NeWG: In Search of the Rat’s World Graph

NeWG: In Search of the Rat’s World Graph

Alex Guazzelli¹ and Michael. A. Arbib²

Center for Neural Engineering - University of Southern California

Los Angeles, CA 90089-2520

E-mail addresses: (1) [e-mail] and (2) [e-mail]

Abstract

The World Graph theory developed the hypothesis that cognitive and motivational states interact. This paper describes NeWG, a hybrid neural network implementation of this theory as well as a modeling environment for the investigation of motivated spatial behavior. NeWG comprises a modified Fuzzy ART network, the START network, which incorporates the world graph properties to produce goal-oriented behavior. Neurophysiological data are then used to support a model of the rat’s cognitive map encoded as an internal world graph.

Keywords: Cognitive maps, world graph, navigation, motivation, mazes, ART Networks.

1 Introduction

Cognitive knowledge and motivated behavior produce actions that allow animals to survive in their environment. Successful spatial navigation requires both local and global knowledge of the environment. Whereas local spatial knowledge encodes the location of places to be approached and avoided in a particular limited area, global spatial knowledge is concerned with transitions from one region to another [1]. Many data suggest that rats (i) have associative memory for complex stimulus configurations, (ii) can encode the spatial effect of their own movements, and (iii) are able to form sequences of actions to go from a starting location to a goal. In other words, rats have a cognitive map. To understand this notion, introduced by Tolman [2] to explain place learning in rats, we must first distinguish egocentric representations from allocentric representations. The former, based on the organism’s current view of the world, are appropriate for looking, reaching, grasping, and locomotion with respect to directly visible features of the landscape. The latter can be understood in terms of a road map used by the driver of a car. Such a map is not drawn from the viewpoint of any driver, but nonetheless sets out the spatial relations between different places and the roads that link them. To go from this familiar type of map to a cognitive map we must augment the map with the processes needed to use it. To use a road map, we must be able to locate (the representations of) where we are and where we want to go on the map, and then find a path on the map which we can use as we navigate towards our goal. In sum, the ingredients of a cognitive map are (i) an allocentric spatial framework; (ii) a mechanism for the animal to locate itself and places of interest (e.g., goals) in that framework; and (iii) the means to combine current location and intended movement to infer new location, or current location and desired location to infer movement.

A motivational system is required to select goals to be pursued and to organize the animal’s commerce with appropriate goal objects. Motivated behavior is usually goal-oriented; the goal may be associated with a drive, such as hunger or thirst. According to Dorman & Gaudiano [3], motivation is the internal force that produces actions on the basis of the momentary balance between our needs and the demands of our environment. However, motivation is also closely tied to sensory stimuli, in the sense that an animal will not usually exhibit eating behavior unless food is presented. Moreover, the motivation to eat is not directly controlled by feelings of hunger (when presented with the opportunity to eat, animals eat in anticipation of hunger and continue to eat after satiation to maintain themselves until the next meal). An external factor, like the site of food, can play a role in stimulating motivation, and for this reason can be called an incentive.

For Toates [4], motivation arises as a function of both internal state and incentive. In this way, changes in either internal state or incentive would change motivation. For him a motivational system is one that selects goals to be pursued and organizes the animal’s commerce with appropriate goal objects. Motivation played a significant role in many theories of behavior, especially Hull’s theory (as described in [3]) who proposed that motivation is the initiation of learned, or habitual, patterns of movement or behavior. In Hull’s theory, events that threaten survival give rise to internal drive states, and behaviors that reduce the drive are rewarding. In this way, lack of food causes an increase in the hunger drive, and the consumption of food is rewarding because it leads to a reduction in the hunger drive.

Arbib & Lieblich [5,6] represented the cognitive map as a graph, with nodes corresponding to a recognizable situation in the animal's world, and with each edge representing a path from a recognizable situation to the next. This "world graph" (WG) is constructed so that the organism has the ability to move from one point to another, under a specific hypothesis that cognitive knowledge and motivational states interact. It can then be used to analyze how the brain can encode sequences of action required to pass from one spatial representation to another and, likewise, how an animal builds up a model of the world around it in such a way that, when under the influence of a particular drive, it can find its way to a location where it has learned that the drive will be reduced (in a goal-directed fashion).

