Dynamical Field Theory of Infant Reaching and its Dependence on Behavioral History and Context

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1 Dynamical Field Theory of Infant Reaching and its Dependence on Behavioral History and Context a theoretical study on human development Evelina Emilova Dineva PhD thesis March 2005, Bochum

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3 This dissertation was submitted to the International Graduate School of Neuroscience, Bochum in partial fulfillment of the requirements for the degree of Doctor of Philosophy referees: Prof. Dr. Gregor Schöner (principal adviser) Institut für Neuroinformatik Ruhr-Universität Bochum, Germany Prof. Dr. Irene Daum Institut für Kognitive Neurowissenschaft Ruhr-Universität Bochum, Germany John P. Spencer, Ph.D., Associate Professor Department of Psychology University of Iowa Tag der mündlichen Prüfung: 1 Juli 2005

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5 to my family

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7 Acknowledgment This thesis was accrued during my scholarship from the International Graduate School of Neuroscience in its first three years, and was funded by the Theoretical Biology department at the Institut für Neuroinformatik for an additional six months. It is a theoretical work, which benefited greatly from the cooperation with the Infant Motordevelopment Laboratory at Indiana University, who supplied all the empirical evidence, understanding and data. It is a hard and rewarding job to do interdisciplinary research as a neophyte. I learned much and am extremely grateful, especially to Gregor Schöner and Ester Thelen. Working with them added a new dimension to my understanding of life. I am very happy that I met such a great person as Ester Thelen, who, despite being herself one of the leading theoreticians, has a sense even for the littlest step her students make and a talent to encourage them to go deeper. Her loss is painful for everyone who knew her. Under Gregor Schöner s supervision I felt always safe, although success could not be foreseen for a long time. The process of intense training and long discussion (often very late in the day) helped me to grasp the linking of theory with empiricism. Working in the Institut für Neuroinformatik affords one enormous creative power for it is a wonderful conglomerate of people from different disciplines and nations. Many thanks also to all the people whose work we appreciate because we do not face the problems which ultimately would arise without it. So effective are they, one does often even not notice when all the computer and other administrative work is done. Special thanks go to my colleagues Doc, alias Stefan Schneider, and Junior, alias Christian Igel, for their help on theoretical modeling and for opening my mind to the local Ruhrpott culture, to Christian Faubel, with whom I especially enjoy our science-at-home sessions accompanied with good food and wine, for his support with all kinds of technical devices, and to Marian for bringing Bulgaria to my office and my home. I would like to thank my family, especially my grandparents, for encouraging my curiosity and bringing me up to encounter academic life. I thank my parents Sasha and Emil for the trust which they have in me and which was especially needed when it felt like nothing would ever be work. Thanks to dreben, alias my big brother Borislav, my aunt Rumi, and my cousin Alexander who spiced up my life (and work) with their charming spirit and humor. I am grateful to my sexy friend Kent Welch, who keeps my feet warm (mostly trans the Atlantic) when I type long hours, and who spent many pleasant moments helping me phrase precisely and spell correctly; indeed, to improve my style. Thank you all! vii

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9 Abstract Studying development is particularly revealing about the organization of behavior because mechanisms of change are analyzed. We focus on the question of how infants represent a reach toward a target. For this we use the classical Piagetian A-not-B paradigm, where after having induced a habit to reach to A on the initial A trials, an infant is then asked to respond to the same stimulus, but now presented at an alternative B location. Infants typically perseverate at A if a delay is imposed before reaching is allowed, that is, they make the A-not-B error. But infants behavior is strongly and non-linearly affected even by small changes of the context (e.g. distinct hiding locations). The older infants are, the longer periods they can tolerate before perseverating, which is a developmental aspect that we seek to understand. Previous theories fail to account for infant decision making because they neglect the role of behavior. In the current work we focus on infants reaching decisions on the A trials. By regarding infants spontaneous switches B-on-A reaches we can establish that a reach to a location induces a bias to reach to the same location again. We also argue that it is due to this kind of accumulated preshape that infants make the A-not-B error. We propose a dynamical field model to account for how infants organize their reaching decisions within the context of the A-not-B paradigm. In our theory behavior is represented through motor planning activation that is distributed along the relevant behavioral dimension (the reaching direction). The motor planning field has non-linear cooperative interactions, that is, decisions are realized through local excitation and distant inhibition, like in a real neural field. A decision to act is a stable and positive activation peak of the motor planning dynamics. Therefore, it is possible to introduce preshape dynamics which memorizes previous actions. The precise context position, intensity and duration of stimuli is providing stimulating activation to the motor planning field. Our theory explains three aspects about infants target-guided reaching. First, through preshape dynamics we establish that recent behavioral history is a relevant factor. This accounts for both the pattern of spontaneous B-on-A errors and the perseverative A-not-B errors as resulting from building a strong history to reach to A. Second, we can replicate earlier accounts that increased cooperativity within the motor planning field is crucial for the developmental effect (toleration of a longer delay and correct response). Because we require behavior to be stable at any age, we do link the open gap between models accounting for younger infants motor planning with a more general theory of reaching based on memory. Finally, we analyze the role of context. By varying the stimulating landscape (stimuli are defined through their intensity in space and time), we can explain the highly nonlinear organization of young infant target guided reaching in the face of competing cues. In sum, infants reaching is strongly supported by the current context, and short term behavioral habits alters target perception and action attractors. ix

