Complexity of learning in artificial neural networks
Some basic issues in the statistical mechanics of learning from examples are reviewed. The approach of statistical physics is contrasted with the analysis of learning within the framework of mathematical statistics and the question of the algorithmic complexity of explicit learning prescriptions is addressed. Even in very simple learning scenarios, the typical properties of which can be analyzed in great quantitative detail by methods from statistical mechanics, the determination of a suitable hypothesis approximating the target rule may be an NP-complete problem. Some special learning setups are suggested as model systems for the comparison between the approaches of statistical mechanics and computer science to the theory of computationally hard problems. (C) 2001 Elsevier Science B.V. All rights reserved.
neural networks statistical mechanics algorithmic complexity learning theory