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Generalized connectionist associative memory
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IWANN'03 Proceedings of the Artificial and natural neural networks 7th international conference on Computational methods in neural modeling - Volume 1
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The problems encountered when using multistate neurons in attractor neural networks are discussed. In particular, straightforward implementations of neurons with Q states leads to information storage capacities, &, that decrease like @e ~ log"2Q/Q^2. More sophisticated schemes yield capacities that decrease like @e ~ log"2Q/Q, but with retrieval times increasing proportional to Q. There also exist schemes whereby the information capacity reaches its maximum value of unity, but the retrieval time grows with the number of neurons, N, like O(N^3) instead of O(N^2) as in conventional models. Furthermore, since Q-state models approximate analog neurons when Q is large, the results demonstrate that the use of analog neurons is not feasible. After discussing these problems, a solution is proposed in which the information capacity is independent of Q, and the retrieval time increases proportional to log"2Q. The retrieval properties of this model, i.e., basins of attraction, etc., are calculated and shown to be in agreement with simple theoretical arguments. Finally, a critical discussion of this approach is given.