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11 Contents Title Acknowledgment Abstract i vii ix I Introduction 1 1 On the Development of Cognition Piaget s A-not-B Paradigm Embodied Cognition Approach to the A-not-B Task Avalanche of A-not-B Research Why Is a New A-not-B Model Necessary? II Methods 21 2 Dynamical Field Theory of Behavior Signature of the Dynamics of Reaching Decisions Representation of Motor Decisions in Dynamic Fields Dynamics of A-not-B Decision Making III Results 49 3 Behavioral History Matters Empirical Analysis of Spontaneous Errors Dynamics of Preshape and Its Influence Account for the Classical A-not-B Effects Context Dependency of Infants Perseveration Role of Transient Stimulus Presentation Role of Asymmetry Used for Training Role of Target Distinctiveness Role of Targets Specification xi

12 xii CONTENTS IV Discussion Skilled Reaching is a Consequence of Acting Young Infants Reaches are Stimulus Guided Strengths of the Dynamical Field Approach Development as Self-Action in a Structured World V Appendices 141 A Analysis of Preshape Dynamics 143 A.1 Single Trial Analysis, Without Noise A.2 Considering Action and Reaction Times B Simulation of the A-not-B Model 147 VI Bibliography 149 Bibliography 151 Curriculum Vitae 155 Declaration 157

13 Part I Introduction: A-not-B Paradigm and its Role in Understanding Cognitive Development from Embodied Cognition Point of View 1

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15 Chapter 1 On the Development of Cognition One of the remarkable properties of nervous systems is that they do not come into existence fully functional, but that they develop to a considerable extent during the early phase of life, as the organism already behaves, and the nervous system is exposed to a rich sensory environment. This is particularly true of the human species which is characterized by a very long phase of development of the nervous systems, associated with a very long childhood and adolescence. A full understanding of nervous function can therefore not be achieved if the development of the nervous system is not understood. Conversely, insight into developmental processes breeds understanding of nervous function in mature organisms. Another remarkable property of the adult nervous system is that it can master an enormous variety of tasks in accordance with the imposed requirements. This implies enormous flexibility and adaptivity. As task conditions change, we can fluently merge and switch reliance among sensorimotor systems to encounter the novel situation. This mastery is not there to begin with, but emerges during the course of development. Infancy provides an insight into the emergence of cognition from sensorimotor interactions with the outer structure. An advantage of studying infants, while still free from strategic considerations, is also that the access to organization of behavior is direct. On a more general level, motordevelopment, the metamorphoses from seemingly inane action patterns to skillful behavior, reflects the properties of the nervous system to reorganize adaptively (Thelen 2000b). How does infants spontaneous arm-waving transform into the ability to reach toward a target out of memory? The present work focuses on the last period of this long developmental proses. We describe the mechanisms governing the reaching decisions of seven to twelve month olds, who reach perseverativelly, as demonstrated in the Piagetian A-not-B task (Piaget 1954). After having developed a habit to reach to A, one out of two locations, then infants reach back to A, when the same stimulation is presented at the alternative location B. To explain the appearance and disappearance of the A-not-B behavior, we suggest a theory which links infants perseveration (repetition of an action, even when no longer appropriate) with the stabilization of goal directed reaching. The theory emphasizes the role, which the environmental situation plays for supporting the emergence of target driven behavior. 3

