1717 lines
89 KiB
Plaintext
1717 lines
89 KiB
Plaintext
Computational Genetics, Physiology, Metabolism,
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Neural Systems, Learning, Vision, and Behavior
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or PolyWorld: Life in a New Context
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Larry Yaeger
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Apple Computer, Inc.
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20525 Mariani Ave., MS 76-2H
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Cupertino, CA 95014
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larryy@apple.com
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1. Introduction
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The study of living systems has taken many forms, from
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research into the fundamental physical processes to ethological
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studies of animal behavior on a global scale. Traditionally these
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investigations have focused exclusively on ÒrealÓ biological systems
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existing in our worldÕs ecological system. Only recently have
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investigations of living systems begun to occur in ÒartificialÓ systems
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in computers and robotic hardware.
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The potential benefits of an enhanced understanding of living
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systems are tremendous. Some are of a grand scale, and are
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intuitively obvious, such as improvements in our ability to manage
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our own real ecosystems, the development of true machine
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intelligence, and the possibility of understanding our own mental and
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physiological processes. Some are of a more prosaic scale, but more
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accessible thereby, and, perhaps, of more immediate utility, such as
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simple learning systems, robust pattern classifiers, general purpose
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optimization schemes, robotic controllers, and evolvable software
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algorithms. The technological issues of the study of Artificial Life
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(ALife) are well laid out by Langton [27] in the proceedings of the
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first ALife workshop; the societal and philosophical implications of
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ALife are well presented in Farmer and Belin [16] in the proceedings
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of the second ALife workshop.
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The ecological simulator, PolyWorld (PW), presented and
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discussed in this paper, is one instantiation of these ALife
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motivations and principles. PolyWorld attempts to bring together all
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the principle components of real living systems into a single artificial
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living system. PolyWorld does bring together biologically motivated
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genetics, simple simulated physiologies and metabolisms, Hebbian
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learning in arbitrary neural network architectures, a visual
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perceptive mechanism, and a suite of primitive behaviors in artificial
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organisms grounded in an ecology that is hopefully just complex
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enough to foster speciation and inter-species competition. Predation,
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mimicry, sexual reproduction, and even communication are all
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supported in a straightforward fashion. The resulting survival
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strategies, both individual and group, are purely emergent, as are the
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functionalities embodied in their neural network ÒbrainsÓ. Complex
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behaviors resulting from the simulated neural activity are
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unpredictable, and change as natural selection acts over multiple
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generations.
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PolyWorld is a tool for investigating issues relevant to
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evolutionary biology, behavioral ecology, ethology, neural systems,
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and computer science. This paper will discuss the design principles
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employed in PW, along with some of the resulting behavior patterns
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observed in ÒspeciesÓ evolved in PW, their neural architectures, and
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the genetic variations observed in large populations under different
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ecological conditions.
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2. Background
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This work owes much in terms of inspiration to the work of W.
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Grey Walter [44,45,46], Valentino Braitenberg [3], Richard Dawkins
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[9,10,11], John Holland [21], Ralph Linsker [28,29,30], and John
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Pearson [36].
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WalterÕs early work with simple electronic ÒturtleÓ nervous
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systems, and BraitenbergÕs ÒvehiclesÓ suggested the approach of
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utilizing simulated organisms. PolyWorld diverges from these works
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by encapsulating these organisms in a simulated world, and
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employing neural systems and learning rules from the world of
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computational neurophysiology, and by supporting a range of
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interactions between organisms. And though a number of other
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researchers (Travers [43]; Wharton and Koball [47]; and even a
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commercial product from Bascom software, the author of which is not
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known) have built simple Braitenberg vehicle simulators (or actual
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physical models in the case of Wharton and Koball), these typically
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concentrated on a wiring-diagram user interface, and implemented
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vehicles through only level number 2 (of 14). PW, on the other hand,
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takes note of the fact that by as early as Vehicle 4, Braitenberg
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invoked a form of natural selection, and supports the evolution of its
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organismsÕ Òwiring diagramsÓ, rather than having them specified by
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hand. The neural systems of PW also utilize Hebbian learning during
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the lifetime of an individual, which is undoubtedly purposefully
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similar to BraitenbergÕs Òmnemotrix wireÓ.
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Richard DawkinsÕs writings communicate both the beauty and
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the effectiveness of evolutionary dynamics. In personal
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communications, he has also brought out key issues in speciation,
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such as the isolation of populations and the reduced viability of
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divergent species interbreeding, that have become important
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elements of this simulator.
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The artificial neural systems employed in PW are based on
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Hebbian learning, and a novel approach to network architecture
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specification. Besides the obvious importance of Donald HebbÕs [18]
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research and speculations, their instantiation in the work of Ralph
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Linsker and John Pearson has guided the selection of these particular
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techniques for use in PW. LinskerÕs work demonstrated that Hebbian
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learning, as employed in PW, can and will self-organize important
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types of neural response patterns observed in early visual systems
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of real organisms. John Pearson, working with Gerald Edelman,
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utilized a variant of Hebbian learning and successfully demonstrated
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important principles of neuronal and synaptic self-organization Ñ
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cooperation and competition(for representing their observed inputs)
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Ñ that again correspond well to phenomena observed in real living
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systems. PolyWorld takes this unsupervised learning technique, and
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embeds it in arbitrary, evolving neural architectures, and then
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confronts the simulated neural system with survival tasks in a
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simulated ecology.
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In the last couple of decades, a number of researchers have
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developed computational ecologies targeted at various scientific
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issues. Conrad [7,8] and Packard [34] have built systems to explore
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fundamental principles of evolutionary dynamics. Jefferson et al
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[23], and Collins and Jefferson [6] have constructed systems dealing
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with evolutionary mechanisms, behavioral goals, and learning
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architectures (Finite State Automata vs. Neural Networks). Taylor et
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al [40] developed a system to investigate the relationship between
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individual behavior and population dynamics. Ackley & Littman [1]
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built such a simulator to demonstrate a novel mechanism by which
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evolution can guide learning. Peter Todd and Geoffrey Miller
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[31,41,42] have explored evolutionary selection for different learning
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algorithms in organisms with simple vision systems and an innate
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sense of ÒsmellÓ that functions with varying degrees of accuracy.
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Danny Hillis [19,20] has used simple computational ecologies to
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evolve ÒrampsÓ, and exchange-sort algorithms. Core Wars [13,14,15]
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is a non-evolving ecology of code fragments, and RasmussenÕs VENUS
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[37] is an evolving system based largely on Core Wars. Thomas Ray
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[38] has also developed a computational ecology, TIERRA, based on
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evolving code fragments. And John Koza [26] has developed a
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system for evolving LISP functions that he terms ÒGenetic
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ProgrammingÓ. PolyWorld, in its original conception, was targeted
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principally at the evolution of neural architectures for systems faced
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with complex behavioral tasks; however, its biologically motivated
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behavioral and reproductive strategies, and the evolutionary
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mechanisms employed also make it suitable for use in behavioral
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ecology and evolutionary biology. The extent of PWÕs fidelity to
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biological systems, together with its unique use of a naturalistic
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visual perceptive system to ground its inhabitants in their
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environment distinguish it significantly from previous ecological
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simulators.
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John HollandÕs ECHO system explicitly models a form of
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predation, involving ÒoffenseÓ and ÒdefenseÓ genes that determine
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the outcome of violent encounters. Holland notes that in his system,
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this form of predation was essential to the evolution of complex
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genomes. Though not as crucial to PWÕs genetic complexity,
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predation was also designed into PW from the beginning. In PW,
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genes also affect the outcome of violent encounters between
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organisms, but more indirectly through their ÒphysiologicalÓ
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characteristics (strength and size). There is also a behavioral
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component to the outcome of these encounters in PW, namely the
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degree of ÒvolitionÓ associated with the ÒfightingÓ behavior (the
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activation level of a predefined ÒfightÓ neuron), that differs from
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ECHOÕs handling of predation.
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Belew et al [2] give an excellent overview of recent work in the
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area of evolving neural networks. Reviewed briefly there, and
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presented in detail in their own paper, Harp et al [17] have
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developed a scheme for evolving neural architectures that has an
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element of ontogenetic development. Their approach involves a set
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of synaptic projection radii between neuronal ÒareasÓ. PolyWorldÕs
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scheme for evolving architectures relies on the specification of
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connection densities and topological distortion of connections
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between neuronal groups. These architectural criteria are
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represented in the genome, and then expressed as an organismÕs
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neural architecture at ÒbirthÓ. This technique, though perhaps not
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quite as developmental as HarpÕs approach, or the non-neural, but
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very biologically motivated cellular growth work of de Boer et al
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[12], has the strengths of being much more developmental (and
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representationally compact) than a simple encoding of synaptic
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efficacy in the genes, and being computationally very efficient. It
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captures the statistical results of development, without the necessity
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of modeling the developmental process itself.
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David Chalmers [4] has experimented with evolving supervised
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neural network learning algorithms, successfully evolving the classic
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"delta rule" for a linear, single layer perceptron, and speculated on
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applying this "genetic connectionism" approach to other architectures
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and learning algorithms. He also varies the diversity of his learning
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tasks, and demonstrates a correlation between this diversity and the
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generality of the evolved learning algorithm, similar to the
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correlation observed between amount of training data and
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generalization in supervised, "Back-Prop" neural networks. Though
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the evolution of unsupervised learning algorithms is one area of
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special interest to the author, the current version of PW has the
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classic "Hebb rule" built in. Neural architectures are, however,
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evolved in PW. Interestingly, by permitting free movement in a
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simulated environment, PW effectively can generate an unlimited
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amount of diverse input for the neural mechanisms employed by its
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denizens.
