Abstract
Using the cavity method I derive the microscopic equations and their stabilitycondition for information learning in neural networks, optimized with arbitraryperformance functions in terms of the aligning fields of the examples. Inthe thermodynamic limit the aligning fields are well defined functions of thecavity fields. Iterating the microscopic equations provide a general algorithmfor network learning, supported by simulations in the maximally stable perceptronand the committee tree....