16 4 Piaget s A-not-B Paradigm 1.1 Piaget s A-not-B Paradigm Representation, Emerging from Interaction with the World In the 1950 s Piaget was the first to set a framework for investigating cognitive development. His research points at the necessity of infants sensorimotor interactions with the environment for the emergence of cognition. The book The Construction of Reality in the Child (Piaget 1954) is aimed at revealing how infants develop their understanding of the world. It details how infants knowledge about properties of objects and space develops. This basic knowledge transforms, through further experience, into the understanding of concepts, as time or causality, up to abstract reasoning. Fundamental to Piaget s work is a rich collection of detailed observations of infants everyday behavior throughout development, and longitudinal series of smartly set experiments. Those games are designed to tab the emergence of an object concept, and how it becomes independent of immediate sensation. In his theory, objects and their physical characteristics form the world in the infants minds. Objects, by being permanent, removable, different, etc. build the understanding of spatial and temporal relationships of the external world. Such an understanding emerges from the interaction of the infant with the objects, i.e. with the external world. Piaget s Stages of Object Representation: Piaget differentiates six stages, which infants undergo until they have a full, adult-like, understanding of objects and their properties. At the beginning (stages I and II), an object is merely something that might evoke an action pattern, such as sucking on it. Infants do not reach for objects prior to three to four months of age. Reaching is characteristic for stage III: Between three and six months of age, [... ] the child begins to grasp what he sees, to bring before the eyes the objects he touches, in short to coordinate his visual universe with the tactile universe (Piaget 1954, p. 13, ed. 1971). At stage III, infants do not show searching behavior related to occluded objects out of sight, out of mind. Even if attending the occlusion of a desired object, they perform no actions related to retrieval. It is not until the age of circa seven months when infants begin to search for hidden objects, that s stage IV. Signature for that stage is the so-called A-not-B error which infants make by linking an object with the action of retrieving it. Stage IV infants search repetitively at a previously visited location, even though they see the desired object vanishing at another location. Infants ability to correctly retrieve a hidden object, and to infer a novel location when the object has been displaced impalpably after hiding, mark stages V and VI, respectively. Most intriguing is infant behavior during stage IV, and explaining it part of this thesis. Therefore, we will present Piaget s account of that stage in detail. A-not-B Error Marks Missing Object Permanence : When infants are older than seven or eight months they start to search for hidden objects. Up to the age of about twelve months they display the A-not-B error: a baby observes a toy being hidden in one of two hiding locations, then a short delay is imposed before the infant is allowed to search. The first hiding location is named the A location. On those A trials the infant usually correctly retrieves the toy. After successive hiding and retrieving at A, the toy is hidden at the other, the B location. Despite the fact that the baby observes the toy disappear at the new location, and despite that it was correctly retrieving the toy when hidden in its first location, the baby now, if a short

17 ON THE DEVELOPMENT OF COGNITION 5 delay is imposed, searches the A location it produces the A-not-B error. For Piaget this error was a marker for stage IV no object permanence on the way to a fully developed concept of objects (which would be stage VI). He believed perseverative search is due to infants perceiving objects as extensions of their own actions, and not as permanent things. In Piaget s own theory, the A-not-B effect is just a step towards the accomplishment of the understanding of how objects relate with each other to define a individual representation of the external reality. As such, the A-not-B error reveals how infants develop their world model.

18 6 Embodied Cognition Approach to the A-not-B Task 1.2 Embodied Cognition Approach to the A-not-B Task Our view of cognition and development changes profoundly when we consider everything as process in time rather than static structures and modules. Ester Thelen, in her Presidential Address for the first issue of Infancy, 2000a. Cognition Emerges from Interactions with the Environment In line with Piaget, the embodied cognition approach also tabs the sensorimotor origin of cognition. But, it has enriched the quest with several new perspectives. Core one is the awareness that developmental stages are not sharply separated, as is been assumed in classical approaches, but overlap continuously (Thelen and Smith 1994). Next, during a transition phase, behavior is characterized through great and context-dependent variability the question is not whether a behavior is there or not, rather what are the necessary supporting conditions. Therefore, analyzing the transition phases (what behaviors must be there before a new one may emerge, and how does the environmental context control this emergence and its variability) reveals the driving forces of development. Another theoretical add-on, coming from the embodied cognition approach, is to stress the importance of the here and now. That is seeking to understand how behavior unfolds both in real time and in a given situation. This, in turn, allows one to apply the formal mathematical language of dynamical systems theory for the description of behavioral and developmental states (Thelen 2000a). Behavior, a Stable State of Coupled Dynamics: A comprehensive summary why the questions of embodied cognition approach are questions of coupled dynamical systems (stability and flexibility of behavior, adaptive to and dependent on the situatedness) is provided by Thelen (2000a). On a most gross level of coupling, the embodied cognition approach suggests that the nervous system is in permanent dynamic interaction with the body, which is in permanent dynamic interaction with the environment (figure 1.1). A direct implication of Nervous System World Body Figure 1.1: The embodied cognition approach regards the nervous system, the body, and the environment as coupled dynamical systems. This implies that there is no mind without a body; and no perception, action, or learning are possible without a structured world. Figure is adopted from Thelen (2000a). this view is that adaptive behavior emerges as a stable state from the coupled dynamics. A similar picture is given by Chiel and Beer (1997), who present an overview on the biological coupling of the nervous system and the body as manipulation on the body leading to cortical re-organization; or joints constraining the degrees of freedom and thus the control

