Improved bidirectional retrieval of sparse patterns stored by Hebbian learning
✍ Scribed by Friedrich T. Sommer; Günther Palm
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 288 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0893-6080
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✦ Synopsis
The Willshaw model is asymptotically the most efficient neural associative memory (NAM), but its finite version is hampered by high retrieval errors. Iterative retrieval has been proposed in a large number of different models to improve performance in auto-association tasks. In this paper, bidirectional retrieval for the hetero-associative memory task is considered: we define information efficiency as a general performance measure for bidirectional associative memory (BAM) and determine its asymptotic bound for the bidirectional Willshaw model. For the finite Willshaw model, an efficient new bidirectional retrieval strategy is proposed, the appropriate combinatorial model analysis is derived, and implications of the proposed sparse BAM for applications and brain theory are discussed. The distribution of the dendritic sum in the finite Willshaw model given by Buckingham and Willshaw [Buckingham, J., & Willshaw, D. (1992). Performance characteristics of associative nets. Network, 3, 407-414] allows no fast numerical evaluation. We derive a combinatorial formula with a highly reduced evaluation time that is used in the improved error analysis of the basic model and for estimation of the retrieval error in the naive model extension, where bidirectional retrieval is employed in the hetero-associative Willshaw model. The analysis rules out the naive BAM extension as a promising improvement. A new bidirectional retrieval algorithm -called crosswise bidirectional (CB) retrieval -is presented. The cross talk error is significantly reduced without employing more complex learning procedures or dummy augmentation in the pattern coding, as proposed in other refined BAM models [