The next section describes the WG theory together with NeWG, its neural implementation. In section 3, two experiments and their respective neural simulations are described and discussed. Section 4 extends the discussion of the WG to the biological level, linking theory and implementation to brain mechanisms related to motivated spatial navigation. Finally, section 5 offers the conclusion together with a brief description of future work.

2 NeWG - A Neural Implementation of the World Graph Theory

In the present work, the WG theory was implemented by the use of a well know neural network paradigm, the Adaptive Resonance Theory (ART). In particular the Fuzzy ART model was chosen [7]. Fuzzy ART deals with a system involving self-stabilizing input patterns into recognition categories, while maintaining a balance between the desirable properties of plasticity and stability.

An ART module is basically composed by two layers of neurons (Figure 1). The first layer, called F1, is responsible for receiving the information from the environment and presenting it to the network. The output of this layer is then sent to the second layer of neurons, called F2, through the multiple adaptive filter pathways emanating from F1. It is the F2 layer that contains the neurons responsible for the creation of the aforementioned recognition categories. After receiving the information being conveyed by F1, the F2 neurons undergo a winner-take-all process to select the category that best represents the incoming signal, i.e., the F2 neurons make a hypothesis about the incoming signal. The winning category then sends a signal back to the F1 neurons where a pattern matching process takes place between the information represented by the winning recognition category in F2 and the pattern of activity registered by the input signal in F1. If the similarity is greater than a given vigilance parameter, the network enters into a resonant state, in which the connection weights between F1 and the winning category in F2 are changed to incorporate the input pattern. If no current category is found to be a good representative of the input pattern, a new category will be formed in F2 and the weights of the connections between this category and F1 will be modified to represent the new input. ART models have been used to help explain and predict a large body of cognitive and neural data about recognition learning, recall, attention, priming, and memory search [8,9]. Besides, ART systems have the advantage of learning prototypes, rather than exemplars. Also, the learning process is fast, usually one-shot-learning, and the creation of recognition categories plastic, exactly what was needed for a neural implementation of the WG theory.

Figure 1: An ART module.

In NeWG, a neuron, or category, of the F2 layer represents a particular local view of the environment. From a single place, the animal is able to sense at most eight different local views, since in NeWG the rat can orient towards at most eight different directions. Moreover, the ART network had to be "modified" to incorporate the WG node and edge concepts. In the WG theory, a place or situation is formed by at least one local view, but the same place can comprise several local views experienced from different directions or points of view, like when turning around in the same place. For this reason, another layer of neurons had to be incorporated to the ART network to represent the concept of place. This layer, called P, was placed atop the F2 layer. Each neuron in F2 has at least one and at most eight on connections to a neuron in P. A new neuron is allocated in P when a neuron is created in F2 to represent a new experienced local view. In the WG, there is an edge from node y to node y' in the graph for each distinct path the animal has traversed. This is implemented in NeWG as a link between two P neurons. If, for example, a node y is currently active in P at time t, but by deciding to move one step north the animal activates a different local view in F2 and so a distinct category y’ in P at time t+1, a link will be created from node y to node y’ in P. Appended to each link/edge will be sensorimotor features associated with the corresponding movement/path (e.g., one step north). In doing so, we are actually working with what we called the START network, i.e., a Symbolic-Tagged ART network. In the START network, neurons and links can be tagged with symbolic information (Figure 2).

Figure 2: The START network

The edge information is crucial for navigation in the dark. In this condition, no visual inputs are available and the animal has to rely on its path integration capabilities. Sensory signals provided by angular and linear displacements have been shown to allow animals to accurately navigate on a certain distance in the absence of visual cues, that is, in total darkness [10]. This kind of information, usually referred as kinesthetic information, is very complex and includes at least vestibular, somatosensory, and proprioceptive components [11]. NeWG, by means of its edge information, facilitates the activation of P nodes that are directly connected to the current active node in P. This, combined with vestibular and head direction inputs allows the animal to successfully navigate in the dark.