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Nolfi et al [33] and Parisi et al [35] have explored evolving the
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connection strengths in small, fixed-architecture feed-forward neural
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networks controlling simple movement strategies in organisms
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evolved to seek food. The organisms are directly provided with
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angle and distance to food items, and are alone in their environment.
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Nolfi, Parisi, et al also introduce a "self-supervised" learning
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technique, using the traditional back-propagation of error algorithm,
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and demonstrate an improvement in evolved foraging efficiency
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associated with a learned ability to predict the sensory consequences
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of motor activity. PW employs an unsupervised learning algorithm
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and arbitrary neural architectures, with a more biologically-
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motivated vision mechanism, as well as a competitive ecology.
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For the purpose of computer graphics animation, Renault et al
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[39] have experimented with visual systems for controlling computer
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generated characters. Their system goes beyond visual processing,
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however, to include unique object identification and distances to
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objects as part of the input to the character control programs. These
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control programs are rule-based and completely hand-crafted,
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specifically to provide obstacle avoidance. In contrast, PW uses only
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the pixel colors associated with visual processing, and provides these
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as input to the non-rule-based neural systems of evolving organisms,
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without specifying the meaning or use of this information.
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Dave Cliff [5] has implemented a neural visual system for a
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simulated fly, and states that it is only by a grounding perceptive
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mechanism such as vision that neural models can be made sense of.
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For the purposes of his simulation, the model fly is attached to a
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rotating, but otherwise unmoving test-stand similar to real
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experimental setups. Organisms in PW use vision as their primary
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sense mechanism, but are free to explore their environment, and
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must do so effectively Ñ using their vision to guide a suite of
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primitive behaviors Ñ in order to survive and reproduce.
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The study of real living systems has spanned many physical
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and temporal scales, from molecular level biochemical processes that
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take place in nanoseconds, through cellular level neural processes
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with time scales of a few milliseconds, to global evolutionary
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processes occurring over geological time scales. One of the first
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decisions necessary to commence an investigation into artificial living
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systems is that of scale: At what level of detail is it desirable to
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specify the parameters and underlying models of the simulation, and
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at what level does one wish to observe the resultant behaviors?
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Given current constraints on compute power, it is simply not feasible
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to begin computation with sub-atomic physics and expect to observe
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ethological behaviors. Since ecology-level dynamics were the desired
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output level of the system being designed, it was clear that behavior
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models for PWÕs individual organisms could not be too complex.
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However, a desire to avoid rule-based behavior specification led to a
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decision to model the organismsÕ behaviors at the neuronal level.
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Since even natural evolutionary forces are constrained by their
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previous successes, the real world has filled up with organisms
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exhibiting a wide range of variations on assemblages of neuronal
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cells (in addition to other cell types, of course). Modeling PWÕs
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organisms at this level permits us to sidestep millions of years of
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evolution, while still taking advantage of its results to date. In many
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ways, PW may be thought of as a sort of electronic primordial soup
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experiment, in the vein of Urey and MillerÕs [32] classic experiment,
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only commencing at a much higher level of organization, with light-
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sensitive and neuronal cells as the ingredients, and a simple ecology
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that includes all the other assemblages of those cells Ñ the other
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organisms in the world Ñ as the environment.
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3. Overview
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PolyWorld is an ecological simulator, of a simple flat world,
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possibly divided up by a few impassable barriers, and inhabited by a
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variety of organisms and freely growing ÒfoodÓ. The inhabiting
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organisms use vision as input to a neural network brain that employs
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Hebbian learning at its synapses. The outputs of this brain fully
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determine the organismsÕ behaviors. These organisms and all other
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visible constituents of the world are represented by simple polygonal
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shapes. Vision is provided by rendering an image of the world from
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each organismÕs point of view, and using the resulting pixel map as
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input to the organismÕs brain, as if it were light falling on a retina.
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A small number of an organismÕs neurons are predetermined to
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activate a suite of possible primitive behaviors, including eating,
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mating, fighting, moving forward, turning, controlling their field of
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view, and controlling the brightness of a few of the polygons on their
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bodies. Organisms expend energy with each action, including neural
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activity. They must replenish this energy in order to survive. They
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may do so by eating the food that grows around the environment.
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When an organism dies, its carcass turns into food. Because one of
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the possible primitive behaviors is fighting, organisms can
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potentially damage other organisms. So they may also replenish
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their energies by killing and eating each other. Predation is thus
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modeled quite naturally.
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The organismsÕ simulated physiologies and metabolic rates are
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determined from an underlying genome, as are their neural
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architectures. When two spatially overlapping organisms both
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express their mating behavior, reproduction occurs by taking the
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genetic material from the two haploid individuals, subjecting it to
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crossover and mutation, and then expressing the new genome as a
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child organism.
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One way to look at this artificial world is as a somewhat
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complex energy balancing problem. The fittest organism will be the
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one that best learns to replenish its energies by eating, and to pass
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on its genes by mating. The particular patterns of activity that a
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successful organism engages in - the methods by which it sustains
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and reproduces itself - will be optimal for some particular fitness
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landscape. But since that fitness landscape depends upon the
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behavior of the world's other inhabitants, it must, per force, be a
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dynamic landscape. Since there is considerable variation in the
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placement and behavior of food and other organisms in the world,
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that fitness landscape is also fundamentally stochastic. Indeed, if the
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"fittest organism in the world" fails to find a suitable mate in order to
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pass on the important bits of its genetic material, then those genes
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will be lost... possibly for all time. Accordingly, every world has the
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potential to be quite different from every other world.
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Once an Evolutionarily Stable Strategy (ESS) has emerged, there
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is no fitness function except survival. Until an ESS has emerged, PW
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is run in a sort of Òon-line Genetic Algorithm (GA)Ó mode, with an ad
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hoc fitness function. During this stage, a minimum number of
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organisms may be guaranteed to populate the world. If the number
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of deaths causes the number of organisms extant in the world to
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drop below this minimum, either another random organism may be
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created by the system, or the offspring of two organisms from a table
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of the N fittest may be created, or, rarely, the best organism ever
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may be returned to the world unchanged. This ad hoc fitness
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function rewards organisms for eating, mating, living their full
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lifespan, dying with reserve energies, and simply moving. Each
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reward category is normalized by the maximum possible reward in
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each category, and has a specifiable scale factor to permit easy
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tuning of the fitness function. Some simulation runs acquire an ESS
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in the first seed population and never require this on-line GA stage.
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Throughout this paper, the term created is applied to organisms
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spontaneously generated by the system, while born is used to refer
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to organisms resulting from the mating behaviors of the organisms.
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Current high end simulations typically involve over 300
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organisms, with up to approximately 200 neurons each, and require
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about 13 seconds per time-step on a Silicon Graphics Iris 4D/240-
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GTX. With an average lifespan of about 500 time-steps, and a time-
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to-first-offspring of about 100 time-steps, this means that 500
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generations can be run at this complexity in about 1 week. More
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modest simulations with around 100 comparable organisms require
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about 4 seconds per frame, and take a day or two for the same task.
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And at the low complexity end, simple demonstration worlds can be
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run in Òreal timeÓ, at a few frames per second, and allow a more
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interactive experience for learning the system.
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Figure 1 shows a sample view of the PolyWorld terrain,
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populated with three related but distinct sub-species. The largest
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panel shows a broad view of the world: the dark green ground
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plane, the brown, impassable barriers, the bright green pieces of
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food, and the multicolored organisms. Just above this oblique world
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view are four graphs of various informative simulation parameters.
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Above these at the top of the figure are many small views of the
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world drawn from the point of view of each of the organisms in the
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world; these are the images seen by the those organisms. At the top
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right are a few numerical statistics. And in the bottom right pane is
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a close-up view of the current ÒfittestÓ organism.
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4. Genetics
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An organismÕs genes completely encode both its ÒphysiologyÓ
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and its neural architecture. Table 1 lists the full complement of
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genes present in the organisms of PW.
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¥ size
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¥ strength
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¥ maximum speed
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¥ ID
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¥ mutation rate
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¥ number of crossover points
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¥ lifespan
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¥ fraction of energy to offspring
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¥ number of neurons devoted to red component of vision
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¥ number of neurons devoted to green component of vision
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¥ number of neurons devoted to blue component of vision
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¥ number of internal neuronal groups
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¥ number of excitatory neurons in each internal neuronal
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group
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¥ number of inhibitory neurons in each internal neuronal
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group
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¥ initial bias of neurons in each non-input neuronal group
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¥ bias learning rate for each non-input neuronal group
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¥ connection density between all pairs of neuronal groups and
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neuron types
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¥ topological distortion between all pairs of neuronal groups
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and neuron types
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¥ learning rate between all pairs of neuronal groups and
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neuron types
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Table 1. List of genes in organisms of PolyWorld.
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All genes are 8 bits in length, and may be Gray-coded or
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binary-coded. All but the ID gene are used to provide 8 bits of
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precision between a specifiable minimum and maximum value for
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the corresponding attribute. For example, if the minimum possible
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size is minSize, and the maximum possible size is maxSize, and the
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value of the size gene (scaled by 255 to lie between 0.0 and 1.0) is
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valSizeGene, then the size of the organism with this gene will be:
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size = minSize + valSizeGene * (maxSize - minSize)
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These extrema values, along with a variety of other controlling
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parameters for the simulation, are contained in a Òworld fileÓ that is
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read by the simulator at startup.
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The first 8 genes control the organismÕs simulated physiology.