19 ON THE DEVELOPMENT OF COGNITION 7 of a movement; or, in the course of evolution, the co-emergence of changes on body and nervous system. They stress on the physical constraints posed by one system on the other. In the embodied cognition approach (Thelen 2000a) the stress lies also on the dynamical interactions of the systems in real and on developmental time. To study the dynamics of something means to study the rules of its change. That the systems are coupled means that the current state of one system effects the dynamics of the other. The three parts the nervous system, the body, and the situatedness are real time dynamical systems in their own right. Because the systems are coupled, the current state of each single system constrains how each other system may transform. Behavior is an emergent pattern of the coupled dynamics. Through self-organization, the coupled dynamics relaxes coherently into a stable state of resonance. Consistent behavior emerges when the relative states of the individual parts contribute together to stabilization. Nature of Coupling Changes During Development: A far reaching implication of the dynamical systems approach to embodied cognition is that development results from those coupled interactions of the nervous system via the body with the environment (Thelen 2000a; Thelen and Smith 1998). As one aspect, neural re-organization is itself a dynamical system, which is observable on a developmental time scale. Because those changes are induced by the individual s interactions with its environment, the individual gains and restructures cognitive control to action. Thereby it acquires concepts of both, the properties of its own body and of the outer world. In sum, acting implies changes to the nature of coupling of mind, body and world. As a consequence, the relative stability and variability of behavioral patterns changes throughout development. This explains why (beside a similar situatedness) different typical behaviors are observed at different developmental stages. In this light, observing variability and context dependence of behavior are crucial for understanding cognitive development. Example of the Coupling of Body, Mind, World How does this theory apply to, or even explain, infants behavior? In their chapter Lessons from Learning to Walk, Thelen and Smith (1994) review the transitions between different phases of erect locomotion. Newborns, when held upright, display a coordinated step-like movement. This coordinated pattern disappears at about two months, to reappear at about eight months. A closer look, by Thelen and her colleagues, revealed that the decline of step rate is correlated with weight gain. Simply, the legs become to heavy for the infant to lift against gravity. To prove the hypothesis that the being there of the stepping pattern depends on the physical properties of their bodies, and not as much on cognitive control, the researchers made simple manipulations. Adding weights on the legs of infants who can step reduces stepping. On the other hand, reducing gravity for the infants who usually do not step (by submerging their legs into warm water) recovers stepping. Coupling of the Systems: This series of experiments exemplifies two aspects of the coupled dynamics, as pictured above (figure 1.1). Although stepping is a behavioral pattern controlled by the nervous system, the actual performance depends on both the body a baby has and the current context. Changes to the body weight gain hinders a behavioral pattern

20 8 Embodied Cognition Approach to the A-not-B Task that otherwise is stable. Changing the environment gravity increase or decrease alters either stepping or non-stepping, respectively. Variability of Behavior During Development: Stepping, after it reappears at about six to seven months, transforms into walking at about eight to ten months. However, as Esther Thelen and colleagues discovered, this developmental pathway is not fixed. When put on a treadmill, where their legs are supported by the movement of a belt, seven month olds perform coordinated stepping that is adjustable to speed changes and similar to adult walking. In other words, when supported by the environmental context (the treadmill), walking emerges from the stepping pattern which six to seven months old infants perform spontaneously. Walking becomes an action that infants can perform independent of mechanical support later at the age of eight to ten months, when they are able to support their own weight. This study encompasses two important messages. First, appropriate environmental support can bring to the surface a behavior that is about to emerge, but still not present. Second, it reveals the developmental changes, that are necessary for the behavior to be performed without support. In this example the relevant change for independent walking is that infants must gain control of their posture while moving forward and their muscles must become strong enough to support the body in an upright position. On a treadmill an infant is held upright, i.e. up-right posture is mechanically supported. What Has A-not-B Error in Common With Stepping? The pursuit of this thesis is the developmental question: What changes between seven and twelve months, such that infants become capable of consistently following a cue that is no longer present? From the point of view of the embodied cognition approach, like walking, memory-guided reaching (as it is required by an A-not-B experiment) is an emergent property. In particular correct reaching in an A-not-B task can be induced by an appropriate and supporting experimental set-up (we devote our entire chapter 4 to examine the details of the effect, which the design of the experimental device has on guiding reaching). Also like learning to walk, the period during which infants perseverate is a transition phase, which bridges different states of infants reaching abilities. Here we like to introduce the developmental pathway of goal directed reaching, which is a necessary condition for memory directed reaching to emerge. Clearfield and Thelen (2001) give a detailed review on infant reaching skills. Onset of Goal Directed Reaching: Like walking is preceded by a spontaneous stepping pattern, so is reaching preceded by spontaneous waving of the arms before it becomes a goal directed action. Spencer and Thelen (2000) discovered that infants use different muscle groups for moving their arms before after they are able to reach. This change of muscle activity is not leading the infant s arms in novel positions. When movements within a limited spatial region are examined, the authors show that before and after reaching onset, infants are using different muscle groups to bring their arms in similar positions in space. That sharp discontinuity in co-activation of predominant muscles indicates that for goal directed reaching to emerge, other changes must happen as well. One such change is improvement of posture. Infants ability to control their heads and to maintain midline position precedes

