Sensitivity to Noise in Bidirectional Associative Memory (BAM)

Abstract

Original Hebbian encoding scheme of bidirectional associative memory (BAM) provides a poor pattern capacity and recall performance. Based on Rosenblatt's perceptron learning algorithm, the pattern capacity of BAM is enlarged, and perfect recall of all training pattern pairs is guaranteed. However, these methods put their emphases on pattern capacity, rather than error correction capability which is another critical point of BAM. This paper analyzes the sensitivity to noise in BAM and obtains an interesting idea to improve noise immunity of BAM. Some researchers have found that the noise sensitivity of BAM relates to the minimum absolute value of net inputs (MAV). However, in this paper, the analysis on failure association shows that it is related not only to MAV but also to the variance of weights associated with synapse connections. In fact, it is a positive monotone increasing function of the quotient of MAV divided by the variance of weights. This idea provides an useful principle of improving error correction capability of BAM. Some revised encoding schemes, such as small variance learning for BAM (SVBAM), evolutionary pseudorelaxation learning for BAM (EPRLAB) and evolutionary bidirectional learning (EBL), have been introduced to illustrate the performance of this principle. All these methods perform better than their original versions in noise immunity. Moreover, these methods have no negative effect on the pattern capacity of BAM. The convergence of these methods is also discussed in this paper. If there exist solutions, EPRLAB and EBL always converge to a global optimal solution in the senses of both pattern capacity and noise immunity. However, the convergence of SVBAM may be affected by a preset function.