It allows for abstract and, at the same time, complete specifications of artificial neural networks. It is easy to combine different paradigms, and to modify or extend given network descriptions. Also, the generated class can easily be integrated with other software components. Future work goes into two directions. There are many dynamical processes, which cannot be described explicitely by mathematical means, but which are characterized by numerous data and qualitative, heuristic knowledge.
Examples are processes occuring in sewage treatment plants.
We are interested in combining connectionist and other artificial intelligence methods with the goal of modelling and controlling such processes. It is important for model selection to study the bounds on how fast we can learn as a function of the number of patterns in the training set. Presently study we consider the case of optimal early stopping and cross-validation stopping to avoid overfitting. It is shown analytically that the asymptotic gain in the generalization error is small if we perform early stopping, even if we have access to the optimal stopping time. The analysis treats realizable stochastic neural networks, trained with Kullback-Leibler loss in the asymptotic case.