Expansion of a Matrix In Terms of External Products of Configuration Vectors

摘要

The paper proposes a neural-net iterative algorithm that allows us to represent any random symmetrical N × N matrix as a weighted Hebbian series of configuration vectors with a given accuracy. The iterative algorithm is shown to demonstrate the fastest convergence when the vectors of expansion are stable nods of the N-dimensional space corresponding to the extremums of the neural-net energy functional. It so proves that all conclusions about neural networks and optimization algorithms that are based on Hebbian matrices are true for any other type of matrix.