The capacity of the Hopfield associative memory
IEEE Transactions on Information Theory
Learning internal representations by error propagation
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Nonlinear quantization on Hebbian-type associative memories
Applied Intelligence
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The existence of principal interconnections useful in solving the proliferation problem in higher order Hebbian-type associative memories is introduced. Among all legal interconnections, we prove there exists a subset Tpr that carries more information than the others. Regardless of the network order p, the elements in Tpr are shown to be those interconnections T that fall within the range of$$\sqrt {m_s} \le \left| T \right| \le 2 \sqrt {m_s},$$where ms equals the number of stored codewords. Memories that use only Tpr can maintain original generalization performance, using less than 50 percent of the total number of interconnections.