21 ON THE DEVELOPMENT OF COGNITION 9 the onset of reaching, as examined by Spencer, Vereijken, Diedrich, and Thelen (2000). Stability in positioning head and torso is needed to reach successfully toward a goal. However, since the onset of reaching at about four months, it is not until the age of seven months that an infant is able to reach precisely. Right after onset, reaching is characterized by highly jerky patterns which are highly variable, they differ greatly between a reach and its repetitions. The A-not-B Error Accompanies Reaching Stabilization: Perseverative reaching, as in the A-not-B task, occurs as reaching looses its variability. Clearfield, Thelen, Smith, and Scheier (prep) provide direct evidence that the A-not-B error is related to the stability of reaching. In a simpler version of the task, such that only reaching is required (but not retrieving a toy, what infants younger than seven months cannot do) infants as young as five months could be tested (Smith et al. 1999, showed that when to cue the baby only a lid is waved, nine month olds perseverate in the same proportion as when a toy is hidden). Infants at about five months do not perseverate, but perseveration increases with increasing age to ca. eight months. Furthermore when looking at who perseverates and who does not, proves that non-perseveration is linked to jerky and unskilled reaching. A similar result is given by another study, where Diedrich, Thelen, Smith, and Corbetta (2000) traced nine month old infants reaches as they performed the lids-only version of the task. Infants, who perseverate, have highly repetitive converging paths and kinematics of their reaches. Whereas, those who do not make the A-not-B error demonstrate divergent reaching. Perseveration accompanies the on-line stabilization of young infants reaching. But, as Thelen et al. (2001) propose, on a developmental time scale, reaching stability increases together with infants capability to sustain a transient goal (tolerance of a longer delay in the A-not-B task). We will explain the underlying dynamic mechanisms in chapter 3. The theory we are going to present allows us to address the open question of how the on-line stabilizing leads to permanent stabilization of reaching. A-not-B and The Coupled Dynamics of Mind, Body, Word Traditionally, the transition between perseveration and non-perseveration in the A-not-B task has long been thought to be revealing about a certain cognitive aspect. In those accounts, the challenging part of explaining the A-not-B error seems to be its sensitivity to a vast variety of factors which reduce or enhance it (Thelen et al. 2001, for a recent overview). Increasing the delay for instance, increases the error, but also the older an infant is, the longer the delay it will tolerate. Manipulations to the context, like distinct hiding locations, or more interesting toys, reduce perseveration. Number of reaches to A increases perseveration as well. The common proposal of the classical accounts is that a certain cognitive achievement, needed to solve the A-not-B task, comes with maturation. An implication usually not discussed is that the transition between not having that certain ability is preassigned. From embodied cognition point of view, the A-not-B task, because of the dependence of the error on such a vast variety of factors, is revealing about the dynamics of how infants organize goal directed reaching. With figure 1.1 in mind, we see the following coupled interactions: The current state of the nervous system matters! Repeated reaching to one location alters the state of the nervous system by preshaping it; preshape biases subsequent

22 10 Embodied Cognition Approach to the A-not-B Task reaching, thus generates perseveration. Environment plays a role! Appropriate changes to context (e.g. salient cueing event) can support correct reaching, despite preshape. Intensity of the cueing event and delay, together, are revealing about dynamic properties of spatial memory. Memory for the cue location fades away during the delay, but decay rate is reduced when the stimulus is intense. The age-delay effect reveals underlying developmental changes. The system gradually transforms from one that is purely stimulus driven to one that can act from memory (by sustaining a cue location over a delay). The embodied cognition approach naturally lends itself to the formal language of dynamical systems. This allows for rigorous mathematical formulation of the theory. For the A-not-B task we will present a dynamical field model which meets and explains the above points. Still unexplored are the processes that drive the change of the dynamics from being stimulusdriven (young infants) to memory-driven (older infants). The question remaining is, what drives infants behavioral transition. What are the mechanism of change to the coupling of the systems. How do new behaviors emerge from the interactions of the systems? Those questions are largely unanswered. However, the current model, allows to be realized in robotic simulation because behavior is understood as a stable state. Which, in turn, allows to address the questions, yet still open. Before introducing the details of the dynamical systems theory, we would like to introduce the classical accounts on perseverative reaching and its meaning for development. Those differ conceptually from the embodied cognition approach and its dynamical systems formulation.

