Categorization in a Hopfield network trained with weighted examples. (I). Finite number of concepts

Rogério L. Costa and Alba Theumann

Physica A: Statistical Mechanics and its Applications, 1999, vol. 268, issue 3, 499-512

Abstract: We consider the categorization problem in a Hopfield network with a finite number of concepts and trained with s examples of weight λτ, τ=1,…,s. We find that the retrieval capacity of an example with weight λ1, and the corresponding categorization error, depends also on the arithmetic mean λm=(1/(s−1))∑τ=2sλτ of the other weights. For λ1/λm<1, the categorization process is similar to that in a network trained with Hebb's rule, but for λ1/λm>1 we find that the line of first-order transitions between the retrieval and categorization phases ends at a critical point in the s, T plane. When two solutions are present, the global minimum of the free energy corresponds to the solution with the highest weight.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:268:y:1999:i:3:p:499-512

DOI: 10.1016/S0378-4371(99)00043-6

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