Programmed interactions in higher-order neural networks: The outer- product algorithm (Q1186511)

The paper estimates the maximum number of arbitrarily specified vectors that can be reliably stored by the outer-product algorithm in a higher- order network of some degree \(d\). The principal results are the following: the static dynamic storage capacities of all variants of the outer-product algorithm generalized to degree \(d\) are of the order of \(n^ d/\log n\) memories. The statements are proved in the body of the paper. Some basic definitions, such that for higher-order neural networks, capacity function and outer-product algorithm, are summarized. Formal neural network models of densely interconnected polynomial threshold gates have recently found considerable applications in a variety of problems.