Topologically Continuous Associative Memory: A Theoretical Foundation

We introduce a neural network with associative memory and a continuous topology, i.e. its processing units are elements of a continuous metric space and the state space is Euclidean and in¯nite dimensional. This approach is intended as a generalization of the previous ones due to Little and Hop¯eld. Thus we integrate two levels of continuity: continuous response units and continuous topology of the neural system, obtaining a more biologically plausible model of associative memory. A theoretical background is provided so as to make this integration consistent. We ¯rst present some general results concerning attractors and stationary solutions, including a variational approach for the derivation of the energy function. Then we focus on the case of orthogonal memories, proving theorems on their stability, size of attraction basins and spurious states. Finally, we get back to discrete models, i.e. we discuss new viewpoints arising from the present continuous approach and examine which ...

• Type: Conference
• Year: 2007
• Where: IICAI
• Authors: Enrique Carlos Segura
• Keywords: Artificial Intelligence, Associative Memory, Continuous Metric Space, Continuous Topology, IICAI 2007