Based on the hypothesis that drives can be viewed as states [12], the WG theory posits a set d₁, d₂, ..., d_k of discrete drives to control the animal’s behavior. At time t, each drive d_i in (d₁, ..., d_k) has a value d_i(t). Drives can be appetitive and aversive. The idea is that each appetitive drives spontaneously increases with time towards dmax, while aversive drives are reduced towards 0, both according to a factor ad intrinsic to the animal. An additional increase occurs if an incentive I(d,x,t) is present such as the aroma of food in the case of hunger. Drive reduction a(d,x,t) takes place in the presence of some substrate - water reduces the thirst drive. If the animal is at the place it recognizes as being node x at time t, and the value of drive d at that time is d(t), then the value of d for the animal at time t+1 will be

d(t+1) = d(t) + a d |dmax - d(t)| - a(d,x,t)|d(t)| + I(d,x,t) |dmax - d(t)|

In the current implementation of NeWG, drive information is treated as a black box separate from the neural network. However, after processing, it will influence the creation of the ART categories, together with the environmental stimuli, which, at a certain time t, include goal-related factors as well as distal and local cues. These together, by means of the process describe above, will let the animal determine whether it is experiencing a view already represented by a recognition category x of F2 or whether a new category must be created. In this case, a new neuron x’ will be added to F2 to represent the first recognizable view along the new path. In addition, a new neuron y’ will also be added to P to represent the new place, together with an edge from y (pointed by node x in F2) to y’. In the WG theory, merging of two nodes can occur if the animal decides that two nodes represent the same situation. In NeWG, if two neurons x and x’ in F2 are activated at the same time with a similarity bigger than the current vigilance parameter, and x has a smaller activation than x’, then node y in P which is connected to neuron x in F2 will be merged to node y’ in P which is connected to neuron x’ in F2. Before the actual merge, any connections from other neurons in F2 to node y are removed and new connections from those neurons in F2 to node y’ are created. Besides, any edge in P pointing to node y is updated to point to node y’. Finally, neuron x is also merged to x’ in F2.

As subsumed by the START network, each F2 neuron and P node contains recognition features as well as knowledge of the situation that it represents. However, as previously mentioned pertinent symbolic information is also attached to each P node (Figure 2). This is represented by a vector [R(d₁,x,t), ..., R(d_k,x,t)] of the animal’s current expectations at time t about the drive-related properties of situation x. R(d,x,t) does not change when the animal is not at node x at time t, but if the animal is at node x, then the expected drive reduction factor R(d,x,t) will be changed towards the actual drive reduction factor, with the change being greater the more intense the value of drive d(t). The animal will then move based on a specific combination of the hypotheses taken from the following two groups:

1. For locality of decision making, two hypotheses were defined: (a) the

   Local Hypothesis, in which the weights assigned to node

   x in the node selection process depend only on its expected drive reductions

   R(d,x,t); and (b) the

   Nonlocal Hypothesis, in which the weights assigned a node

   x -

   W(d,x,t) in the node selection process depend not only on the

   R(d,x,t) for that

   x, but also on the

   R(d,x',t) for nodes

   x' reachable on paths through

   x.

2. Regarding the relation between drive levels and the choice of the next node, two hypotheses are possible, (a) the

   Dominant Drive Hypothesis, in which the animal goes to a node most likely to reduce its dominant drive, and (b) the

   Competing Nodes Hypothesis, in which the animal goes to a node with the greatest expected reduction of all drives. While hypothesis (a) is implemented in NeWG simply by finding out which node the current node links to that has the biggest weight

   W for the dominant drive (the drive with the biggest value of all drives), hypothesis (b) is implemented by multiplying the weights

   W of each node linked to the current node by their respective drive values. In this way, the animal will go to the node with the greatest computed value, i.e., the greatest expected reduction of all drives.

In NeWG, the internal state of the animal at time t includes (Figure 3): the START network; the current active category in F2 and its correspondent active node in P, which are the animal's internal representation of its situation; and the vector of its drive levels [d₁(t), ..., d_k(t)].

Figure 3: Animal’s internal state.

