Randall D. Beer

Information Processing and Dynamics in Minimally Cognitive Agents

There has been considerable debate in the literature about the relative merits of information processing versus dynamical approaches to understanding cognitive processes. In this article, we explore the relationship between these two styles of explanation using a model agent evolved to solve a relational categorization task. Specifically, we separately analyze the operation of this agent using the mathematical tools of information theory and dynamical systems theory. Information-theoretic analysis reveals how task-relevant information flows through the system to be combined into a categorization decision. Dynamical analysis reveals the key geometrical and temporal interrelationships underlying the categorization decision. Finally, we propose a framework for directly relating these two different styles of explanation and discuss the possible implications of our analysis for some of the ongoing debates in cognitive science.

Beyond Control: The Dynamics of Brain-Body-Environment Interaction in Motor Systems

Discussions of motor behavior have traditionally focused on how a nervous system controls a body. However, it has become increasingly clear that a broader perspective, in which motor behavior is seen as arising from the interaction between neural and biomechanical dynamics, is needed. This chapter reviews a line of work aimed at exploring this perspective in a simple model of walking. Specifically, I describe the evolution of neural pattern generators for a hexapod body, present a neuromechanical analysis of the dynamics of the evolved agents, characterize how the neural and biomechanical constraints structure the fitness space for this task, and examine the impact of network architecture.

The cognitive domain of a glider in the game of life

This article examines in some technical detail the application of Maturana and Varelas biology of cognition to a simple concrete model: a glider in the game of Life cellular automaton. By adopting an autopoietic perspective on a glider, the set of possible perturbations to it can be divided into destructive and nondestructive subsets. From a gliders reaction to each nondestructive perturbation, its cognitive domain is then mapped. In addition, the structure of a gliders possible knowledge of its immediate environment, and the way in which that knowledge is grounded in its constitution, are fully described. The notion of structural coupling is then explored by characterizing the paths of mutual perturbation that a glider and its environment can undergo. Finally, a simple example of a communicative interaction between two gliders is given. The article concludes with a discussion of the potential implications of this analysis for the enactive approach to cognition.

The whole worm: brain-body-environment models of C. elegans.

Brain, body and environment are in continuous dynamical interaction, and it is becoming increasingly clear that an animals behavior must be understood as a product not only of its nervous system, but also of the ongoing feedback of this neural activity through the biomechanics of its body and the ecology of its environment. Modeling has an essential integrative role to play in such an understanding. But successful whole-animal modeling requires an animal for which detailed behavioral, biomechanical and neural information is available and a modeling methodology which can gracefully cope with the constantly changing balance of known and unknown biological constraints. Here we review recent progress on both optogenetic techniques for imaging and manipulating neural activity and neuromechanical modeling in the nematode worm Caenorhabditis elegans. This work demonstrates both the feasibility and challenges of whole-animal modeling.

Exploring the space of viable configurations in a model of metabolism-boundary co-construction

We introduce a spatial model of concentration dynamics that supports the emergence of spatiotemporal inhomogeneities that engage in metabolism–boundary co-construction. These configurations exhibit disintegration following some perturbations, and self-repair in response to others. We define robustness as a viable configurations tendency to return to its prior configuration in response to perturbations, and plasticity as a viable configurations tendency to change to other viable configurations. These properties are demonstrated and quantified in the model, allowing us to map a space of viable configurations and their possible transitions. Combining robustness and plasticity provides a measure of viability as the average expected survival time under ongoing perturbation, and allows us to measure how viability is affected as the configuration undergoes transitions. The framework introduced here is independent of the specific model we used, and is applicable for quantifying robustness, plasticity, and viability in any computational model of artificial life that demonstrates the conditions for viability that we promote.

Characterizing autopoiesis in the game of life

Maturana and Varelas concept of autopoiesis defines the essential organization of living systems and serves as a foundation for their biology of cognition and the enactive approach to cognitive science. As an initial step toward a more formal analysis of autopoiesis, this article investigates its application to the compact, recurrent spatiotemporal patterns that arise in Conways Game-of-Life cellular automaton. In particular, we demonstrate how such entities can be formulated as self-constructing networks of interdependent processes that maintain their own boundaries. We then characterize the specific organizations of several such entities, suggest a way to simplify the descriptions of these organizations, and briefly consider the transformation of such organizations over time.

Animals and Animats: Why Not Both Iguanas?

