Controlling energy landscapes with correlations between minima

Abstract: Neural network models have been used to construct energy landscapes for modeling biological phenomena, in which the minima of the landscape correspond to memory patterns stored by the network. Here, we show that dynamic properties of those landscapes, such as the sizes of the basins of attraction and the density of stable and metastable states, depend strongly on the correlations between the memory patterns and can be altered by introducing hierarchical structures. Our findings suggest dynamic features of energy landscapes can be controlled by choosing the correlations between patterns