The perceptron algorithm is fast for nonmalicious distributions
Neural Computation
Learning by choice of internal representations
Advances in neural information processing systems 1
Training a 3-node neural network in NP-complete
Advances in neural information processing systems 1
Neural net algorithms that learn in polynomial time from examples and queries
IEEE Transactions on Neural Networks
Designing multilayer perceptrons from nearest-neighbor systems
IEEE Transactions on Neural Networks
Multilayer neural networks and polyhedral dichotomies
Annals of Mathematics and Artificial Intelligence
On the complexity of recognizing regions computable by two-layered perceptrons
Annals of Mathematics and Artificial Intelligence
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It is mathematically investigated as to what kind of internal representations are separable by single output units of three-layer perceptrons. A topological description is given for the necessary and sufficient condition that hidden layer representations of input patterns are separable by the output unit. An efficient algorithm is proposed for checking whether or not a hidden layer representation is linearly separable and, if not, for specifying inseparable portions in the partition. Application of the algorithm to learning of three-layer perceptrons is presented in which redundant units are utilized to reduce inseparable partition into separable one. Polynomial learnability from examples and queries is shown for the proposed learning algorithm.