As mentioned above, the environmental stimuli provide the cues which enable the animal to recognize the situation it is in as being represented by node x. In the current version of NeWG, the input pattern is composed of the animal’s current view of the environment and its head direction information (the SEE arrow in Figure 4). The view of the environment may eventually comprise distal and local cues as well as goal information. For this to be possible, a maze is divided in several distinct cells or locations (the actual number of cells depends on the kind of maze being used). Each cell can represent distinct information relevant to the experiment being performed. For example, in a T-maze, a cell may contain a local cue on the right wall and a pellet of food, while another cell may contain just a local cue. The rat is able to sense its environment at most eight cells ahead. The distance from the rat to a particular distal cue and the angle between its current head direction and the cue are captured in the current view if they are inside a 300 degrees field of view. In addition to view information, F1 also receives head direction information, a binary vector indicating one of the eight possible directions. The internal drive information, which indicates the kind of behavior the animal is engaged in, is also used to adjust the vigilance parameter of the ART network. NeWG implements four distinct drives: hunger, thirst, sex (appetitive), and fear (aversive). So, for example, the more hungry the animal is, the more vigilant it will be to its surrounding environment.

Figure 4: NeWG - inputs, states, and outputs.

NeWG was implemented in Java on a UNIX platform (Sun Workstation), with an interactive interface allowing the user to execute different experiments using distinct mazes (8-arm radial, cross, T, diamond, etc.) and observe their results in real time. The system is part of the Brain Models on the Web repository at the University of Southern California and can be currently accessed through the World Wide Web at the following URL:http://www-hbp.usc.edu/HBP/bmw/.

3 Experiments, Simulations, and Results

Suppose that a rat has been trained in a T-maze, where the door at each end of the T-bar can bear + or a O, and suppose that the + is consistently reward with food (Figure 5). Because each location in space might be represented by more than one node, according to the WG theory, four rather than just two nodes would be added to the world graph. These four additional nodes would be:

(L,+), (L, O), (R, +), (R, O)

where (L, +) is the door to the left of the choice point with a + on it, and so on. According to Lieblich & Arbib [6], as a result of its training, the animal may well associate (L, +) and (R, +) - but not (L, O) and (R, O) - with food. Because of their commonalities in both sensory features and food reward, (L, +) may merge with (R, +), and (L, O) may merge with (R, O). The edge from the start node to the (+) node resulting from merging (L, +) and (R, +).

Figure 5: (a) T-maze with a + cue and a reward cup on the left arm and a O cue on the right arm. (b) T-maze with a O cue on the left arm and a + cue and a reward cup on the right arm.

In its current version, however, NeWG’s behavior will be quite different, it will depend on the value of its vigilance parameter. Once this is low enough, NeWG will indeed show at the end of training the same results foreseen by the WG theory, i.e., the existence of two nodes: (+) and (O), "Turn toward the +" and "Turn toward the O", respectively. In the first trial (Figure 5a), NeWG, like in the WG theory, will learn nodes (L,+) and (R, O), but in the second trial (Figure 5b) instead of creating nodes (L,O) and (R, +), NeWG, by means of its learning rule and not the merging process, will modify its (L,+) category to (+) and (R,O) to (O). Like the WG theory, NeWG is rich enough to allow generalization over dimensions other than spatial ones.

Gough [13] performed an experiment which was first offered as evidence against the nonlocal hypothesis. Actually, the same experiment can be in fact consistent with the nonlocal hypothesis if interpreted from another perspective. In Gough’s experiment, a rat was trained in a diamond shape maze (Figure 6a). During training, barriers were placed at B and B’ so that the rat could not get from A to C. The rat learned that it could go from A to B or B’ to get food, and from B to C to get food. Moreover, the drive reduction at C was greater than at B or B’.

Figure 6: (a) The diamond shape maze used in Gough’s experiment. (b) "Bird’s eye view" of the diamond maze simulated in NeWG. Black circles around the maze represent distinct distal cues. (c) Rat’s local view of the environment. In the depicted situation, the rat is located in the corridor going from B’ to A. Distal cues are not shown.

After training, the barriers were removed. Gough argued (using the terminology of Arbib & Lieblich [5]) that if the nonlocal hypothesis were correct, the effect of the high value of R(hunger,C,t) would cause W(hunger,B,t) to well exceed W(hunger,B’,t), and so the rat should choose B over B’. In fact, in the first trial after barrier removal, rats were just as likely to choose B’ as B. Gough took this as evidence of the rat’s inability to chain segments it had learned separately.

