Cognitive knowledge and motivated behavior give rise to actions that allow animals to survive in their environment. 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. Arbib & Lieblich (1977; Lieblich and Arbib, 1982) 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. In the present work, the WG theory was partly implemented by the use of the Adaptive Resonance Theory - ART (Grossberg, 1976). However, in NeWG (the Neural World Graph), the Fuzzy ART network (Carpenter et al., 1991) had to be modified to incorporate the WG edge concept. In the WG theory, there is an edge from node x to node x' in the graph for each distinct path the animal has traversed. This is implemented in NeWG as an excitatory link between two F2 neurons in the Fuzzy ART module. If, for example, a category x is currently active at time t, but by deciding to move one step north the animal activates a distinct category x at time t+1, a link will be created from node x to node x. Appended to each edge will be sensorimotor features associated with the corresponding movement/path (e.g., one step north). NeWG, by means of its edge information, facilitates the activation of F2 nodes that are directly connected to the current node, or active category. This, combined with vestibular and head direction inputs allows the animal to succesfully navigate in the dark.Based on the hypothesis that drives can be viewed as states (Milner, 1977), the WG theory posits a set d1, d2, ..., dk of discrete drives to control the animal's behavior. The idea is that each appetitive drives spontaneously increases with time, while aversive drives are reduced according to an intrinsic factor to the animal. Drive reduction takes place in the presence of some substrate - water reduces the thirst drive. In the current implementation of NeWG, drive information is treated as a black box separate from the neural network. However, after processing, it is presented to the F1 neurons, together with the environmental stimuli, and head direction information. These together will let the animal determine whether it is in a situation already represented by a recognition category x of F2 or whether a new category must be created. Pertinent symbolic information is also attached to each recognition category. This is represented by a vector [R(d1,x,t), ..., R(dk,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. By incorporating symbolic information, we are actually working with what we called the START network, i.e., a Symbolic-Tagged fuzzy ART network.
Since the WG theory assumes processes that were not yet implemented in NeWG, like the merging of nodes, what follows is a description of some observed differences. 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 0, and suppose that the + is consistently reward with food. 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,0), (R,+), (R,0), where (L,+) is the door to the left of the choice point with a + on it, and so on. According to Lieblich & Arbib (1982), as a result of its training, the animal may well associate (L,+) and (R,+) - but not (L,0) and (R,0) - with food. Because of their commonalities in both sensory features and food reward, (L,+) may merge with (R,+), and (L,0) may merge with (R,0). In its current version, however, NeWG's behavior will be quite different, it will depend on the value of the vigilance parameter of the START network. Once this is low enough, however, 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 (0), Turn toward the + and Turn toward the 0, respectively. Like the WG theory, NeWG is rich enough to allow generalization over dimensions other than spatial ones. In a different experiment, the simulated rat was allowed to explore a cross maze without local or distal cues during one hundred steps, which resulted in the generation of twenty nodes in its neural world graph. These were obtained by setting the vigilance parameter of the START network to 0.9. With a vigilance parameter equals to 0.3, only two nodes were created. This happens due to the generalization capabilities of the network. Analysis of the two nodes revealed that they differentiated between the end of a corridor and the remaining parts of the maze: the 4-arm junction and the middle sections of the corridors.
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. Future work involves the replacement of the START network by a fully neural implementation. 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 and observe their results in real time. The system is currently accessible under Brain Models on the Web at the University of Southern California (http://www-hbp.usc.edu/models/)