Object Units

 

Object units (OUs) are units with a relative phase angle in addition to an activation. As in a number of other recent models [Hummel and Biederman, 1992, Shastri and Ajjanagadde, 1993, Sporns et al., 1989], synchronization functions to bind together the features of distinct objects. Units with the same phase angle are part of the same object, and units with different phase angles belong to different objects.

The connection between each pair of OUs has not only a weight but also an associated coupling function, a function of the difference in phase angles of the two units. The coupling function must be symmetric about 0, and its derivative must be anti-symmetric about 0; see the Appendix for why these constraints must hold. Both the activation and the phase angle of an OU are potentially modified each time a unit is updated, and both depend on the coupling function on the weights into the unit. The input h and change in phase angle to an OU i are given by

where n is number of units in the network, is the activation of unit j, is the weight connecting units i and j, and is the coupling function associated with units i and j. A stable state of the network is, then, a state in which neither activations nor phase angles are changing.

The most common coupling function used in the network is . For positive weights, the system consisting of the two units with this coupling function has an attractor at the state where the units are in phase and a repeller at the state where they are out of phase. The two units excite each other at all phase angle differences except . For negative weights, there is an attractor at the out-of-phase state and a repeller at the in-phase state, and the units inhibit each other except when they are out of phase.

Demo 1 illustrates the behavior of a small network of OUs.

The units in Playpen's lexicon representing nouns are also OUs. Learning the meaning of a noun would involve creating positive connections between the noun unit and the associated non-linguistic visual/spatial feature units. These connections would tend to cause the connected units to align their phase angles, so that in the comprehension or production of a phrase the word is ``bound'' to its meaning. Figure 9 illustrates the relationship between noun OUs and the associated non-linguistic ``semantic'' OUs.

 

 

Figure 9: OUs in the Representation of Noun Meaning. Nouns and visual objects are both represented by OUs; during production or comprehension synchronized phase angles bind together nouns and their internal ``referents''. Unit activation is represented by brightness, and phase angles are indicated by the blue triangles. The dashed green arrows represent trainable connections which have developed positive weights. Only a minimum number of units is shown.