Modelling constituent order despite symmetric associations in memory

Mathematical models of association memory (study AB, given A, recall B) either predict that knowledge for constituent order of a word pair (AB vs. BA) is perfectly unrelated, or completely dependent on knowledge of the pairing itself. Data contradict both predictions; when a pair is remembered, constituent-order is above chance, but still fairly low. Convolution-based models are inherently symmetric and can explain associative symmetry, but cannot discriminate AB from BA. We evaluated four extensions of convolution, where order is incorporated as item features, partial permutations of features, item-position associations, or by adding item and position vectors. All approaches could discriminate order within behaviourally observed ranges, without compromising associative symmetry. Only the permutation model could disambiguate AB from BC in double-function lists, as humans can do. It is possible that each of our proposed mechanisms might apply to a different, particular task setting. However, the partial permutation model can thus far explain the broadest set of empirical benchmarks.