Connectionism, Processing, Memory

Abstract

Abstract computing devices such as Turing machines resolve the dilemma between the necessary finitude of effective procedures and the potential infinity of a function's domain by distinguishing between a finite-state processing part, defined over finitely many representation types, and a memory sufficiently large to contain representation tokens for any of the function's arguments and values. Connectionist networks have been shown to be (at least) Turing-equivalent if provided with infinitely many nodes or infinite-precision activation values and weights. Physical computation, however, is necessarily finite. The notion of a processing-memory system is introduced to discuss physical computing systems. Constitutive for a processing-memory system is that its causal structure supports the functional distinction between processing part and memory necessary for employing a type-token distinction for representations, which in turn allows for representations to be the objects of computational manipulation. Moreover, the processing part realized by such systems provides a criterion of identity for the function computed as well as helps to define competence and performance of a processing-memory system. Networks, on the other hand, collapse the functional distinction between processing part and memory. Since preservation of this distinction is necessary for employing a type-token distinction for representation, connectionist information processing does not consist in the computational manipulation of representations. Moreover, since we no longer have a criterion of identity for the function processed other than the behaviour of the network itself, we are left without a competence-performance distinction for connectionist networks,