23 ON THE DEVELOPMENT OF COGNITION Avalanche of A-not-B Research The question, what happens during the Piagetian stage IV when an infant can reach correctly on the A trials but loses this ability on the B trials, has engaged much research. The A-not-B experiment has been repeated many times and in countless variations. The A-not-B error, also referred to as perseverative reaching (infants perseverate in searching at an old location), appears to be very sensitive to the exact experimental conditions. Traditionally, the task has been understood as a marker for maturation of a brain area, which is thought to be the residence of a particular cognitive function, which in turn is assumed to be necessary to solve the task correctly (Smith et al. 1999, for a summary of maturational accounts). There is an almost unlimited number of explanations, nearly each effect has its own account. However, such a reductionist view one task, the corresponding functions, their hard wired implementation proves not to explain how manual perseveration might be part of a developmental process. But, as we report in section 1.2, the task in question is a good example of the relevance in viewing phenomena as a part of a developmental process. This constrains vastly the possible explanations. Further reduction is achieved if we require one single theory to explain the context dependency of the A-not-B error. A Meta-Analysis and its Consequences To bring some structure into the unconnected diversity of A-not-B effects Wellman, Cross, and Bartsch (1986) conducted a meta-analysis. They analyzed the canonical version of the task (two similar hiding locations and the same toy is hidden across trials) versus versions, where significant variations to the experimental conditions had been made (e.g. distinct or additional hiding locations). Two major findings were revealed by their analysis. On one hand, the canonical version of the experiment confirmed a robust dependency of perseverate searching on age and on delay. A combined age-delay effect was found by Diamond (1985). The A-not-B error increases with the imposed delay, and the maximal delay tolerated before perseverating increases with infants age. On the other hand, the main effect is highly sensitive to variations from the canonical version of the task. Aside from age and recency, the A-not-B error is reduced by distinct hiding locations, increased number of hiding locations, and wide separation between targets. Except long delays, no conditions that increase perseverative reaching are obvious yet. Further, no systematics ware detected, how contextual factors reduce the error. As criticized by Diedrich, Thelen, Smith, and Corbetta (2000), the analysis performed by Wellman et al. (1986) could not detect the significance of an infant s choices on the A trials, for A trial performance was not registered in the studies subject to it. Not aware of that simplification, the authors stated that the number of A trials is irrelevant for perseveration. As a consequence, reaching on the A trials continues not to be taken into account in most of research. The lines set by the meta-analysis are obvious from Harris (Harris 1986) commentary: there are two search modes, one leading the infant to search at A and the other leading to search at B. It seemed self-evident that two different cognitive processes are involved, and which are available at different ages. The context-dependency seemed to hold the key for the difference between the two. Such a view, combined with the belief that each strategy has its anatomic counterpart in the brain, produces the assumption that infants perseveration is

24 12 Avalanche of A-not-B Research reduced through maturation. Maturation A Reduced Neuro-Scientific Account: More recent summary on explanations for the A-not-B effect is provided by Smith et al. (1999), Marcovitch and Zelazo (1999), or Haith and Benson (1998). We will illustrate the maturational accounts by means of Diamond s and Munakata s studies, to draw the most influential thinking about infants perseveration. Diamond (1985) has shown that the older babies are, the longer delays they will tolerate before producing perseverative reaching, but babies at any age will err more if the delay is increased. She explains the data as a trade-off between two cognitive abilities: memory for where the desired object is, and inhibition of a prepotent response. That babies are correct on the A trials is a sign that they remember the cued location over the imposed delay. Their erring on the B trials Diamond explains as the infants inability to resist the conditioned tendency to reach back to A. Later, Diamond and Goldman-Rakic (1989) show that rhesus monkeys with a lesion of the dorsolateral prefrontal cortex perform similarly on an A-not-Blike task as seven to twelve month old human infants do. By this comparison the authors deduce that the A-not-B error is a marker for maturity of the dorsolateral prefrontal cortex, on which the ability to control intended behavior depends. Connectionists Account Consolidates a Reductionist View Munakata (1998) maintains the idea that the A-not-B error is a signature for prefrontal maturation, but is reflecting the infants abilities to use working memory for active representation of objects. To explain the A-not-B error she introduces two kinds of competitive memories: experience based, posteriorly located latent memory for A, and a prefrontally active representation of B. She proposes a recurrent neural network model of the A-not-B task, as pictured in figure 1.2. This is a connectionist network with partially distributed processing (a Gaze A B C Reach A B C A B C Hidden Units A B C C 1 C 2 T 2 T 1 Location Cover Toy Figure 1.2: Munakata s PDP model for the A-not-B task. It consists of three hierarchically connected layers: an input layer that models experimental conditions, a hidden layer for the memory, and an output layer for the response. Figure reprinted from Munakata (1998). PDP network), suggesting an coupling-architecture spread across several processing layers. Each of the network layers two input, one hidden, and two response layers is engaged in processing a separate aspect of the task. A layer contains discrete number of neurons (two