Arbib & Lieblich (1977) offered a different hypothesis. They suggested that after training the WG of the rat had a form like that show in Figure 7a. The important point, according to them, is that B is represented by two distinct nodes, one for each side of the barrier, and despite the fact that Gough took care to provide distinctive features at each junction of the maze, there is no reason why the rat should have merged x_BA and x_BC on the basis of its training experience.

Figure 7: Rat’s world graph as hypothesized by the WG theory. (a) World graph after the rat has been trained in the diamond maze with the barriers in place. Rat was trained to go from A to B’, from A to B, and from B to C. (b) World graph after the rat has experienced the maze without the barriers (see text for more details).

Once the rat has gone from A to B with the barriers down, Gough finds that it does indeed proceed to C (food having been removed from B and B’ with the barriers), but that if it goes from A to B’, it does not go to C. Arbib & Lieblich prefer to explain all the data as consistent with the nonlocal hypothesis, with the idea that, once the barriers are down, the animal can, once it has reached B, recognize x_BA and x_BC as representing the same situation, and so can merge x_BA and x_BC into a single x_B (Figure 7b) A slightly different behavior was obtained in NeWG. Figure 8 shows a typical simulation of NeWG when the rat was trained in the diamond maze shown in Figure 6b. In this simulation, the ART vigilance parameter was set to a baseline value of 0.9 and the initial hunger level d_hunger was set to 5.0 (dmax equals to 20.0 and the increasing factor ahunger equals to 0.01). All the other drives were set to zero.

(a)
(b)
(c)

(e)

Figure 8: Rat’s world graph as built by NeWG. From (a) to (e) it is depicted the rat’s world graph when this was trained with the barriers up and food in B and B’. The crossed node represents the current active world graph node. (a) Rat’s world graph after being trained to go from A to B’ and from A to B (and vice-versa) during 41 simulated steps (the animal takes exactly 7 simulated steps to go from A to B or from A to B’). (b) When transported to the segment of the maze between B and C, the rat immediately creates a new node to represent the new situation. This node (crossed) is created apart from the world graph built to represent segments A to B and A to B’. (c) The rat makes one step towards B and creates another node in the new world graph. (d) Rat upon arriving in B creates yet another node. (e) The recently created node is merged to the node representing place B in the world graph created when the rat was exploring segment A to B. The two world graphs are thus united.

Like predicted by the WG theory, NeWG will merge the two nodes corresponding to B into a single one, uniting the two previously separated world graphs, but in NeWG, this is done even before the barriers were removed (Figure 8e). This can be explained by the fact that a big number of distal cues were used in the simulated experiment which collaborated in making B a unique place in both world graphs even with the barrier in B up, since this is treated as a single local cue in the current implementation of NeWG. After barrier removal, by means of the nonlocal hypothesis, the rat will indeed go from A to C via B to get to the food. If it goes from A to B’, it will not proceed to C based on expectations, since the world graph from B’ to C has not yet been created. It may go to C, however, based on its bias to explore the environment.

The taste (incentive) value of a food or drink goal-object is a property that can be easily manipulated and quantified. Experiments designed to test the validity of the local and nonlocal hypotheses can take advantage of a simple physiological paradigm - sodium appetite - where the incentive value of the goal-object can be very simply and robustly manipulated [14, 15]. When given a choice under normal non-challenge conditions, rats prefer to drink saline solutions with a concentration of around 0.9% [15]. However, under certain conditions (sodium depletion, hypovolemia, mineralocorticoid treatment) animals develop a strong preference for much higher concentrations. Although alterations in sodium appetite are mediated by changes in internal state, they are manifested by a measurable change in stimulus-incentive; the incentive value of high concentrations of saline increases, while that of lower concentrations decreases. Such experiments would enable the study of how efficiently an animal can learn and act upon new goals based upon its underlying drives - the new goal being the location of the newly preferred saline solution. By allowing the animal to learn the locations of saline solutions of various concentrations in a maze to asymptote, and then altering the incentive value of the preferred solution, either by adrenalectomy or mineralocorticoid treatment [15], it could be possible to determine the storage efficiency of the other non-preferred locations: does the animal have to completely re-learn the maze to find the newly preferred solution (as would be predicted by the local hypothesis), or is the location of the goal easily retrievable (predicted by the nonlocal hypothesis)? Finally, by altering the conditions so that the animal’s preference reverts to the original solution, it should be possible to determine how long this type of spatial formation is maintained.