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Its size and strength affect both the rate at which it expends energy
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and the outcome of ÒfightsÓ with other organisms. In addition, its
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size is related directly to the maximum energy that it can store
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internally. The next gene, maximum speed, also affects its
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ÒmetabolicÓ rate.
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The ID geneÕs only function is to provide the green component
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of the organismÕs coloration at display time. Since organisms can
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actually see each other, this could, in principle, support mimicry. For
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example, a completely passive species could evolve to display the
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green coloration of a very aggressive species if it were of selective
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advantage. It might also be possible to attract potential mates by
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displaying the green coloration of food, though this might be of
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limited survival value. (In practice, however, neither of these
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somewhat sophisticated evolutionary responses has yet been
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observed.)
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Mutation rate, the number of crossover points used during
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reproduction, and maximum lifespan were placed in the genes in
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order to permit a kind of meta-level genetics, and in recognition of
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the fact that these parameters were themselves evolved in natural
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systems. They are, however, typically constrained to operate within
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ÒreasonableÓ limits; 0.01 to 0.1 for mutation rate, 2 to 8 for number
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of crossover points, and a few hundred to a few thousand Òtime-
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stepsÓ for lifespan.
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The final physiology gene controls the fraction of an organismÕs
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remaining energy that it will donate to its offspring upon birth. The
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offspringÕs total available energy on birth is the sum of these
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contributions from the two parents. Accordingly, at least one aspect
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|
of sexual reproduction may be captured by PWÕs evolutionary
|
|
ÒbiologyÓ: it is entirely possible for two interbreeding sub-species to
|
|
be almost identical genetically, differing only in the amount of
|
|
personal energy devoted to the reproductive process. PolyWorld has
|
|
not yet been instrumented to observe for this phenomenon.
|
|
|
|
The remaining genes are used to define the organismÕs neural
|
|
architecture. These control parameters will be discussed in the
|
|
section on Neurons and Learning. It should be noted here, however,
|
|
that one of the motivations for this method of specifying the neural
|
|
architecture was to reduce the number of genes necessary to specify
|
|
the neural system. Early versions of PW used a simpler, fully
|
|
recurrent neural architecture, and maintained a complete matrix of
|
|
synaptic efficacies between all pairs of neurons in the genes. For 200
|
|
(NN) neurons, this older model required 40,000 (NN2) genes. The
|
|
current scheme supports evolving neural architectures which are
|
|
fully specified by 12NG2 + 232NG + 1026, where NG is the number of
|
|
internal neuronal ÒgroupsÓ or clusters (output group sizes are fixed to
|
|
1, and input groups do not need biases, bias learning rates, or
|
|
incoming synaptic connections). Thus, for 4 internal groups, with up
|
|
to 32 neurons per group, plus up to 16 neurons per vision group (of
|
|
which there are 3, one for each color component: red, green, blue),
|
|
plus 2 other input groups (one neuron per group), plus the standard
|
|
7 output groups (one neuron each), a network of up to 185 neurons
|
|
can be fully specified by just 2,146 genes. The large constants in this
|
|
equation (232 and 1026) are due to the fixed set of input and output
|
|
groups, and, especially, the desire to maintain each output neuron as
|
|
a distinct group. Though the number of specifications are
|
|
significantly reduced from a full crossbar matrix, this number still
|
|
heavily outweighs the number of genes devoted to physiology. To
|
|
permit a more robust exploration of the space of possible
|
|
physiologies, then, the first crossover during genetic reproduction is
|
|
always forced to occur somewhere within the set of physiology
|
|
genes.
|
|
|
|
An organismÕs genome is allocated and interpreted such that
|
|
space is available for the maximum possible number of neuronal
|
|
groups. That is, one of the parameters specified per pair of groups in
|
|
a network with 3 groups out of a maximum of 5 groups would be
|
|
accessed as:
|
|
|
|
1,1 1,2 1,3 -- -- 2,1 2,2 2,3 -- -- --
|
|
3,1 3,2 3,3 -- --
|
|
|
|
where the entries marked Ò--Ó serve simply as place holders. This is
|
|
as opposed to an access scheme looking like:
|
|
|
|
1,1 1,2 1,3 2,1 2,2 2,3 3,1 3,2 3,3
|
|
|
|
where the entries are contiguous. The reason for this is to permit a
|
|
smoother evolution of these neural architectures. The addition of a
|
|
fourth group would leave the old connections intact in the first
|
|
representation, but not in the second. It is even possible for a useful
|
|
subcomponent of the architecture to ride along dormant in the genes
|
|
to be expressed at a later time.
|
|
|
|
Though learning is supported in the neural network model
|
|
employed in PW, only the architecture and some initial values are
|
|
encoded in the genes; hence evolution in PW is purely Darwinian, not
|
|
Lamarckian.
|
|
|
|
As in most GAÕs, when an organism is created from scratch, the
|
|
bits in its genes are first zeroed, and then turned on with a certain
|
|
bit probability. Unlike most GAÕs, it is possible to specify a range of
|
|
legal bit probabilities, rather than always using 0.5. The bit
|
|
probability for an individual organism is then randomly selected
|
|
from this range and used to initialize the organismÕs bit-string
|
|
genome. So the probability of a bit being on in a particular organism
|
|
will depend on the value randomly selected from the specified range,
|
|
while the probability of a bit being on in the population as a whole
|
|
will just be the mean of the specified range (0.5 if the range is 0.0 to
|
|
1.0). This permits a wider variance in local, organism-specific bit
|
|
probabilities in early populations, rather than depending entirely on
|
|
mutation and cross-over to so shuffle the bits. Whether this is of any
|
|
real value should be tested in a simpler GA system, and may be
|
|
problem-specific in any event. Here it was felt that both the older
|
|
fully-recurrent neural network architecture and the later evolving
|
|
neural architectures were more likely to have
|
|
behaviorally/evolutionarily useful solutions with lower bit densities;
|
|
this provided a mechanism for so biasing the initial seed population
|
|
without ruling out selection towards the unexpected end of the
|
|
spectrum.
|
|
|
|
There is an optional Òmiscegenation functionÓ (so dubbed by
|
|
Richard Dawkins), that may be used to probabilistically influence the
|
|
likelihood of genetically dissimilar organisms producing viable
|
|
offspring; the greater the dissimilarity, the lower the probability of
|
|
their successfully reproducing. This function is not typically invoked
|
|
until after a (specifiable) ÒsignificantÓ number of births without an
|
|
intervening creation in order to allow the early stages of the
|
|
simulation to explore as many genetic recombinations as possible.
|
|
|
|
|
|
5. Physiology and Metabolism
|
|
|
|
As discussed above, the simulated physiology of PolyWorldÕs
|
|
organisms is determined by their genes. The size of the organism
|
|
directly affects the maximum amount of energy that the organism
|
|
can store. If an organismÕs size is allowed to range between minSize
|
|
and maxSize, and its energy capacity ranges between minECap and
|
|
maxECap, then a given organismÕs actual energy capacity, ECap is
|
|
given as:
|
|
|
|
ECap = minECap + (size - minSize) * (maxECap - minECap) /
|
|
(maxSize - minSize)
|
|
|
|
Similar linear relations are used to determine the influence of an
|
|
organismÕs size on the rate at which it expends energy during
|
|
forward or turning movement (relative to a specifiable maximum-
|
|
size-penalty), and a size-advantage it will have during a fight with
|
|
another organism (relative to a specifiable maximum-size-
|
|
advantage).
|
|
|
|
An organismÕs strength also affects both its energy expenditure
|
|
and its advantage in a fight. Strength directly scales the total energy
|
|
used in a given time step, and thus usually ranges around 1.0
|
|
(typically 0.5 to 2.0). An attackerÕs strength also scales the effect on
|
|
the victimÕs energy loss (fighting is discussed in more detail below in
|
|
the section on Behavior).
|
|
|
|
The energy expended by an organismÕs neural processing is
|
|
determined linearly from the number of neurons and the number of
|
|
synapses it has. A maximum number of neurons and synapses is
|
|
determined from the control parameters for the entire world, then
|
|
each individualÕs neural energy expenditure is computed relative to
|
|
these maxima. Globally applied Òneuron-to-energyÓ and Òsynapse-to-
|
|
energyÓ conversion factors then multiply these scaled neuron and
|
|
synapse counts to determine the actual energy expended per time
|
|
step.
|
|
|
|
There are similar behavior-to-energy conversion factors for
|
|
each of the primitive behaviors (eating, mating, fighting, moving,
|
|
turning, focusing, and lighting). The total energy expended in a time
|
|
step is then the activation (0. to 1.) of the corresponding
|
|
output/behavior neuron multiplied by that behaviorÕs energy-
|
|
conversion factor, summed over all behaviors, plus the neural energy
|
|
expenditure, plus a specifiable fixed energy drain, with this sum
|
|
finally scaled by the organismÕs strength.
|
|
|
|
As should be evident, there are clear energy conservation
|
|
benefits to being small and weak, yet there are clear predatory
|
|
advantages to being large and strong. Size also permits an overall
|
|
greater capacity to store energy, thus making energy available for
|
|
additional behavioral activity, including reproduction. The interplay
|
|
between these opposing advantages is intended to produce niches in
|
|
the fitness landscape, which may change over time. There are
|
|
similar opposing pressures between energy expenditure and visual
|
|
acuity on the number of input neurons devoted to vision.
