TODAM2, a theory of distributed associative memory, shows how item and associative information can be considered special cases of serial-order information. Consequently, it is important to get the right model for serial-order information. Here, we analyze and compare three distributedmemory models for serial-order information that use TODAM'sconvolution-correlation formalism. These models are the chaining model, the chunking model, and a new model, the power-set model. The chaining model associates each item with its predecessor; the chunking model uses multiple convolutions and n-grams to form chunks; and the power-set model interassociates all items in a set in a particular way to form a chunk. The models are compared in terms of their performance on seven basic tests of serial-order information-namely, serial recall, backward recall, recall of missing items, sequential probe tests, positional probe tests, serial-to-paired-associate transfer, and item recognition. The strengths and weaknesses of each model are discussed.
631If we are to understand human memory in any detail, we must distinguish three types of information: (1) Item information, which underlies the recognition of single objects ("items"); (2) associative information, which underlies the relation or association between two objects or items; and (3) serial-order information, which preserves the temporal order in a string ofthree or more items. Evidence for these distinctions was presented in Murdock (1974), and TODAM (an acronym for theory ofdistributed associative memory) has always preserved these distinctions.TODAM2 (Murdock, 1993b) is an attempt to provide a unified theoretical account of the storage and retrieval of item, associative, and serial-order information. To give a brief overview, it is a distributed-memory model in which items are represented by random vectors, associations are represented by the convolution of item vectors, information is stored in a common memory vector, the dot product is the comparison operation for recognition, and correlation is the retrieval operation for recall; these operations are assumed to go on in working memory, part of the general system architecture. Chunks are represented as sums of n-grams, and n-grams are n-way autoassociations (autoconvolutions) of the sums of n item vectors. Ifn = I, we have item information; ifn = 2, we have associative information; and if n ;:::: 3, we have serial-order information. Each of these concepts will be explained shortly. The TODAM2 analysis makes it clear that item and associative information are special cases of serial-order information, so it is crucial to get the right model for serial-order information. The serial-order model we used in TODAM2 was the chunking model (Murdock, 1992), but that is only one possibility. In this paper, we analyze and compare three possible distributed-memory models for serial-order information: The chaining model of Lewandowsky and Murdock (1989); the chunking model; and the power-set model, a new model for serialorder information th...