4 In Search of the Rat’s World Graph

At least two distinct spatial encodings are considered to be maintained in the rat’s brain. The first is a metric representation that supports a limited form of vector arithmetic. The second is a local view representation derived from landmarks [16, 17, 18]. The brain learns relationships between place descriptions in these two representations, and the hippocampal complex appears to operate on, and may be responsible for maintaining, the conjoint representation; a cognitive map of the rat’s environment.

Single-unit recordings from CA3 and CA1 pyramidal cells in the hippocampus show a high correlation between spike rate and the location of the animal in the environment, hence the name "place cells". These cells were found to fire at an elevated rate over a continuous, compact area, called the place field of the cell [19]. However, McNaughton et al. [20] do not refer to place cells which fire regardless of the animal’s position but to "local view" cells. The firing of these cells, which have been identified in the 8-arm radial maze, depends not only on the animal’s location, but also on the direction in which it is facing. Moreover, Eichenbaum et al. [21] extended the view of hippocampal "place cells" by recording from rats when these repetitively performed a sequence of behaviors in a single odor-discrimination paradigm. Eichenbaum et al. established evidence that behavioral facts can be at least as powerful as spatial location in descriptions of hippocampal cell correlates. Lately, Markus et al. [22] also found that hippocampal neuronal activity appears to encode a complex interaction between locations, their significance and the behaviors the rat is called upon to execute. Behavioral facts, or contextual information, can also be used to explain directionality of place cell activation.

One of the categories of cells reported by Eichenbaum and colleagues was the goal-approach cells. These cells fired selectively during specific orientation or locomotor movements, such as approach to the odor port or to the reward cup in the particular paradigm used. As mentioned before, a motivational system, in part implemented by NeWG, is required to select goals to be pursued and to organize the animal’s commerce with appropriate goal objects. Moreover, a significant amount of motivation-related neural circuitry (the WANT box in Figure 9) appears to be located in the hypothalamus (assumed to be responsible for basic motivations). In particular, there appear to be discrete hypothalamic areas that play significant roles in the control of homeostatic signals relating to feeding, drinking, and temperature regulation [23]. Clark et al. [24] report that rats bearing excitotoxic lesions of the lateral hypothalamus are hypodipsic and hypophagic, but responses to 24 h food or water deprivation are normal, as are responses to different taste stimuli. They also found that lateral hypothalamic-lesioned rats are unable to respond as controls to dehydrating, dipsogenic or glucoprivic challenges. For Winn [25] these findings can be explained if one consider the lateral hypothalamus to be a principal route that communicates signals from the internal environment with the structures concerned with planning and executing behavior. In this view, the lateral hypothalamus stands as an interface between two different domains, the structures responsible for computing the internal state (e.g., area postrema) and the prefrontal cortex.

