An embodied dynamical approach to relational categorization

An Embodied Dynamical Approach to Relational Categorization Paul L. Williams 1 (plw@indiana.edu) Randall D. Beer 1,2,3 (rdbeer@indiana.edu) Michael Gasser 1,2 (gasser@cs.indiana.edu) 1 Cognitive Science Program, 2 Dept. of Computer Science, 3 Dept. of Informatics Indiana University, Bloomington, IN 47406 USA Abstract us to take seriously the view that cognition is situated, em- bodied, and dynamical. On this view, cognition is a contin- uous, ongoing interaction between a brain, a body, and an environment. After successfully evolving agents, we apply the tools of dynamical systems theory to analyze the result- ing brain/body/environment systems. The ability of dynamical neural circuits to perform rela- tional tasks has been demonstrated several times in previous work. For example, in one study a simple recurrent network was trained to recognize string sequences of the form a n b n , and thus to identify a same count relationship between se- quences of inputs (Rodriguez, Wiles, & Elman, 1999). How- ever, in this study the relational task was disembodied and computational in nature, whereas the work here is concerned with relational behavior in situated embodied agents. In another study, a neural model was proposed that captured findings from a relational task performed by nonhuman pri- mates (Miller, Brody, Romo, & Wang, 2003). In this case, though, the relational mechanism was hand-designed, while in the work presented here we employ evolutionary tech- niques, thereby attempting to minimize a priori assumptions about how the relational mechanisms should work. This paper has two primary aims. The first is to contribute to a growing body of research on minimally cognitive behav- ior, which studies simple behaviors of cognitive interest in or- der to develop and refine our conceptual and analytical tools for understanding cognition (Beer, 1996; Slocum, Downey, & Beer, 2000). The second is to show how the approach used here may inform the study and modeling of relational mecha- nisms more generally. To this end, we discuss how relational categorization is addressed by other models and identify some of the specific advantages of our approach. The rest of this paper is organized as follows. In the next section, we discuss the basic challenge posed by rela- tional categorization tasks and how this challenge has been addressed in previous models. The following section then describes the agent, neural network model, and evolutionary algorithm used here. Next, we briefly discuss the results of the evolutionary simulations. After, we present an analysis of the relational mechanism used by the best evolved agent. Fi- nally, we conclude with some general remarks, and an outline of ongoing and future work. This paper presents a novel approach to the study of relational categorization based on the evolution of simulated agents in a relational task. In contrast to most previous models of rela- tional categorization, which begin by assuming abstract rep- resentations and role-filler binding mechanisms, we begin by studying relational behavior in embodied dynamical agents, which results in a wider range of possibilities for relational mechanisms. The mathematical tools of dynamical systems theory are used to analyze the relational mechanism of the best evolved agent, and we then identify some of the insights of- fered by this analysis. Keywords: continuous-time recurrent neural networks; dy- namical systems; genetic algorithms; relational categories Introduction Recent research in cognitive science has seen flourishing in- terest in relations and relational categories (e.g., Gentner & Kurtz, 2005; Markman & Stilwell, 2001). Relational cate- gories are categories determined by common relational struc- ture among category members, rather than intrinsic similar- ities between category members. For example, same and smaller are instances of relational categories. There is a vast body of research on relational categorization in a wide range of species, including humans (Kurtz & Boukrina, 2004), pi- geons (Wills, 1999), rats (Saldanha & Bitterman, 1951), and insects (Giurfa, Zhang, Jenett, Menzel, & Srinivasan, 2001). Moreover, relational categories are of particular importance for cognitive science because they are fundamental to many topics, such as analogy and language. In recent years, a number of authors have proposed connec- tionist (Gasser & Colunga, 1998; Tomlinson & Love, 2006) and hybrid symbolic-connectionist (Hummel & Holyoak, 1997) models of relational categorization. These models put forth various mechanisms for the implementation of re- lational categories in cognitive systems. However, because these models are largely hand-crafted, they are limited to the space of possible mechanisms considered by their designers. In contrast, the work presented here takes an entirely dif- ferent approach to the study of relational mechanisms. We use an evolutionary algorithm to evolve dynamical neural controllers for simulated agents in a relational categorization task. There are numerous benefits of using this kind of ap- proach to study cognition (Beer, 1996; Harvey, Di Paolo, Wood, Quinn, & Tuci, 2005), two of which are central to our purposes. First, by evolving agents we are able to make minimal prior assumptions about how various behav- iors should be implemented. Second, this approach allows Relational Categorization Relational categorization tasks can be described in terms of two sets of features of the related objects (sometimes, but not