Cascade associative memory storing hierarchically correlated patterns with various correlations

In conventional models for storing hierarchically correlated patterns, correlations between ancestors (first-level patterns) and their descendants (second-level ones) are assumed to be uniform, so that the descendants are distributed around their ancestors with equal distances. However, this assumption might be unnatural. We believe that objects are encoded into patterns by preserving the similarity between them. In this case, descendants are distributed around their ancestors with various distances, so that the assumption is invalid and the conventional models become inapplicable. To overcome this, we propose a model CASM3 for storing hierarchically correlated patterns with various correlations. In CASM3, critical load levels vary with the descendants, and become higher with increasing correlations. Increase in load level successively destroys the memories of the descendants in descending order of their correlations. The size of the basins of attraction depends on the range of the correlations, and becomes larger as the correlation range is shifted toward lower levels.