As described before, NeWG uses head direction information in the construction of edges between recognition categories and in the formation of the recognition categories themselves. Cells that show a unimodal tuning to head direction independent of location have been reported in several areas of the rat brain, like the postsubiculum [26, 27] and the posterior parietal cortex - PPC [28, 29]. When landmarks in a familiar environment are rotated about the animal, tuning curves of head direction cells rotate accordingly [27]. But in unfamiliar environments vestibular information dominates and the rat does not respond to the rotation. Thus, like place cells, head direction cell responses can be controlled by visual landmarks when the configuration is familiar. Head direction cells continue to fire in the dark. But if the animal wanders about in a darkened circular arena with no other positional cues available, they eventually drift. Hippocampal place fields appear to drift in synchrony with the head direction system [30]. Head direction cells provide the animal with an internal representation of the direction of its motion. McNaughton et al. [31] also found a few cells in rat PPC with location specificity that were dependent on visual input for their activation. 40% of the cells had responses discriminating whether the animal was turning left, turning right, or moving forward. Some cells required a conjunction of movement and location, e.g. one parietal cell fired more for a right turn at the western arm of a cross-maze than for a right turn at the eastern arm, and these firings were far greater than for all left turns. For Arbib, Érdi, and Szentágothai [32] this location information is perhaps better seen as affordance information, signaling recognition of situations where a certain range of motor behavior is possible (see affordances in Figure 9). The idea of PPC cells computing affordances for locomotion is similar to the situation for grasping [33]. In grasping, parietal cells can use vision of an object to determine an appropriate grip, which can then be signaled to premotor cortex. Further computations, perhaps prefrontal activity modulated by the basal ganglia are needed to determine which action will be executed. McNaughton et al. [31] also found another parietal cell that fired for left turns at the center of the maze but not for left turns at the ends of the arms, or for any right turns. As reported by them, turn-direction information was varied, with a given cell responding to a particular subset of vestibular input, neck and trunk proprioception, visual field motion and possibly efference copy from motor commands. According to Save and Moghaddam [11], the posterior parietal cortex plays a role of interface between the egocentric and allocentric coding, first by integrating kinesthetic information and second by incorporating some visual information. We hypothesize that the WG nodes are implemented by the parietal cortex and the hippocampal formation. As mentioned before, it has been demonstrated that the hippocampal formation plays a central role in the formation of allocentric representation of spaces [16]. In this way, PPC may provide some information to the hippocampus which would complete the formation of spatial mapping.

In 1982, Lieblich and Arbib [6] emphasized that "there is one crucial shortcoming of data on the hippocampus if it is to be viewed as a cognitive map. The world graph is used to determine which path is to be taken. Thus, one would expect to see the brain region used for exploring the world graph exhibit activation of place cells before the animal leaves the previous place". Nowadays, this deficiency can no longer be considered crucial. Eichenbaum and colleagues concluded that the observed goal-approach cells’ activity is usually better correlated with a location-to-be-occupied than with the current location, which is partly in agreement with the findings of Muller and Kubie [34] that suggest that hippocampal unit activity predicts the animal’s future location on a short time scale. Also, in 1996, Blum & Abbot [35] proposed a model of navigation in which an animal travels through its environment causing different sets of place cells to fire. In their model, information about both temporal and spatial aspects of the animal’s motion is reflected in changes of the strengths of synapses between place cells in the hippocampus. Since the observed long term potentiation affects subsequent place cell firing, it can shift the spatial location collectively coded by place cell activity. They use this information to suggest that an animal could navigate by heading from its present location toward the position coded by place cell activity.

Figure 9: Abstract view of the rat’s internal world graph.

5 Conclusion

The Neural World Graph, by implementing the Dominant Drive Hypothesis and Competing Nodes Hypothesis and by incorporating behavioral facts (motivational information in the form of drives) and head direction information into the self-adaptive ART categories, provides a model that can be used to answer how behavioral and spatial representations are compiled and how they are selected for use. In trying to answer these questions, it suffices to explain much spatial behavior, while not postulating an a priori system for organizing sensations into an absolute spatial framework, as postulated by O’Keefe and Nadel [16]. For this reason, NeWG can be used as a modeling environment for the investigation of motivated spatial behavior. It can also be viewed as a tool to help us develop biologically testable models of the cooperative computation of multiple brain regions as the animal explores its world in a goal-driven way.

In ART, there is a single vigilance parameter that regulates how generalized or specialized the ART network will be when creating its recognition categories. Future work involves the exploration of the notion that there is a set of vigilance parameters which can be related to the drive levels in the motivational component of the world graph. The important contribution from having one vigilance parameter per drive is to explicitly code for situations currently interesting because of a specific drive. Future work will also involve the replacement of the START network by a fully neural implementation. It is also desirable to use NeWG to replicate the whole set of behavior experiments described by Arbib & Lieblich [5].

Acknowledgments

This work was partially supported by CAPES Research Foundation - Brazil, and by a Program Project (P20) grant from the Human Brain Project (P01MH52194).

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Publication Dates

• Publication in this collection
  07 Oct 1998
• Date of issue
  July 1997