|
|
|
|
There are two classes of energy storage in each organism:
|
|
health-energy, and food-value-energy. Both are replenished by
|
|
eating food. Both are depleted by neural activity and by engaging in
|
|
the various behaviors. But when an organism is attacked, only its
|
|
health-energy is depleted by the attack. If this health-energy
|
|
reaches zero, the organism dies. When an organism dies it is
|
|
converted into a piece of food containing an amount of energy equal
|
|
to the organismÕs food-value-energy. This separation of health-
|
|
energy from food-value-energy makes the predator-prey
|
|
interactions quite natural; i.e., it is possible for an organism to be
|
|
killed by having its health-energy driven to zero, while still
|
|
maintaining a relatively high food value for the attacker.
|
|
|
|
An organismÕs food-value-energy will always be greater than
|
|
or equal to its health-energy, yet both classes of energy have the
|
|
same maximum capacity. Accordingly, an organism may continue to
|
|
eat to replenish its health-energy after its food-value-energy has
|
|
reached capacity. It is the health-energy that is provided as input to
|
|
the neural network (see next section), and that is used to determine
|
|
the amount of energy to be transferred to offspring.
|
|
|
|
Purely for the purposes of display, an organismÕs length and
|
|
width are scaled by (the square root of) its maximum speed, length
|
|
being multiplied, width being divided. Thus faster individuals will
|
|
appear longer and sleeker, while slower individuals will appear
|
|
shorter and bulkier. Since an organismÕs visual acuity is subject to
|
|
evolutionary pressures, it is conceivable that an organism might
|
|
emerge that was able to ascertain another organismÕs maximum
|
|
speed purely from its shape, if there was a great enough advantage
|
|
to the acquisition of this information (though this is not expected to
|
|
be the case).
|
|
|
|
|
|
6. Neural Systems and Learning
|
|
|
|
The inputs to an organismÕs neural network ÒbrainÓ are its
|
|
ÒvisionÓ, the current normalized level of its internal health-energy
|
|
store, and a random value. The outputs are the suite of 7 possible
|
|
primitive behaviors (eating, mating, fighting, moving, turning,
|
|
focusing, and lighting). The internal neurons and all of the synaptic
|
|
connections have no prespecified functionality; their utility is
|
|
determined entirely by genetics and natural selection.
|
|
|
|
The form of an organismÕs brain, or neural system, is fully
|
|
characterized by a set of parameters that are encoded in its genes.
|
|
Referring back to Table 1, notice that the number of neurons devoted
|
|
to each color component of vision is specified separately, permitting
|
|
a specialization for more resolution in the most effective color, should
|
|
this be of selective advantage. These numbers typically range
|
|
between 1 and 16 neurons per color.
|
|
|
|
Next is a parameter that specifies the number of internal
|
|
neuronal groups or clusters. This typically ranges from 1 to 5. In
|
|
addition, there are 5 input groups (red vision, green vision, blue
|
|
vision, energy level, and random), plus 7 output groups (the
|
|
behaviors listed above).
|
|
|
|
Each neural group may have distinct populations of excitatory
|
|
(e-) and inhibitory (i-) neurons. The number of e- and i-neurons
|
|
are specified on a per group basis, and typically range between 1 and
|
|
16 neurons of each type. Synaptic connections from e-neurons are
|
|
always excitatory (ranging from 0.0 to a specifiable maximum
|
|
efficacy). Synaptic connections from i-neurons are always inhibitory
|
|
(ranging from -1.e-10 to the negative of the maximum efficacy).
|
|
|
|
Though the bias on each of the non-input neurons varies
|
|
during the simulation, the initial values for these biases and their
|
|
learning rates are specified on a per group basis, for each of the non-
|
|
input neural groups. Biases are updated by a Hebbian learning rule,
|
|
as if it were a synaptic connection to a neuron that was always fully
|
|
activated, but unlike other synapses in this network, the bias may
|
|
change sign. Biases typically range from -1.0 to 1.0, and bias
|
|
learning rates typically range from 0.0 to 0.2.
|
|
|
|
The remaining parameters - connection density (CD) ,
|
|
topological distortion (TD), and learning rate (LR) - are all specified
|
|
for each pair of neuronal groups and neuron types. That is, separate
|
|
values for each of these parameters are specified for the excitatory-
|
|
to-excitatory (e-e), excitatory-to-inhibitory (e-i), inhibitory-to-
|
|
inhibitory (i-i), and inhibitory-to-excitatory (i-e) synaptic
|
|
connections between group i and group j, for each pair of groups i
|
|
and j.
|
|
|
|
Connection density, as the name suggests, is used to determine
|
|
the extent of the connectivity between neuronal groups. The number
|
|
of e-e synapses between group i and group j is given by the nearest
|
|
integer to CDe-e(i,j) * Ne(i) * Ne(j), where CDe-e(i,j) is the e-e CD
|
|
from group j to group i, Ne(i) is the number of e-neurons in group i,
|
|
and Ne(j) is the number of e-neurons in group j. Similar expressions
|
|
hold for the other types of connections between all pairs of groups.
|
|
CD can range from 0.0 to 1.0.
|
|
|
|
Topological distortion is used to determine the degree of
|
|
disorder in the mapping of synaptic connections from one group to
|
|
the next. That is, for a TD of 0.0, synapses are mapped to perfectly
|
|
contiguous stretches of neurons in the adjacent layer; for a TD of 1.0,
|
|
synapses are mapped in a completely random fashion between
|
|
adjacent layers. Thus retinatopic maps such as are observed in
|
|
natural organisms can be enforced (or not) at the architectural level
|
|
(as well as resulting from the learning process). TD typically ranges
|
|
from 0.0 to 1.0.
|
|
|
|
Learning rate controls the Hebbian learning process at the
|
|
synapses between each pair of neuronal groups. This permits
|
|
natural selection to favor hardwired, ÒinstinctiveÓ connections for
|
|
some neural pathways, while supporting learning in other pathways.
|
|
LR typically ranges from 0.0 to 0.2.
|
|
|
|
This method of specifying the neural architecture is fairly
|
|
general, and is not biased for any particular neural organization.
|
|
Possibly, one might expect to evolve a preponderance of inhibitory
|
|
connections, especially locally, if the simulated neural architectures
|
|
evolve to match real neural systems; yet the possibility exists for
|
|
establishing local excitatory connections (such as are found in CA3 in
|
|
the hippocampus). The technique does not, however, explicitly
|
|
model architectures whose characteristics are heavily based upon
|
|
spatial organization (such as the parallel fibers originating from the
|
|
granule cells in the cerebellum). A straightforward extension to the
|
|
current method, that allowed unique specifications of the same
|
|
parameters along multiple spatial dimensions, could account for such
|
|
organizational schemes. However, with the limited compute
|
|
resources currently being applied to PW simulations, and thus the
|
|
limited number of neurons permitted in each brain, it was not
|
|
deemed worthwhile to further decompose the groups into these
|
|
spatial subcategories.
|
|
|
|
When an organismÕs brain is ÒgrownÓ from its underlying
|
|
genome, the synaptic efficacies are randomly distributed between
|
|
specifiable minimum and maximum values. The brain is then
|
|
exposed to a sequence of mock visual inputs consisting of random
|
|
noise, for a specifiable number of cycles. This is all pre-birth. In this
|
|
fashion, it is unnecessary to store any synaptic efficacies in the
|
|
genes. This approach was inspired by LinskerÕs simulations of visual
|
|
cortex, which gave rise to on-center-off-surround cells, orientation-
|
|
selective cells, and so on, when exposed only to noise. The crucial
|
|
aspects of the networks in this case are their architecture Ñ layered
|
|
receptive fields in LinskerÕs case, evolved arbitrary topology in PW Ñ
|
|
and the learning rule Ñ Hebbian learning in both cases.
|
|
|
|
It was debated whether to update all the organismsÕ brains
|
|
synchronously or not. That is, whether each organismÕs neural
|
|
network should be allowed to make a complete neural activation and
|
|
synaptic learning pass with each time step. Even though it was
|
|
desired to penalize organisms that evolved additional neurons and
|
|
synapses, synchronous updating was ultimately selected, primarily
|
|
because the corresponding structures in nature are executed in
|
|
parallel, and penalties based on their serial implementation would be
|
|
excessive. The penalty is more properly derived from the additional
|
|
energy use associated with these additional neural structures.
|
|
|
|
At each time step, the input neurons are set to the appropriate
|
|
values, corresponding to the organismÕs visual field, its current
|
|
health-energy level, and a random number. New neuronal
|
|
activations are computed by the simple formulae:
|
|
|
|
xi = S ajt sijt
|
|
|
|
ait+1 = 1 / (1 + e-axi)
|
|
|
|
where ajt is the neuronal activation of neuron j at time t (the
|
|
beginning of this time step), sijt is the synaptic efficacy from neuron
|
|
j to neuron i at time t, ait+1 is the neuronal activation of neuron i at
|
|
time t+1 (the end of this time step), and a is a specifiable logistic
|
|
slope.
|
|
|
|
The synaptic efficacies are then updated according to a Hebb
|
|
rule, as:
|
|
|
|
sijt+1 = sijt + hckl (ait+1 - 0.5) (ajt - 0.5)
|
|
|
|
where sijt+1 is the synaptic efficacy from neuron j to neuron i at time
|
|
t+1, and hckl is the learning rate for connections of type c (e-e, e-i, i-
|
|
i, or i-e) from group l to group k. An optional multiplicative decay
|
|
term may also be applied to the synaptic efficacy.
|
|
|
|
This simple Òsumming and squashingÓ neuron and Hebbian
|
|
update rule are certainly coarse abstractions of the complexities
|
|
observed in real neural systems. Credence is lent to these particular
|
|
abstractions by the previously quoted simulation work of Linsker,
|
|
Pearson, and others, and by LinskerÕs and othersÕ information-
|
|
theoretic analytical work on such systems, which suggest that they
|
|
may capture the information-processing attributes of real neural
|
|
systems, if not their precise method of action. These neuronal and
|
|
learning models were selected for use in PW based on these results
|
|
and the modelsÕ computational tractability.
