The Kernel Hopfield Memory Network

The kernel theory drawn from the work on learning machines is applied to the Hopfield neural network. This provides a new insight into the workings of the neural network as associative memory. The kernel “trick” defines an embedding of memory patterns into (higher or infinite dimensional) memory feature vectors and the training of the network is carried out in this feature space. The generalization of the network by using the kernel theory improves its performance in three aspects. First, an adequate kernel selection enables the satisfaction of the condition that any set of memory patterns be attractors of the network dynamics. Second, the basins of attraction of the memory patterns are enhanced improving the recall capacity. Third, since the memory patterns are mapped into a higher dimensional feature space the memory capacity density is effectively increased. These aspects are experimentally demonstrated on sets of random memory patterns.