation Pick an individual ◦ Best used here ◦ Smallest in case of ties (or random) Pick a trait at random ◦ Node start state ◦ Node connection ◦ Network size Test for error (p e = 0.5 here) which moves connection +/- 1 node id

Size Imitator is smaller ◦ Copy next node in imitatee and connect into network Imitator is larger ◦ Cut end node and reassign connections to it Same size ◦ Randomly add a copied node or cut last node Size limited [inputs+outputs, max.]

Unorganised Machines as Circuits Input 1 Input 2 Input Output Each node encoded as two integers and a binary start state. Nodes are initialised, inputs applied, network run for T cycles, and the output node(s) value is read.

Multiplexer  =20, T=15, N=I+O+30

a0 a1 d1 d2 d3 d4 out

Demultiplexer

Comparison with Evolution EP [Fogel et al., 1966] was designed for graph representations using mutation: ◦ Change output ◦ Change transition ◦ Add state ◦ Remove state ◦ Change initial state One operator used per offspring here. (  +  ’) selection AB AC 1/  0/  1/  0/  1/  0/ 

Multiplexer – IP vs EP

Demultiplexer – IP vs EP

Summary of Brief Comparison Imitation always faster and smaller. But selection process in particular is very different. IP described akin to a population of hill- climbers. If alter imitation to copy a randomly created individual stat. same on demux but still better on mux.

Conclusions Culture appears to be a somewhat under- explored source of ideas for AI. Imitation a ubiquitous process in nature. Can be viewed as both a component-wise xover operator and mutation. Initial results suggest competitive with genetic evolution schemes. Much more exploration needed.