Skip to main content

Order within associations as a test of association-memory models

In learning associations (e.g., a pairing of items, A-B), the hippocampus appears to implement Associative Symmetry, namely, when learning a forward association (A->B), picking up the backward association (B->A) for free [3], a characteristic of human association-memory that has been replicated numerous times (e.g., [5]). A mathematical operation that does this automatically, and thus might be carried out by the hippocampus, is the convolution operation, the operation used to store associations in a range of influential behavioural memory models [2]. Convolution-based models lead to a specific prediction about within-pair order memory (the participant’s ability to retrieve the relative orders of the A and B items), namely, that within-pair order memory should be at chance levels. In contrast, models based on the outer product, known as matrix models [1] the way they have been applied, lead to perfect within-pair order memory (assuming the pairing is retrieved); likewise for numerous other models that assume associations are stored by concatenating the vector representations of paired items [6].

Here we test within-pair order memory with a verbal double-function list paradigm in which participants are presented with pairs of words in which the left-handed item of one pair is the right-handed item of a different pair. Thus, within-pair order information is critical for later effective cued recall. The results suggested that human participants have neither poor nor near-perfect memory for within-pair order, challenging all current models to our knowledge. Our recently proposed positional coding model for paired-associate memory [4], which already incorporates within-pair order in the same manner as between-pair order. Even this positional coding model requires some additional assumptions to fit the fine structure of the behavioural data.

In sum, our findings suggest that within-pair order memory is neither poor nor perfect, pointing to a fallible mechanism for within-pair order learning in verbal association memory tasks and constraining the computational mechanisms the hippocampus could plausibly use to learn pairs with the property of Associative Symmetry.


  1. Anderson JA: Two models for memory organization using interacting traces. Mathematical Biosciences. 1970, 8 (z): 137-160. 10.1016/0025-5564(70)90147-1.

    Article  Google Scholar 

  2. Borsellino A, Poggio T: Holographic aspects of temporal memory and optomotor responses. Kybernetik. 1972, 10: 58-60. 10.1007/BF00288785.

    Article  CAS  PubMed  Google Scholar 

  3. Bunsey M, Eichenbaum HB: Conservation of hippocampal memory function in rats and humans. Nature. 1996, 379: 255-257. 10.1038/379255a0.

    Article  CAS  PubMed  Google Scholar 

  4. Caplan JB: Associative Isolation: unifying associative and order paradigms. Journal of Mathematical Psychology. 2005, 49: 383-402. 10.1016/

    Article  Google Scholar 

  5. Kahana MJ: Associative symmetry and memory theory. Memory & Cognition. 2002, 30: 823-840.

    Article  Google Scholar 

  6. Mensink G, Raaijmakers JGW: A model for interference and forgetting. Psychological Review. 1988, 95: 434-455. 10.1037/0033-295X.95.4.434.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Jeremy B Caplan.

Rights and permissions

Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Caplan, J.B., Rehani, M. Order within associations as a test of association-memory models. BMC Neurosci 11 (Suppl 1), P78 (2010).

Download citation

  • Published:

  • DOI:


  • Matrix Model
  • Memory Model
  • Order Information
  • Outer Product
  • Convolution Operation