Generalization by Neural Networks
IEEE Transactions on Knowledge and Data Engineering
Optimization and Knowledge-Based Technologies
Informatica
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WE FORMALIZE A NOTION OF LEARNING IN CONNECTIONIST NETWORKS THAT CHARAC- TERIZES THE TRAINING OF FEED-FORWARD NETWORKS. CONSIDERING DIFFERENT FAM- ILIES OF NODE FUNCTIONS, WE PROVE THE LEARNING PROBLEM NP-COMPLETE AND THUS DEMONSTRATE THAT IS HAS NO EFFICIENT GENERAL SOLUTION. ONE FAMILY OF NODE FUNCTIONS STUDIED IS THE SET OF LOGISTIC-LINEAR FUNCTIONS, AS USED BY THE POPULAR BACK-PROPOGATION ALGORITHM. SEVERAL IMPLICATIONS OF THE THEOREM ARE DISCUSSED, INCLUDING WHY THIS RESULT IS ACTUALLY HELPFUL FOR CONNECTION IST LEARNING RESEARCH.