The stationarity equations of both models are in general inhomogeneous integral equations. Similar equations appear for example in quantum mechanical scattering theory, where the inhomogeneities, in analogy to templates or data, represent the measurable asymptotic states (``channels'') of the system [9]. As nonlinear equations they have to be solved by iteration. An iteration procedure (``learning algorithm'') for solving a (linear or nonlinear) equation of the form is obtained by selecting a possibly iteration step and -dependent operator and relaxation factor and using the updating rule . For any positive definite the error decreases till reaching a local minimum provided is chosen small enough. An equal to the identity, for example, corresponds to the gradient algorithm and requires no inversion. A Gaussian can approximate local correlations induced by differential operators. Choosing corresponds for error functional to the EM algorithm and selecting the negative Hessian results in the Newton method.
Figure (1) summarizes the temperature dependence which have been found in numerical studies of a model with error = . This corresponds to a data template AND-ed to a probabilistic OR of two continuous prior templates . Here the data template is a sum of standard mean square error terms and the prior concepts measure the (``Laplace'') distance between and prior template . The actual data and the two continuous prior templates are displayed on the right hand side of the figure.