Power law decay of stored pattern stability in sparse Hopfield neural networks

Fei Fang,Zhou Yang,Sheng-Jun Wang

Figure 12. The overlap difference φ − φ0 versus the number of patterns n on randomly degree distribution networks on a log-log scale for two average degree ⟨k⟩=25(squares) and ⟨k⟩=50(circles). Data points from n=21 to 10 000 are used in fitting(squares). Data points from n=59 to 10 000 are used in fitting(circles). The size of networks is N=10000. Inset: the overlap φ versus the number of patterns n on randomly degree distribution networks on a linear coordination. The final overlap φ0 is 0.21(squares) and 0.19(circles). Each data point is averaged over 1000 realizations.