Cognitive Computation

, Volume 6, Issue 1, pp 74–88 | Cite as

Analogical Mapping with Sparse Distributed Memory: A Simple Model that Learns to Generalize from Examples

  • Blerim Emruli
  • Fredrik Sandin


We present a computational model for the analogical mapping of compositional structures that combines two existing ideas known as holistic mapping vectors and sparse distributed memory. The model enables integration of structural and semantic constraints when learning mappings of the type \(x_i \rightarrow y_i\) and computing analogies \(x_j \rightarrow y_j\) for novel inputs x j . The model has a one-shot learning process, is randomly initialized, and has three exogenous parameters: the dimensionality \(\mathcal{D}\) of representations, the memory size S, and the probability χ for activation of the memory. After learning three examples, the model generalizes correctly to novel examples. We find minima in the probability of generalization error for certain values of χ, S, and the number of different mapping examples learned. These results indicate that the optimal size of the memory scales with the number of different mapping examples learned and that the sparseness of the memory is important. The optimal dimensionality of binary representations is of the order 104, which is consistent with a known analytical estimate and the synapse count for most cortical neurons. We demonstrate that the model can learn analogical mappings of generic two-place relationships, and we calculate the error probabilities for recall and generalization.


Analogical mapping Compositional structures Distributed representations Holistic processing Sparse distributed memory 



We thank the anonymous reviewers for their constructive suggestions that helped us to improve this article, Serge Thill for reviewing and commenting on an early version of the manuscript, Ross Gayler for helping us to improve the final text, and Jerker Delsing for comments and encouraging support. This work was partially supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT) and the Kempe Foundations.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.EISLAB, Luleå University of TechnologyLuleåSweden

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