On the dynamics of neural networks realizing associative memories of first and higher order

This paper presents a new study on the dynamics of neural networks realizing associative memories of first and higher order. This is accomplished by focusing on the dynamics of a system of coupled differential equations that is shown to be equivalent to the neural network which behaves as an associative memory. This equivalence allows the assignment of a Lyapunov function to neural networks realizing associative memories of any order. This analysis provides some new interpretations for the outer product rule, or correlational learning, and also a basis for the development of more sophisticated learning schemes. A fundamental difference in the behaviour of associative memories of even and odd order is also investigated.