A novel associative memory model is proposed in which both the stable and optimal (minimum error) association are realized even when noisy input key vectors are given. The performance of the model is compared with that of typical associative memory models (Kohonen's model and the stabilized model) theoretically and experimentally (by computer simulation). The proposed model takes full consideration of the input noise conditions (magnitude of noise). Since the relationship between the proposed model and Kohonen's model is similar to that between the Wiener filter and the inverse filter, the proposed associative memory model is more practical than Kohonen's model.>

An improvement of the Moore-Penrose generalized inverse associative memory method is presented. It is known that for noisy input key vectors the associative memory is extremely sensitive (unstable) and association errors become unacceptably large, particularly as the number of vectors approaches the number of components per vector. Using singular value decomposition the association behavior of the associative memory is analyzed theoretically and its association error is shown to consist of two kinds of errors. One is due to the linear dependency of the key vectors (dependency error), and the other is due to the input additive noise (noise error). For noisy input key vectors the noise error is greatly increased when at least one small eigenvalue of the key space exists. It is found that the noise error can be changed to the dependency error by eliminating the corresponding eigenvalues. Therefore, if the eigenvalues are appropriately eliminated, stable association behavior can be realized and the association error reduced. In the proposed improvement method an elimination condition of the eigenvalues is given. The proposed method is greatly effective for noisy input key vectors.

The purpose of this correspondence is to propose a new construction method of distributed associative memory which operates with discrete-valued signals. In this method, memorized pairs of vectors (cue vectors and data vectors) are recorded in the form of a matrix W and a vector T. From an input vector X, the data vector is recalled by an operation u(XW + T) where X is a cue vector or a noisy cue vector. and u is a quantizing function. The methods of memorization and recall are similar to the Associatron; however, the proposed model can recall the data vectors optimally in Bayesian sense even when noisy cue vectors are given as the input vectors.

This note discusses the generation of ternary threshold functions of three variables. Merrill's generation method to generate ternary threshold functions is modified. The number of ternary threshold functions of three variables is counted by a computer, the number is 85629. Tables of characterizing parameters of canonical ternary threshold functions of two and three variables are presented. A table-lookup method to realize ternary threshold functions is given. It is verified that the complete monotonicity (three-value extension of the complete monotonicity in two-valued logic) is a sufficient condition for a ternary three-variable switching function to be a ternary threshold function.