A Quantitative Comparison of the Performance of Three Discrete Distributed Associative Memory Models

Monte Carlo methods have been used to study the recall accuracy of three discrete distributed associative memory models: a discrete correlation matrix model (DCM), the Bayes discriminant rule model developed by Murakami and Aibara (MA), and a discrete version of the generalized inverse model of Kohonen (DGI). The key (input) and data (output) vectors have nc components restricted to the values − 1 and + 1. The elements of the nc × nc recall matrix may take on any floating point value. Auto-associative (key and data vectors identical) and hetero- associative operation have been examined with both noiseless (perfect) and noisy key vectors. Simulations have been performed over a range of nc from 20 to 100 and of nv, the number of vector pairs stored, from 1 to 50. The recall accuracy, defined as the probability that a component of the output vector is correct, depends strongly on the ratio nv/nc. The DGI model is the only one able to provide perfect hetero-associative recall with perfect input for nv ≤ nc, but is extremely sensitive to input noise. If the probability that a component of the input vector is correct is 0.9 the three models will provide perfect output only if nv is less than about 0.15 nc. For more noisy inputs the MA model provides the highest probability that a component of the output will be correct.