Associative memories based on lattice algebra

The theory of artificial neural networks has been successfully applied to a wide variety of pattern recognition problems. In this theory, the first step in computing the next state of a neuron or in performing the next layer of neural network computation involves the linear operation of multiplying neural values by their synaptic strengths and adding the results. Application of a nonlinear activation function usually follows the linear operation in order to provide for nonlinearity of the network. In this paper, we discuss a novel class of artificial neural networks, based on lattice algebra, in which the operations of multiplication and addition are replaced by addition and maximum (or minimum), respectively. By taking the maximum (or minimum) of sums instead of the sum of products, computation is nonlinear before the application of a nonlinear activation function. As a consequence, the properties of these networks, which are also known as morphological neural networks, are drastically different than those of traditional neural network models. The main emphasis of the results presented in this paper is on morphological associative memories. We define the basic computational model of a morphological neuron and examine some differences between these novel network models and traditional models.