25 ON THE DEVELOPMENT OF COGNITION 13 or three). When on, they represent possible combination of task situation, working memory states, or responses. The input level consists of three separate input modules, one for locations, one for objects and one for cover-type. By combination it provides activation in accord with the experimental condition to the hidden level. Here the memory for the cued locations is realized by maintaining representations active through self-excitatory connections. Activation from this level is transmitted to the output level which consists of two response modes, one for manual response and one for vision. Long term memory traces are established between simultaneously active neurons. Thus, on the A trials connections from the hidden layer to the A-response units strengthen. On the B trials this longterm memory trace is in conflict with the short-lasting hidden-layer representation. In this model perseveration appears as competition between two different kinds of memories: latent for the previously stimulated A location and active for the cued B location. Due to maturity (age), recurrent connections strengthen, and the model becomes better in persistently representing the hidden objects location. Implications from the PDP Model: According to Munakata (1998), infants solve the A-not-B task correctly if self-excitatory connections of their prefrontal cortices are matured enough to hold the representation of the presented objects over the imposed delay. In this account, the A-not-B task is about object permanence 1, which materializes as the ability to actively keep hidden objects in working memory. Age-dependent strengthening of recurrency improves object permanence. To account for different experimental settings (e.g. for infants perseveration when no objects are presented, or when there is an additional hiding location), she needs to involve a separate input module. However, binding environmental features one-by-one as they are presented is not how a real nervous system processes information. We will present situations where combinations of the parts do not sum-up, as suggested by the pre-wired network. For instance, that different objects (toys and covers) are processed differently by the model results from the extra input-layers for toys and covers. We will provide evidence that this does not automatically lead to the conclusion that infants appreciate toys differently than other stimuli. On the output level, reaching and looking are simply responses, and where they go depends on relative strengths of connections. Neither act couples back into subsequent processing on subsequent trials, processing is entirely top-down. Each trial is initialized with input presentation, processed in the short memory-unit, to form new responses a reach and a look to a location. In certain constellations both responses looking and reaching may disassociate, a behavior that is not consistent with what infants usually do. The coupling of reaching and looking is demonstrated by Smith et al. (1999), who show that if an infants gaze is attracted to a location during the delay then its reaching response will be biased to the locations where it was looking. 1 In fact, it is not clear what the working memory layer is representing: the objects location (A, B, and C are the hidden units in the model), or the actual objects (in Munakata s own interpretation the model explains object permanence).

26 14 Avalanche of A-not-B Research Unifying Accounts for the A-not-B Task The strength of the PDP model (Munakata 1998) is that it gives unifying explanation for the various sensitivities of the A-not-B error: gradual development of a skill (maturation), distribution of activation as a real-time process, that experimental context plays a role, and how the structure of the model changes with experience (on each trial latent traces are laid). However, Munakata s, like all other neuromaturation accounts, fails to reveal the mechanisms producing perseverative reaching, for it completely ignores the role of behavior. What maturational accounts say, is that the more mature the nervous system of a baby is, the longer is the delay this baby will tolerate before making the A-not-B error. Those accounts not only fail to explain how the infant s own behavior is involved in producing the error, but we will prove that they run into contradiction. By regarding spontaneous reaches to B on the A trials, we will provide empirical evidence that the more a baby reaches to one location, the more probable it is that it will return to that location on future trials. This result in particular fortifies the Smith et al. (1999) claim that the more spontaneous reaches to B on the A trials a baby makes, the more likely it will reach correctly on the B trials. If correct reaching on the B trials is a signature for a mature, fully functional control unit (be it prefrontal inhibition of response in Diamond s account, or mature working memory for Munakata), then the babies making many spontaneous errors will be the more mature ones, because they do not err on the B trials. Requirements on an Unifying Theory: A theory accounting for the A-not-B task (and not only for the A-not-B error) needs to regard the time course and situatedness of the entire experiment. Thereby it must explain the on-line processing dynamics and the underlying development change. But, next to the role of current context, it must explain also how recent history (infants own behavior) is integrated to guide reaching. The role of behavior is important not only to explain the dependency of the A-not-B error on recent history (Smith et al. 1999), it also is the link of perseveration as a transition phase toward achieving cognitive guidance of reaching (as discussed in section 1.2). Next to the connections approach, only the dynamical field approach provides an agedependent model (Thelen et al. 2001, presented here in section 1.4) in which the environmental context is an integral part of on-line dynamics that generates action. However, both approaches differ significantly in how environment, nervous system, and body are linked. In contrast to the three layer PDP-model, the dynamical field model regards gradual transformation of activation within a single layer, which represents the entire spectrum of possible actions. Activation changes continuously and with respect to external stimulation, previous experience, and interactions within the field. An action is defined through state of maximal activation. Within a single system the coupled dynamic interactions of nervous system, body, and environment, are described. This meets most requirements set by the embodied cognition approach (figure 1.1), except that behavior is not always a stable state of the dynamical system.

