The Solution

RUs, which are the major innovation of the Playpen architecture, are used to represent relational information; they are ``about'' two different objects. Each RU is made up of a cluster of five units hard-wired in such a way that the unit as a whole is activated to the extent that it is receiving input from two distinct objects. Figure 11 shows a pair of RUs along with four OUs illustrating the connectivity within the RUs and between them and other units of both types. An RU has two interfaces, each consisting of a pair of OUs: one to handle interaction with other RUs, the other to handle interaction with OUs. The two interfaces are connected in such a way that the corresponding arms tend to be in-phase and the opposing arms tend to be out-of-phase. The RU is considered activated when all four of its interface units are activated. Each RU also has a simple unit with no phase angle and negative connections to all four of the OUs. This bias unit has a resting activation of 1.0 and turns off only when its input falls below a threshold. The bias unit functions to prevent the OUs on one interface from turning on those on the other interface unless they are both sufficiently activated. Without the bias unit, ``one-armed'' relations, those in which one arm only is activated on each interface, would be possible.

 

 

Figure 11: Relation Units. Two RUs are shown, each surrounded by a magenta border. Both are in their active state: all four arms are maximally activated and the bias units are inhibited. The two RUs are connected to each other on their RU interfaces, and each RU is also connected to two OUs on its OU interface.

Connectivity between RUs is also constrained, though the weights themselves are trainable. There are four connections joining each pair of connected RUs on their RU interfaces, but only two distinct weights, one for the connections joining corresponding arms, the other for the connections joining opposing arms. The coupling function on these connections is . These connections implement the four possible relationships that can exist between micro-relations:

1. The two micro-relations have no effect on each other. In this case both weights are 0.
2. The two micro-relations correlate negatively with one another; that is, the presence of one leads one to expect the absence of the other. In this case both weights are negative.
3. The two micro-relations correlate positively with one another, and corresponding arms are bound to the same object. In this case the weight for the corresponding arms is positive and that for the opposing arms 0.
4. The two micro-relations correlate positively with one another, and opposing arms are bound to the same object. In this case the weight for the corresponding arms is 0 and that for the opposing arms positive.

In the resting state of an RU, the four OUs have activations of 0 and the bias unit an activation of 1. When an RU is activated on one or the other or both of its interfaces in such a way that the two OUs on an interface are highly activated and out-of-phase, the bias unit is inhibited, and the OUs on the interface (if not already activated) become active and take on the phase angles of the corresponding OUs in the other interface. When the RU is completely activated, the four OUs have activations of 1 and the bias unit an activation of 0. Demo 2 illustrates a simple network of two RUs, one of which is activated by input from a single OU.

Now consider how RUs would permit us to represent the meaning of a spatial relation term. The word itself has an associated RU with a trajector and a landmark arm on both interfaces. The RU interface of this RU connects to appropriate RUs in the Spatial Relation Concepts layer, which in turn connect to OUs specifying the locations associated with features of the two related objects. The nouns representing the trajector and landmark of the relation must be in phase with the corresponding arms of the relation term RU. We are far from a complete account of how this takes place in either production or comprehension. For now, we simply assume that a trajector OU implements this binding process. Figure 12 illustrates these relationships.

 

 

Figure 12: Relation Units in the Representation of Word Meaning. Only one of many possibly relevant units is shown in the Spatial Relation Concepts and Location layers. The RU interfaces of the RUs appear on top, the OU interfaces on the bottom. Only the positive connections between the two RUs are shown; there would be also be connections with weight 0 joining the opposing arms of the two RU interfaces. The trajector OU implements the phase relationship between the trajector arm of the word RU and the corresponding noun OU.