In her target article, Webb contrasts two kinds of models, which she calls animal and animat models, and argues that the latter are unfairly held to less strict standards of scientific relevance than the former, particularly in regards to being subjected to empirical refutation. In order to illustrate her position, she draws upon both her own work on cricket phonotaxis (Reeve & Webb, 2003; Webb, 1995) and our work on the evolution and analysis of model brain–body–environment systems (for a review see Beer, 2008), focusing specifically on our studies of categorical perception (Beer, 2003a). We applaud Webb for engaging the general issue of model interpretation in adaptive behavior and artificial life, since it is far too common for work in these communities to be at best unclear and at worst intentionally ambiguous about their intended scientific relevance. We also completely agree that any scientific research must ultimately be judged by the degree to which it illuminates the actual phenomenon of interest and that, to the extent that animats are scientifically relevant, they are indeed models. However, we could not disagree more strongly with Webb’s overly restrictive conception of the kind of models they must be. Any model can be characterized by its answers to several key questions. What is the model’s target? How does the model relate to its target? What purpose is the model intended to serve? How should the model’s success be evaluated? We will call these questions the fundamental modeling questions. As we understand it, Webb’s central argument turns on her insistence that these questions be answered in a particular way, which is grounded in a specific modeling methodology that we will call datadriven modeling. What she fails to recognize, however, is that there are many other kinds of modeling methodologies that offer different but equally valid answers to these questions. In particular, our own work is grounded in the tradition of theory-driven modeling, which has its roots in physics. In this commentary, we attempt to briefly characterize both data-driven and theory-driven modeling and to contrast the sorts of answers they give to the fundamental modeling questions.

The structure of ontogenies in a model protocell

Emergent individuals are often characterized with respect to their viability: their ability to maintain themselves and persist in variable environments. As such individuals interact with an environment, they undergo sequences of structural changes that correspond to their ontogenies. Ultimately, individuals that adapt to their environment, and increase their chances of survival, persist. This article provides an initial step towards a more formal treatment of these concepts. A network of possible ontogenies is uncovered by subjecting a model protocell to sequential perturbations and mapping the resulting structural configurations. The analysis of this network reveals trends in how the protocell can move between configurations, how its morphology changes, and how the role of the environment varies throughout. Viability is defined as expected life span given an initial configuration. This leads to two notions of adaptivity: a local adaptivity that addresses how viability changes in plastic transitions, and a global adaptivity that looks at longer-term tendencies for increased viability. To demonstrate how different protocell-environment pairings produce different patterns of ontogenic change, we generate and analyze a second ontogenic network for the same protocell in a different environment. Finally, the mechanisms of a minimal adaptive transition are analyzed, and it is shown that these rely on distributed spatial processes rather than an explicit regulatory mechanism. The combination of this model and analytical techniques provides a foundation for studying the emergence of viability, ontogeny, and adaptivity in more biologically realistic systems.

Fitness Space Structure of a Neuromechanical System

This article rigorously characterizes the structure of the entire fitness space of a simple neuromechanical system consisting of a model leg in closed-loop interaction with a neural controller. Using tools from the theory of piecewise-smooth dynamical systems, we derive expressions for the location and layout of the region of high-fitness solutions in parameter space, and we show how both the boundary and the internal structure of this region arise from specific neural, mechanical, and neuromechanical properties of the walking system. In addition, we characterize the structure of the map from neural parameters to gaits to fitness.

From head to tail: a neuromechanical model of forward locomotion in Caenorhabditis elegans

With 302 neurons and a near-complete reconstruction of the neural and muscle anatomy at the cellular level, Caenorhabditis elegans is an ideal candidate organism to study the neuromechanical basis of behaviour. Yet despite the breadth of knowledge about the neurobiology, anatomy and physics of C. elegans, there are still a number of unanswered questions about one of its most basic and fundamental behaviours: forward locomotion. How the rhythmic pattern is generated and propagated along the body is not yet well understood. We report on the development and analysis of a model of forward locomotion that integrates the neuroanatomy, neurophysiology and body mechanics of the worm. Our model is motivated by experimental analysis of the structure of the ventral cord circuitry and the effect of local body curvature on nearby motoneurons. We developed a neuroanatomically grounded model of the head motoneuron circuit and the ventral nerve cord circuit. We integrated the neural model with an existing biomechanical model of the worms body, with updated musculature and stretch receptors. Unknown parameters were evolved using an evolutionary algorithm to match the speed of the worm on agar. We performed 100 evolutionary runs and consistently found electrophysiological configurations that reproduced realistic control of forward movement. The ensemble of successful solutions reproduced key experimental observations that they were not designed to fit, including the wavelength and frequency of the propagating wave. Analysis of the ensemble revealed that head motoneurons SMD and RMD are sufficient to drive dorsoventral undulations in the head and neck and that short-range posteriorly directed proprioceptive feedback is sufficient to propagate the wave along the rest of the body. This article is part of a discussion meeting issue ‘Connectome to behaviour: modelling C. elegans at cellular resolution’.