Simon D. Levy and Jordan B. Pollack
The traditional approach to complex problems in science and engineering is to break down each problem into a set of primitive building blocks, which are then combined by rules to form structures. In turn, these structures can be taken apart systematically to recover the original building blocks that went into them. Connectionist models of such complex problems (especially in the realm of cognitive science) have often been criticized for their putative failure to support this sort of compositionality, systematicity, and recoverability of components. In this paper we discuss a connectionist model, Recursive Auto-Associative Memory (RAAM), designed to deal with these issues. Specifically, we show how an initial approach to RAAM involving arbitrary building-block representations placed severe constraints on the scalability of the model. We describe a re-analysis the building-block and "rule" components of the model as merely two aspects of a single underlying nonlinear dynamical system, allowing the model to represent an unbounded number of well-formed compositional structures. We conclude by speculating about the insight that such a "unified" view might contribute to our attempts to understand and model rule-governed, compositional behavior in a variety of AI domains.