27 ON THE DEVELOPMENT OF COGNITION Why Is a New A-not-B Model Necessary? Dynamical Field Approach to the A-not-B Task Classically, in the A-not-B task infants are asked to reach for objects and their errors are interpreted as the immaturity of a certain abstract cognitive function like inhibition of response or object permanence. Smith, Thelen, Titzer, and McLin (1999) argue instead that the task is about the organization of action, which is strongly guided by the current situation. Their embodied cognition approach reveals that the A-not-B task is not a purely cognitive task (where infants receive inputs from the experimenter, then make a decision in their heads and then send this decision to their arms), but provides a novel insight that the A-not-B task is also a behavioral task. This allows one to pose novel questions: How do sensorimotor inputs guide behavior? How do those interactions with the environment lead to reorganization of the nervous system? Those questions address the dynamics of sensorimotor interactions. In particular, to understand the principles of perseveration, it is necessary to take infants behavior along the entire experiment into account. Smith et al. reveal the dependency on vast variety of factors of the A-not-B error to be signature for the on-line dynamics of infants reaching decisions. Their approach regards the processes that accompany infants reaching to a particular location in their visual space. Constrained by the A-not-B task, infants are asked to move their arms to one location or the other. This is a decision process where infants have to appropriately control their arms and muscles to achieve their reaching goal. In other words, they have to activate the appropriate movement parameters, which will bring their arm to a desired location in their visual space. Within the movement parameter space (the set of all possible motor responses) activation distribution codes for the action to be performed. Crucial assumptions of the theory, on how activation codes for behavior are: (i) representations are body-centered and spread over the visual space, (ii) activation changes continuously in time and space, (iii) activation is induced by environmental cues or events, like landmarks or hiding a toy, and (iv) memories for previous reaching activity are part or the action-perception loop guiding reaching and are coded for in the same behavioral parameters. The Dynamical Field Model: A more formal account for the dynamics of the A-not-B task was elaborated by Thelen, Schöner, Scheier, and Smith (2001). They accomplish the theoretical approach of Smith et al. with a model by means of which the task can be replayed. The model is based on a more general dynamical field theory of movement preparation, as suggested by Erlhagen and Schöner (2002, we detail it in section 2.2). The movement parameter space is regarded as a dynamical field the motor planning field whose activation states change continuously under the influence of stimulation and of interactions within the field. Field interactions match the properties of a real nervous system: activated sites contribute to the field dynamics by local excitation and lateral inhibition. The developmental change is modeled as an increase of the interaction strength. As a consequence, older networks are able to sustain activation by means of neural activation even in the absence of a stimulus. Therefore, the field is able to retain activation induced by, say, hiding a toy. The model of young infants has weak interactions and can, therefore, not sustain activation. They are stimulus driven, for they directly reflect the stimulation landscape presented to them. Part of the stimulation is previous experience, which is coded

28 16 Why Is a New A-not-B Model Necessary? for in an additional so-called preshape field, which receives its inputs from the activation of the motor planning field. Influence of the experimental context is reflected in the model as stimulating activation that is added to the field dynamics. The Act of Reaching Reveals Mechanisms of Perseveration The core of the dynamical field approach to infants perseveration is best formulated by Thelen et al. (2001, p. 4): The A-not-B error is not about what infants have and don t have as enduring concepts, traits, or deficits, but what they are doing and have done. Observing infants behavior during the entire experiment, not only on the B trials, Smith et al. (1999) argued that behavioral history matters. By varying the number of A trials they show that the A-not-B error increases with the number of preceding reaches to A. Further, when regarding the number of spontaneous reaches to B on the A trials, they show that those spontaneous errors are followed by correct reaches to B on the B trials. Thus, if it is not general preference for B, but a bias accumulated by reaching to B, what governs future reaches to B. In analogy, the same mechanism will accumulate a bias to A after subsequent reaches to A, and produce the A-not-B error. Although this is a crucial experimental finding, the dynamical field model by Thelen et al. can account for it (why this is so will be stated later). And indeed, the relevance of the number of reaches is still disputed. For instance, Diamond (2001, in her response to Thelen et al. (2001)) claims there is no effect whatsoever on the number of repeated reaches [to A] within the range of 1-2 or even 2-5. However, her argument does not capture the core of why the model fails to explain the dependency of B trial errors on the number of reaches to A, it simply relies on studies that use a deviated version of the A-not-B task. The procedure is to cue a novel location B after babies have reached a certain number of times to the first one A (Diamond 1985). Before a baby reaches correctly few times in a row to A, reaches vary a lot in their number and are not part of the analysis. Even though Diamond s argument (like other critics too, see Diedrich, Thelen, Smith, and Corbetta (2000)) is based on data that does not really measure dependencies between reaches, we still need to exclude general preference for B as explanation for why babies who reach a lot to B on the A trials usually keep on reaching to B on the B trials too. Based on an enormously rich set of experiments, a total of 348 infants participating in different versions of the A-not-B task, Esther Thelen observes that errors on the A trials follow a consistent pattern. On 15 to 20% of all A trials babies do reach to B. Those errors are not random, but reflect target distinctiveness and recent history. Explaining the pattern of spontaneous errors, which impossible with the old dynamical field model, is the main aim of this thesis. The data is supplied by personal communication and will be reported in detail later (section 3.2). Target Distinctiveness: The more confusable the two locations are, the more likely is an error to the non-specified location. The A location must be clearly distinguishable on the first few A trials, otherwise infants are not motivated to reach. On these training trials the hidden object is partially visible, or the lid (if no objects are involved) is put on the edge closest to the infant. Over the first A trials the salience of the hiding location is gradually decreasing, till both locations look alike. This is what we call decreasing task asymmetry.