|
|
|
|
During the course of a simulation, neural and synaptic activities
|
|
may be monitored for a number of organisms in the world (the top
|
|
five ÒfittestÓ, according to the ad hoc fitness function discussed
|
|
earlier, even if it is not being used to create new organisms). An
|
|
example is shown in Figure 2. Gray-scale is used to denote neural
|
|
activation (between 0.0 and 1.0) and synaptic efficacy (between
|
|
-maxEfficacy and +maxEfficacy). At the very bottom of the grid is
|
|
the color vision buffer. The neural activations at the beginning of
|
|
this time step are shown in a horizontal row just above the color
|
|
vision, along with the red, green, and blue input neuron activation
|
|
levels, and the energy and random input neuron activation levels.
|
|
White frames are drawn around each neuronal group, except for the
|
|
vision neurons which are framed in their corresponding color. Black
|
|
frames are drawn around each synapse, hence the unframed areas
|
|
are regions of null connectivity. Synapses that appear brighter than
|
|
the neutral gray background are excitatory; those that appear darker
|
|
than the background are inhibitory. The leftmost vertical bar shows
|
|
neuronal biases. The non-input neural activations at the end of this
|
|
time step are shown in the adjacent vertical bar; again, neuronal
|
|
groups are framed in white. Hence the diagram may be read as an
|
|
incomplete crossbar connecting the neuronal states at the beginning
|
|
of the time step (horizontally) to those at the end of the time step
|
|
(vertically), through the various synaptic connections.
|
|
|
|
Early simulations with PW had much simpler, fully recurrent
|
|
neural architectures. Though not particularly representative of real
|
|
biological neural architectures, acceptable behavior strategies were
|
|
evolved, and some of the results being presented are from organisms
|
|
using these early networks.
|
|
|
|
|
|
7. Vision
|
|
|
|
The color vision supplied as input to the organism is first
|
|
rendered at the minimum window size permitted on the Iris + 1
|
|
(because even-sized buffers can be accessed faster), or 22 x 22
|
|
pixels. The pixel row just above vertical center is then properly anti-
|
|
aliased into whatever number of visual neurons an organism has.
|
|
Even though organisms and the environment of PW are three-
|
|
dimensional, the organismsÕ vision consists of just this one-
|
|
dimensional strip of pixels, rather than the complete pixel map.
|
|
Since the organisms are confined to motion on a ground-plane, it was
|
|
felt that the benefit derived from computational efficiency
|
|
outweighed the small loss of information resulting from this
|
|
restriction.
|
|
|
|
As was discussed above in the Genetics section, the number of
|
|
neurons devoted to each of the color components is evolved
|
|
independently (though they are adjacent on the genome, and so may
|
|
tend to crossover together).
|
|
|
|
As was discussed in the Neurons and Learning section, an
|
|
organismÕs vision is shown in the display of the brain internals that
|
|
may be invoked interactively for some of the ÒfittestÓ individuals. In
|
|
addition, the full 22 x 22 pixel map for each of the organisms is
|
|
usually displayed at the top of the screen. This is mostly for a
|
|
Òreality checkÓ Ñ visual reassurance that the organisms are seeing
|
|
what they would be expected to see, and may be disabled for a slight
|
|
speed gain.
|
|
|
|
The vertical field of view of the organisms is fixed at 10o, since
|
|
they only see a strip of pixels just above the center of the image.
|
|
Their horizontal field of view, however, is under their own
|
|
ÒvolitionalÓ, neural control. That is, the activation of the focusing
|
|
neuron is mapped between a minimum and maximum field of view
|
|
(typically 20o to 120o). In principle, this might permit some depth
|
|
of field determinations based on cyclic focusing operations, though
|
|
nothing so sophisticated has emerged (or is expected to emerge) in
|
|
the limited neural systems employed by the organisms so far.
|
|
|
|
This type of direct perception of the environment should
|
|
answer one of cognitive psychologyÕs most frequently sounded
|
|
complaints against traditional AI: The organisms of PW are
|
|
ÒgroundedÓ in their environment by their sense of vision.
|
|
|
|
|
|
8. Behavior
|
|
|
|
A suite of primitive behaviors is made available to all
|
|
organisms in PW, namely:
|
|
|
|
¥ eating
|
|
¥ mating
|
|
¥ fighting
|
|
¥ moving
|
|
¥ turning
|
|
¥ focusing
|
|
¥ lighting
|
|
|
|
All of these behaviors are expressed by raising the activation
|
|
level of a prespecified neuron in the brain. Given computational
|
|
constraints, it was felt that a minimum number of cycles should be
|
|
devoted to motor activity, hence this simple one-neuron-one-
|
|
behavior mapping. The first three behaviors, eating, mating, and
|
|
fighting, all have some associated threshold that must be exceeded
|
|
before the activity is initiated. Energy is expended by each of the
|
|
behaviors, including eating. The energy expenditure rates are
|
|
controllable by scale factors (see Physiology and Metabolism) in the
|
|
Òworld fileÓ (see The New Context).
|
|
|
|
Eating is an organismÕs method for replenishing depleted
|
|
energy stores. In order to eat, an organismÕs position must cause it
|
|
to overlap a piece of food. The amount of energy consumed is
|
|
proportional to the activation of the eating neuron, once that
|
|
activation exceeds a specifiable threshold.
|
|
|
|
Mating is an organismÕs method for reproducing. In order to
|
|
reproduce, an organismÕs position must cause it to overlap another
|
|
organism, and both organisms must express their mating behavior in
|
|
excess of a specifiable threshold. The outcome of the reproductive
|
|
attempt may be affected by the miscegenation function (see
|
|
Genetics), or by the maximum number of organisms permitted in the
|
|
world (see The New Context). The organismÕs ÒdesireÓ to mate (the
|
|
activation level of its mating neuron) is mapped onto its blue color
|
|
component for display purposes; this coloration is visible to other
|
|
organisms as well as to human observers.
|
|
|
|
Fighting is an organismÕs method for attacking another
|
|
organism. In order to successfully attack the other organism, the
|
|
attackerÕs position must cause it to overlap the attackee. Only one
|
|
organism need express its fighting behavior to successfully attack
|
|
another. The energy that is depleted from the prey is a function of
|
|
the volitional degree of the attack (the activation of the predatorÕs
|
|
fight neuron), the predatorÕs current health-energy level, the
|
|
predatorÕs strength, and the predatorÕs size. The product of these
|
|
contributing factors from the predator is scaled by a global attack-to-
|
|
energy conversion factor to make the final determination of amount
|
|
of energy depletion applied to the prey. If both organisms are
|
|
expressing their fight behavior, the same computation is carried out
|
|
reversing the roles of predator and prey. Each organismÕs desire to
|
|
fight is mapped onto its red color component for display purposes;
|
|
this coloration is visible to other organisms as well as to human
|
|
observers.
|
|
|
|
Moving refers to an organismÕs forward motion. Unless an
|
|
organism encounters a barrier, or the edge of the world, it will move
|
|
forward by an amount proportional to the activation of its moving
|
|
neuron.
|
|
|
|
Turning refers to a change in an organismÕs orientation on the
|
|
ground-plane (yaw). An organism will turn about its y-axis by an
|
|
amount proportional to the activation of its turning neuron.
|
|
|
|
Focusing refers to an organismÕs control over its horizontal field
|
|
of view. As discussed in the Vision section, the activation of an
|
|
organismÕs focusing neuron will be linearly mapped onto a range of
|
|
possible angles to provide its horizontal field of view. This makes it
|
|
possible for an organism to use its vision to survey most of the world
|
|
in front of it or to focus closely on smaller regions of the world.
|
|
|
|
Lighting refers to an organismÕs control over the brightness of a
|
|
cap of several polygons on the front face of its ÒbodyÓ. The activation
|
|
of an organismÕs lighting neuron is linearly mapped onto the full 0 to
|
|
255 brightness range in all color components of these front polygons.
|
|
Accordingly, a simple form of visual communication is possible, in
|
|
principle, for the organisms inhabiting PW. (No evidence of their use
|
|
of this form of communication has yet been found nor sought to date,
|
|
though evidence of the organismsÕ use of vision for controlling
|
|
locomotion has been observed.)
|
|
|
|
|
|
9. The New Context
|
|
|
|
The ÒworldÓ of PolyWorld is a flat ground-plane, possibly
|
|
divided up by a few impassable barriers, filled with randomly grown
|
|
pieces of food, and inhabited by the organisms previously described.
|
|
|
|
The number of organisms in the world is controllable by
|
|
several means. First, a maximum number of organisms is specifiable,
|
|
in order to keep the problem computationally tractable. Second, a
|
|
minimum number of organisms is specifiable to keep the world
|
|
populated during the early on-line GA stage (see Genetics). Finally,
|
|
an initial number of organisms is specifiable to determine how many
|
|
individuals to seed the world with at the start of the simulation.
|
|
|
|
Food is grown at a specifiable rate up to a specifiable maximum
|
|
number of grown food items. The number of food items may be
|
|
guaranteed to be kept between a specifiable minimum and maximum
|
|
food count. Subject to this maximum, food is also generated as the
|
|
result of an organismÕs death. The amount of energy in a piece of
|
|
food that is grown is randomly determined between a specifiable
|
|
minimum and maximum food energy. The amount of energy in a
|
|
piece of food resulting from the death of an organism is that
|
|
organismÕs food-value-energy (see Physiology and Metabolism) at
|
|
death, or a specifiable minimum-food-energy-at-death.
