When two objects are experienced simultaneously, there is the potential for an explicit connection between features of different objects. An explicit connection between features of different objects is a relation instance. Imagine for example the experience of a small round object on a flat surface. The connection between small and round would be created (or strengthened) within the object instance (and the object category) representation but the connection between small and flat could also be created (or strengthened); this would be a connection between features in different object instance representations. With the presentation of multiple relations instances with similar values for different dimensions, a relational correlation is created.
Consider first the case of a single dimension. Each of the two objects in a relation instance has a value on that dimension; one object, for example, may be big and the other little. Multiple relation instances of this sort, if repeated sufficiently, may lead to a one-dimensional relational correlation. Figure 15 illustrates a relation instance (left) and a one dimensional relational correlation (right). For example, the relation instance might be a small object and a large object represented by the specific values on the input dimension, the small object by the white region for example, and the large object by the black region. If such instances are experienced with regularity, a relational correlation would develop, consisting of the ranges of correlated values, as illustrated on the right. For this kind of a system to work, the relational correlations between distinct objects must be represented in ways that are distinguished from those used to represent the feature correlations presented by a single object instance or object category. We propose that these relational correlations are represented not by simple connections as feature correlations but by separate micro-relation units (MRUs). In the figures, these units appear as diamonds. Note that these units need have no built-in meaning, but are analogous to units in distributed representations of objects in PDP networks. That is, MRUs take on their significance as the weights connecting them to object feature units and other MRUs evolve in response to correlations in input events. In this way, the relational meaning of an event is similarity-based and object based: a generalization across multiple experiences of bundles of object features that co-occur.
With experience, a learner may generalize from narrow regions of values for the two objects as instances of a relation to relative values across the whole dimension. For example, NEAR does not refer to two objects located in a range of specific absolute locations, but rather to the proximity of objects located anywhere. One way to represent such a relation is through the association of more specific absolute relational correlations with each other through a relational category unit, as shown in Figure 16 for NEAR. The category unit must point to each of the relational correlations rather than to the correlated values; thus each relational correlation must take the form of an explicit unit rather than a simple connection. Notice that both the correlations and the category unit are MRUs.
As with a single dimension, a learner can generalize from absolute values to relative values across one or more of the dimensions. For example, the knowledge about the relationship between SIZE and LOUDNESS could take the form of the knowledge that relative size, wherever on the size scale, correlates with relative loudness, wherever on the loudness scale. We believe that many familiar spatial relational categories such as ON are actually learned in terms of cross-dimensional relational correlations of this type. Thus for ON, the relative location of the upper and lower boundaries of two objects, which seems to define the relation for us, correlates with the relative size and movability of the objects.