A new local training rule for higher-order associative memories

Necessary and sufficient conditions are derived for the correlation matrix and thresholds of higher-order associative memories (HOAMs) that can guarantee the recall of all training patterns. A local training rule is presented; this rule iteratively trains the correlation matrix and thresholds so that the complete recall conditions are satisfied. A design algorithm is proposed that ensures each training pattern is stored with as large a basin of attraction as possible. Computer simulations that demonstrate the power of the proposed local training rule are reported.<>