|
|
|
|
An arbitrary number of barriers may be placed in the world,
|
|
which inhibit movement of the organisms. These can serve to
|
|
partially or completely isolate populations of organisms, and as such
|
|
can contribute significantly to speciation (genetic diversity). For
|
|
reasons of computational efficiency, they are typically placed parallel
|
|
to the z (depth) axis, though this is not strictly necessary.
|
|
|
|
It is possible to manage the minimum, maximum, and initial
|
|
numbers of organisms and food items, along with the ad hoc fitness
|
|
statistics, simultaneously for a number of different independent
|
|
ÒdomainsÓ. These domains must be aligned parallel to the z (depth)
|
|
axis, and typically, though not necessarily, coincide with the divisions
|
|
imposed on the world by the barriers. This permits the simultaneous
|
|
ÒculturingÓ of completely independent populations when barriers
|
|
extend the full length of the world, or limits the spread of genes
|
|
between domains to those resulting from actual movement of
|
|
organisms when the barriers are arranged so as to leave gaps for
|
|
organisms to travel through. If the domain fitness statistics were not
|
|
kept separately, then genes from one domain could migrate to
|
|
another domain by virtue of their global fitness during the start-up
|
|
on-line GA phase.
|
|
|
|
It is possible to set a flag such that the edges of the world act
|
|
as barriers (the usual), wrap around, or arenÕt there at all. In this
|
|
last case, PWÕs ground-plane acts much like BraitenbergÕs table top,
|
|
with organisms that move past the edge of the world dying instantly.
|
|
|
|
Various monitoring and graphing tools exist to assist in
|
|
following the progress of a simulation and in developing an
|
|
understanding of the evolutionary and neural dynamics at work. As
|
|
was mentioned earlier (in the section on Neural Systems and
|
|
Learning), a display of the internal workings of any of the five
|
|
ÒfittestÓ organisms may be called up at any time. In addition, a small
|
|
window that maintains an overhead view of the world will
|
|
automatically track that same organism upon request. This overhead
|
|
window may also be zoomed in and out to follow the organism more
|
|
closely.
|
|
|
|
Also available are graphic displays of the time histories of
|
|
certain quantities of interest, including: (1) population sizes (overall
|
|
and per domain), (2) the past maximum, current maximum, and
|
|
current average values of the ad hoc fitness function, (3) the ratio of
|
|
the number of organisms ÒbornÓ (by mating) to the sum of the
|
|
number of organisms born and created, and (4) the ratio of the
|
|
difference of food-energy in and food-energy out to the sum of these
|
|
two values. These last two items in particular are important gauges
|
|
of the course of the simulation. Item (3) will start at 0.0 and
|
|
asymptote to 1.0 for successful simulations, in which at least one
|
|
species has emerged with an ESS; it will peak well below 1.0 for
|
|
unsuccessful simulations. Item (4) ranges from -1.0 to 1.0, and
|
|
should asymptote to 0.0, for a world where energy is conserved.
|
|
Three values are actually plotted for item (4): (a) the total food-
|
|
energy, including the initial seeding of the world, which starts at 1.0
|
|
and should asymptote to 0.0, (b) the average food-energy, excluding
|
|
the initial seeding of the world, which starts at 0.0, and rapidly
|
|
becomes negative, but should also asymptote to 0.0, and (c) the
|
|
current food-energy on a time-step by time-step basis, which
|
|
fluctuates rapidly, but should cluster around the average food-
|
|
energy.
|
|
|
|
One additional display can graphically present the results of an
|
|
analysis of the genetic variability in the population. All pairs of
|
|
organisms are examined to determine the magnitude of the Hamming
|
|
distance between them in gene space, and a gray-scale plot is used
|
|
to display normalized genetic distances for the entire population at
|
|
each time step.
|
|
|
|
All of the simulation control parameters and display options
|
|
are defined in a single Òworld fileÓ that is read at the start of the
|
|
simulation. In addition, some of the display options can be invoked
|
|
interactively at runtime.
|
|
|
|
There isnÕt space to go into many details of the code itself.
|
|
However, it may be worth noting that it consists of about 15,000
|
|
lines of C++, and is entirely object oriented, except for a single
|
|
routine devoted to handling the organism-organism and organism-
|
|
food interactions (for reasons of computational efficiency). The
|
|
organisms, food, and barriers are maintained in doubly-linked lists
|
|
sorted on a single dimension (x). This simple data structure has
|
|
minimal maintenance overhead, yet rules out most non-intersections
|
|
very well, and permits a sorting algorithm to be used that capitalizes
|
|
on the expected frame-to-frame coherency of organism positions. It
|
|
runs on a Silicon Graphics Iris (to take advantage of its hardware
|
|
renderer for all the vision processing), and uses a set of object
|
|
oriented C++ graphics routines (included in the line count above) that
|
|
wrap around the standard Iris graphics library.
|
|
|
|
|
|
10. Results: Speciation and Complex Emergent Behaviors
|
|
|
|
Despite the variability inherent in different worlds, certain
|
|
recurring ÒspeciesÓ have occurred in a number of the simulations run
|
|
to date. By ÒspeciesÓ, I mean groups of organisms carrying out a
|
|
common individual behavior that results in distinctive group
|
|
behaviors. Since the selection of these behaviors are derived from
|
|
the activity of their neural network brains, and the success of these
|
|
behaviors is partially a function of their physiologies, both of which
|
|
are in turn based on the genome of the organism, the behavioral
|
|
differences may generally be traced to the organismÕs genetic code.
|
|
Hence these behavioral differences are representative of different
|
|
genetic species.
|
|
|
|
A simulation is considered ÒsuccessfulÓ if and only if some
|
|
number of species emerge which are capable of sustaining their
|
|
numbers through their mating behaviors, and thus organism
|
|
creations cease. These species can be said to have developed an ESS
|
|
within the ecological environment of PW. The observational reports
|
|
below only refer to ÒsuccessfulÓ simulations.
|
|
|
|
The first of these species has been referred to as the "frenetic
|
|
joggers". In an early simulation without barriers, without a
|
|
miscegenation function, and with borders that wrap around
|
|
(essentially forming a torus), a population emerged that basically just
|
|
ran straight ahead at full speed, always wanting to mate and always
|
|
wanting to eat. That particular world happened to be benign enough,
|
|
that it turned out they would run into pieces of food or each other
|
|
often enough to sustain themselves and to reproduce. It was an
|
|
adequate, if not particularly interesting solution for that world. And
|
|
without the miscegenation function or any physical isolation due to
|
|
barriers, whatever diversity was present in the early world
|
|
population was quickly redistributed and blended into a single
|
|
species that completely dominated the world for as long as the
|
|
simulation was run.
|
|
|
|
The second recurring species has been referred to as the
|
|
Òindolent cannibalsÓ. These organisms "solve" the world energy and
|
|
reproduction problem by turning the world into an almost zero-
|
|
dimensional point. That is, they never travel very far from either
|
|
their parents or their offspring. These organisms mate with each
|
|
other, fight with each other, kill each other, and eat each other when
|
|
they die. They were most prevalent in simulations run before the
|
|
parents were required to transfer their own energies to the
|
|
offspring; the organisms of these worlds were exploiting an
|
|
essentially free energy source. With proper energy balancing, this
|
|
behavior was reduced to only an occasional flare-up near corners of
|
|
the world, where some organisms with limited motor skills naturally
|
|
end up congregating, sometimes for quite extended periods of time.
|
|
It turns out that the primary evolutionary benefit associated with
|
|
this behavior was the ready availability of mates, rather than the
|
|
ÒcannibalisticÓ food supply. This was determined by completely
|
|
eliminating the food normally left behind by an organismÕs death, yet
|
|
still observing the emergence of such species. Large colonies of these
|
|
indolent cannibals look from above like a continuous (non-gridded)
|
|
version of ConwayÕs game of LIFE.
|
|
|
|
The third recurring species has been referred to as the Òedge
|
|
runnersÓ. These organisms take the next step up from the cannibals,
|
|
and essentially reduce their world to an approximately one-
|
|
dimensional curve. They mostly just run around and around the
|
|
edge of the world (which they are forcibly prevented from running
|
|
off of in most of the simulations). This turns out to be a fairly good
|
|
strategy, since, if enough other organisms are doing it, then some will
|
|
have died along the path, ensuring adequate supplies of food. And
|
|
mates are easily found by simply running a little faster or a little
|
|
slower, running in the opposite direction, or simply stopping at some
|
|
point and waiting for other runners to arrive (all of which behaviors
|
|
have been observed). A form of this behavior persists even when
|
|
barriers block access to the rest of the world; organisms still
|
|
sometimes congregate along any edges, including the barriers. It has
|
|
been suggested [22] that this may be a form of behavioral isolation,
|
|
permitting this species to retain its genetic identity to the exclusion
|
|
of other species.
|
|
|
|
Another species recently emerged as the first evolutionarily
|
|
stable solution to a Òtable topÓ world Ñ one with no edges. These
|
|
ÒdervishesÓ evolved a simple rapid-turning strategy that kept them
|
|
away from the dangerous edges of the world, and yet explored
|
|
enough of the world to bring them into contact with food and each
|
|
other. While this basic behavioral strategy persisted for many
|
|
hundreds of generations, evolution continued to explore optimum
|
|
degrees of predation, in a sort of continuous prisonerÕs dilemma over
|
|
optimum degrees of cooperation. Waves of varying levels of
|
|
expression of the fighting behavior could be observed sweeping
|
|
through several
|
|
|
|
distinct populations over evolutionary time-scales, with the greatest
|
|
variation in behaviors clearly seen at the boundaries between these
|
|
populations.
