Recognition of general patterns using neural networks (Q1107333)

New learning rules for Hopfield-like networks are suggested. They permit non-orthogonal patterns to be associatively recalled similarly as orthogonal or pseudoorthogonal ones are treated by the well-known models. The formula for synaptic weight \(T_{ij}=\sum \mu^ s_ i\mu^ s_ j\), where the sum is taken over all taught patterns from their set \(\{\mu^ s\}\), is generalized to \(T_{ij}=\sum \epsilon_ s\mu^ s_ i\xi^ s_ j\), where \(\epsilon_ s\) denotes a relative teaching strength of the s-th pattern and \(\xi^ s_ j\) is a component of the vector \(\xi^ s\), which is constructed as a linear combination of vectors \(\{\mu^ s\}\) in such a way that a modified orthogonality condition is satisfied. The matrix \(\| T_{ij}\|\) is generally not symmetric, yet stability of taught patterns is proved. Global stability has only empirically been tested. A time-dependent energy function is proposed as a tool for further investigation of behaviour of networks with asymmetric memory matrix.