|
|
|
|
The most interesting species and individuals are not so easily
|
|
classified. In some worlds where a single species has become
|
|
dominant, the individualsÕ behaviors have still been quite varied.
|
|
And in many worlds, no single species becomes obviously dominant.
|
|
It is especially in these simulations that a number of complex,
|
|
emergent behaviors have been observed, including:
|
|
1) responding to visual stimuli by speeding up,
|
|
2) responding to an attack by running away (speeding up),
|
|
3) responding to an attack by fighting back,
|
|
4) grazing (slowing upon encountering each food patch),
|
|
5) expressing an attraction to food (seeking out and circling
|
|
food), and
|
|
6) following other organisms.
|
|
|
|
The first item is important in that it implies that conditions
|
|
have been found that will cause evolution to select for the use of the
|
|
organismsÕ vision systems. All four of the earlier, simpler speciesÕ
|
|
behaviors would be appropriate even if these vision systems did not
|
|
exist. Yet PW was built on the assumption that vision would be a
|
|
powerful, useful sense mechanism that evolution could not fail to
|
|
employ. Even a simple speeding up in response to visual stimulation
|
|
could result in reaching food or a potential mate more effectively,
|
|
and this was the first observed visual response to emerge.
|
|
|
|
The second and third items both represent reasonable
|
|
responses to attack by a predator. Fleeing may reduce the effect of
|
|
the attack, and fighting back is an energy-efficient use of the
|
|
organismÕs own ability to fight (as opposed to expressing the fight
|
|
behavior continuously which would expend unnecessary energy).
|
|
|
|
Strategies four and five represent efficient feeding strategies.
|
|
As simple a survival skill as grazing might seem - to simply notice
|
|
when oneÕs internal energy is going up, and cease moving until it
|
|
stops going up - it was not observed until a fairly recent simulation.
|
|
It is still not a wide-spread phenomenon, though a few instances
|
|
have now been observed. Only the most recent simulation, as of this
|
|
writing, has given rise to a population of organisms that seem to be
|
|
able to actively seek out food and ÒorbitÓ it while eating; such
|
|
ÒforagingÓ is clearly a valuable survival trait. These organisms
|
|
appear to be drawn to the food as if there were a magnet or some
|
|
point attractor located in the food and controlling the organismsÕ
|
|
behavior, though no such mechanism exists in PW. Their attraction
|
|
to the food is purely a result of selection forces acting on the the
|
|
neural architecture connecting their vision systems to their motor
|
|
systems.
|
|
|
|
The final, ÒfollowingÓ strategy has also emerged only in this
|
|
most recent simulation. Clearly of value, whether for seeking a prey
|
|
or a mate, this represents the most complex coupling of the vision
|
|
sense mechanism to the organismsÕ motor controls yet observed.
|
|
Small ÒswarmsÓ of organisms, and one example of a few organisms
|
|
ÒchasingÓ each other were even suggestive of simple ÒflockingÓ
|
|
behaviors.
|
|
|
|
All of these behaviors, being inherently temporal phenomena,
|
|
require some sort of temporal medium for display. Short video clips
|
|
of most of the above species and behaviors should be available in a
|
|
companion videotape released by the publisher of this book.
|
|
|
|
|
|
|
|
11. Concluding Remarks
|
|
|
|
Real benefits have already begun to accrue from the studies of
|
|
artificial neural systems. Meanwhile, the study of artificial evolution
|
|
Ñ genetic algorithms Ñ is yielding insights into problems of
|
|
optimization, and into the dynamics of natural selection. One form of
|
|
the study of Artificial Life is the perhaps obvious combination of
|
|
these two fields of research. Adding computer graphics visualization
|
|
techniques yields the basic substrate of PolyWorld.
|
|
|
|
One of the primary goals set out for PW has already been met:
|
|
the evolution of complex emergent behaviors from only the simple
|
|
suite of primitive behaviors built into the organisms of PW, their
|
|
sense mechanisms, and the action of natural selection on their neural
|
|
systems. These recognizable behavioral strategies from real living
|
|
organisms, such as ÒfleeingÓ, Òfighting backÓ, ÒgrazingÓ, ÒforagingÓ,
|
|
ÒfollowingÓ, and ÒflockingÓ, are purely emergent in the PW
|
|
environment. And built as they are from simple, known primitive
|
|
behaviors, in response to simple, understandable ecological
|
|
pressures, they may be able to remove a little bit of the mystery, if
|
|
not the wonder, at the evolution of such behaviors in natural
|
|
organisms. Indeed, the organisms of PW have evolved these higher-
|
|
order behaviors by reproducing the same bottom-up complexity
|
|
ordering of behavioral dynamics as are postulated to drive such
|
|
phenomena in natural organisms: core motor controls, followed by
|
|
approach and avoidance behaviors in individuals, followed by group
|
|
flocking behaviors that emerge naturally from the individual
|
|
approach/avoidance behaviors.
|
|
|
|
The simple but effective strategies evolved by organisms in the
|
|
earlier, simpler simulations may be valuable as sort of Ònull
|
|
hypothesesÓ about certain forms of animal behavior. In particular,
|
|
aggregation and wall-following amongst these simple organisms
|
|
occurs without need for elaborate behavioral strategies. It is
|
|
sufficient that corners and walls obstruct simpler trajectories. Yet if
|
|
enough organisms occupy these locational niches, it becomes a
|
|
behavioral niche as well, by providing readily available mates, and
|
|
an easily achieved form of behavioral isolation.
|
|
|
|
It is, perhaps, easier to contemplate and understand these
|
|
behaviors in the simulated organisms of PW than it is in natural
|
|
organisms, precisely because they are simulated. The blessing and
|
|
the curse of Artificial Life is that it is much more difficult for humans
|
|
to anthropomorphize (zoomorphize? biomorphize?) these organisms
|
|
in a machine than it is natural organisms. This frees us from
|
|
prejudices and preconceptions when observing and analyzing the
|
|
behaviors of artificial organisms, yet the most highly motivated of
|
|
ALife researchers is going to find it difficult to look at an artificial
|
|
organism and declare it unequivocally alive.
|
|
|
|
As more and more sophisticated computational models of living
|
|
systems are developed, it will be only natural to ask whether they
|
|
are in fact really alive. To answer this, however, requires a
|
|
resolution to probably the greatest unanswered question posed and
|
|
addressed by the study of Artificial Life: ÒWhat is life?Ó Farmer &
|
|
Belin offer an analogous question for consideration: ÒIf we voyage to
|
|
another planet, how will we know whether or not life is present?Ó
|
|
One might also ask: If we ÒvoyageÓ to an artificial world, how will we
|
|
know whether or not life is present? Rather than just ignore this
|
|
question, letÕs look briefly at the how the organisms in PolyWorld
|
|
stack up against Farmer & BelinÕs list of Òproperties that we associate
|
|
with lifeÓ (slightly abridged here for brevity):
|
|
|
|
|
|
¥ ÒLife is a pattern in spacetime, rather than a specific material
|
|
object.Ó
|
|
PW organisms are indeed patterns in a computer, rather
|
|
than any specific
|
|
material; they neither extend nor violate this first
|
|
condition.
|
|
¥ ÒSelf-reproduction.Ó
|
|
PW organisms certainly reproduce within the context of
|
|
their world.
|
|
¥ ÒInformation storage of a self-representation.Ó
|
|
PW organisms use an analog of the same storage
|
|
mechanism Farmer & Belin
|
|
mention for natural organisms: their genetic
|
|
representation.
|
|
¥ ÒA metabolism.Ó
|
|
A PW organismÕs metabolism effectively converts food
|
|
found in the
|
|
environment into the energy it needs to carry out its
|
|
internal processes
|
|
and behavioral activities, just as is the case in natural
|
|
organisms. The
|
|
metabolism in PW organisms is much simpler, but if the
|
|
function is the
|
|
same, does the complexity of the underlying process
|
|
matter?
|
|
¥ ÒFunctional interactions with the environment.Ó
|
|
PW organisms interact with their environment, including
|
|
other organisms;
|
|
the more sophisticated ones respond behaviorally to
|
|
changes in the
|
|
environment; such responses are purely under the
|
|
control of the
|
|
organism.
|
|
¥ ÒInterdependence of parts.Ó
|
|
Following Farmer & BerlinÕs reasoning, PW organisms can
|
|
and would die
|
|
were they somehow separated from their internal energy
|
|
store. And
|
|
severing an organismÕs brain in two would not produce
|
|
two organisms
|
|
with behavior anything like the original. Unnecessarily
|
|
(and perhaps
|
|
inappropriately) stepping outside the bounds of the
|
|
simulation, they would
|
|
also die if their various procedures and data were
|
|
destroyed or isolated. In
|
|
either case, half an organism is no longer that organism, if
|
|
it is any
|
|
organism at all.
|
|
¥ ÒStability under perturbations.Ó
|
|
PW organisms can survive small changes to their
|
|
environment. Indeed,
|
|
whole species have reemerged in entirely different
|
|
simulations. Again
|
|
stepping outside the simulation, whole species have
|
|
emerged with and
|
|
without any of a variety of errors in the code.
|
|
¥ ÒThe ability to evolve.Ó
|
|
PW organisms clearly can and do evolve. There are
|
|
undoubtedly limits to
|
|
their evolution; e.g., they could not possibly evolve a
|
|
sense of smell without
|
|
programmer intervention. However, all natural
|
|
organisms we know of
|
|
have limits to their evolutionary capabilities: It is highly
|
|
unlikely that
|
|
humans could evolve a steel appendage; if Einstein is
|
|
correct, it is absolutely
|
|
impossible for them to evolve a method of personal
|
|
locomotion that would
|
|
exceed the speed of light. All organisms, natural or
|
|
artificial, are bound
|
|
by the physics of their universe. Similar to the question
|
|
about metabolism,
|
|
does the complexity of the underlying physics matter?
|
|
|
|
Somewhat surprisingly, then, it would seem that we either need to
|
|
further refine our constraints on the definition of life, or welcome a
|
|
new genus to the world.
|
|
|
|
Ultimately, the resolution to this question of life in artificial
|
|
organisms is probably going to have to be based on a consensus, as
|
|
with TuringÕs famous test for artificial intelligence. Perhaps in this
|
|
case, however, the consensus of a knowledgeable and informed jury
|
|
is needed, rather than that of TuringÕs unspecified, presumably
|
|
average group of individuals. As with the debate about the
|
|
ÒalivenessÓ of natural viruses being properly resident with biologists,
|
|
the question of ÒalivenessÓ in artificial organisms is probably best
|
|
argued by a combination of computer-aware biologists and biology-
|
|
aware computer scientists.
|
|
|
|
|
|
12. Future Directions
|
|
|
|
The various species and behaviors that have emerged in the
|
|
different simulations suggest that PW may be a rich enough
|
|
simulation environment to pursue further evolutionary studies. In
|
|
particular, a way of sort of ÒbenchmarkingÓ PW Ñ the way one
|
|
compares the results of a computational fluid dynamics code to flow
|
|
over a flat plate or a cylinder, or over an airfoil measured in a
|
|
windtunnel Ñ may have presented itself in the form of optimal
|
|
foraging strategies as studied in the field of behavioral ecology. A
|
|
simple, canonical foraging experiment has been defined and
|
|
analyzed, and is now being simulated with PW. Agreement or
|
|
disagreement with the analytical model should be examined and
|
|
understood.
|
|
|
|
The neural architectures that provide the most useful survival
|
|
strategies should be analyzed and understood. It would also be
|
|
fairly straightforward to encode an entire range of learning
|
|
algorithms in the genes of the organisms in PW, and attempt to
|
|
evolve the most effective learning algorithm, rather than assuming it
|
|
to be Hebbian. (Some consideration has even been given the
|
|
possibility of having the fundamental genetic representation of
|
|
information Ñ the genetic code Ñ evolve.) At least it might
|
|
worthwhile implementing cluster-to-cluster initial connection
|
|
strengths, initial connection strength variances, and maximum
|
|
connection strengths, to begin to hint at distinct cell types. Or it may
|
|
be more worthwhile to jump directly to a more sophisticated cell
|
|
model, capable of capturing the actual temporal dynamics of spike
|
|
trains rather than average firing rates.
|
|
|
|
More environmental interactions should be supported,
|
|
including the ability for the organisms to pick up, carry, and drop
|
|
pieces of food, and perhaps even pieces of barrier material. This
|
|
should yield useful reasons for organisms to cooperate, other than
|
|
simply to reproduce.
|
|
|
|
Though not discussed in the earlier parts of the paper,
|
|
energetics of the system have been observed to be crucial to the
|
|
evolution of successful survival strategies. Mimicing the differences
|
|
between energy-rich tropical zones and energy-starved polar zones
|
|
in our one known, natural ecosystem, artificial life flourishes in
|
|
energy-rich simulations, and languishes in energy-starved
|
|
simulations. Perhaps someday it may be possible to make useful
|
|
predictions about viable ranges of energy flux for natural systems
|
|
from artificial ecologies like PW.
|
|
|
|
A quantitative assessment of the degree to which the isolation
|
|
of populations affects speciation may be possible with PW. Some
|
|
tentative first steps have already been taken in this direction, though
|
|
questions remain about the most appropriate comparisons to make
|
|
and the appropriate times at which to make these comparisons. This
|
|
coupled with the problems associated with assuring the emergence of
|
|
an ESS in every population, and the simple magnitude of processing
|
|
time required to perform the simulations has delayed a complete
|
|
series of experiments of this nature.
|
|
|
|
There are thousands of other interesting experiments that one
|
|
might perform with this system, including: Monitoring brain size in
|
|
otherwise stable populations, such as the "dervishes"... are smaller
|
|
and smaller nervous systems actually being selected for? Monitoring
|
|
the frequency and magnitude of attacks on other organisms as a
|
|
function of their genetic (dis)similarity. Monitoring the amount of
|
|
energy given to offspring in a single species... is there any indication
|
|
of an asymmetric split into different relative contributions? Hand-
|
|
tailoring a good neural architecture or two and seeding the world
|
|
with these engineered organisms. Providing multiple internal, neural
|
|
time-cycles per external, action time-cycle. Evolving three
|
|
completely independent domains of organisms, with barriers in
|
|
place, and then removing the barriers to observer the interspecies
|
|
dynamics. It may even be possible to model the entire population of
|
|
Orca whales that frequent the waters around Vancouver, and look for
|
|
an evolutionary split into pods that travel little and eat essentially
|
|
stationary food sources versus pods that travel widely and feed on
|
|
fish, a very mobile food source. And on and on. In hopes that others
|
|
may find PolyWorld to be a useful tool for exploring these kinds of
|
|
questions, it has been made available via ftp from ftp.apple.com
|
|
(130.43.2.3) in /pub/polyworld. Complete source code and some
|
|
sample "world files" are provided.
|
|
|
|
In a more fanciful, and perhaps more visionary vein, it is
|
|
hoped that, someday, one of the organisms in PolyWorld that
|
|
demonstrates all the survival behaviors observed to date, plus a few
|
|
others, could be transferred from its original environment to, say, a
|
|
maze world, and become the subject of some classical conditioning
|
|
experiments. KlopfÕs [24,25] success at demonstrating over 15
|
|
classical conditioning phenomena in a single neuron using differential
|
|
Hebbian learning (he called it Òdrive-reinforcementÓ learning),
|
|
strongly suggests that such phenomena should be demonstrable in
|
|
PolyWorldÕs organisms.
|
|
|
|
And then, of course, there is simply Òmore, bigger, and longerÓ:
|
|
More organisms, with bigger neural systems, evolving longer. As a
|
|
gedanken experiment, consider just how much Òmore, bigger, and
|
|
longerÓ might be useful: The current 102 organisms, 102 neurons,
|
|
and 102 generations (approximately), could be expanded to 106
|
|
organisms, neurons, and generations, through an increase in compute
|
|
power of about 1012. (Though this sounds like a tremendous
|
|
increase to ask for, consider that the current simulation is running on
|
|
a single, scalar workstation processor, not a vectorized, massively
|
|
parallel processor, then extend todayÕs trends in compute power, and
|
|
this ceases to be such a daunting request; in fact, the compute power
|
|
may be significantly less than this due to the greatly reduced motor
|
|
and autonomic nervous systems that would be required by artificial
|
|
organisms.) It turns out that this is a fairly reasonable amount of
|
|
compute power with which to consider modeling a complete human
|
|
brain Ñ basically devoting one of todayÕs fast computers to every
|
|
neuron Ñ but no one understands how to actually construct such an
|
|
artificial brain. However, this same amount of compute power might
|
|
be used to evolve the equivalent of a new species of computational
|
|
lab rat every week... and this is how: by combining evolution, neural
|
|
systems, and ecological dynamics. The leap of (informed) faith is
|
|
this: If it is actually possible to evolve a computational lab rat Ñ and
|
|
the experiments so far in PW suggest that this may indeed be the
|
|
case Ñ then it will be possible to evolve human or higher levels of
|
|
intelligence by the very same methods. At least with this approach
|
|
there can be milestones and benchmarks along the path to human
|
|
level intelligence in a machine.
|
|
|
|
If there is any question about why one would wish to pursue
|
|
these research directions, it is always possible to point to the benefits
|
|
to be derived in the evolutionary, ecological, biological, ethological,
|
|
and even computer science fields. But it may also turn out to be the
|
|
only ÒrightÓ way to approach machine intelligence. One view of
|
|
intelligence is as an evolved, adaptive response to a variable
|
|
environment, that due to historical constraints and opportunism on
|
|
the part of nature happens to be based upon neuronal cells. One
|
|
might further recognize that intelligence is really more a near-
|
|
continuum Ñ a spectrum from the simplest organism to the most
|
|
complex Ñ rather than some singular event unique to humans. Then,
|
|
by utilizing both the method (Natural Selection) and the tools
|
|
(assemblies of neuronal cells) used in the creation of natural
|
|
intelligence, PolyWorld is an attempt to take the appropriate first
|
|
steps towards modeling, understanding, and reproducing the
|
|
phenomenon of intelligence. For while one of the grand goals is
|
|
certainly the development of a functioning human level (or greater)
|
|
intelligence in the computer, it would be an only slightly less grand
|
|
achievement to evolve a computational Aplysia that was fully
|
|
knowable Ñ fully instrumentable, and, ultimately, fully
|
|
understandable Ñ to let us know that we are on the right scientific
|
|
path.
|
|
|
|
|
|
Acknowledgements
|
|
|
|
The author would like to thank Alan Kay and Ann Marion of
|
|
AppleÕs Vivarium Program for their support and encouragement of
|
|
this admittedly exotic research. He would also like to thank his wife,
|
|
Levi Thomas, for her patience, understanding, and support
|
|
throughout the project.
|
|
|
|
|
|
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