Communications of the ACM
Linear function neurons: Structure and training
Biological Cybernetics
The perceptron algorithm is fast for nonmalicious distributions
Neural Computation
On exact specification by examples
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
On the Size of Weights for Threshold Gates
SIAM Journal on Discrete Mathematics
How fast can a threshold gate learn?
Proceedings of a workshop on Computational learning theory and natural learning systems (vol. 1) : constraints and prospects: constraints and prospects
Machine Learning
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The number of adjustments required to learn the average LTU function of d features, each of which can take on n equally spaced values, grows as approximately n^2dwhen the standard perceptron training algorithm is used on the complete input space of n points and perfect classificationis required. We demonstrate a simple modification that reduces the observedgrowth rate in the number of adjustments to approximatelyd^2(log (d) + log(n)) with most, but not all input presentation orders. A similar speed-up isalso produced by applying the simple but computationally expensive heuristic“don‘t overgeneralize” to the standard training algorithm. This performance is very close to the theoretical optimum for learning LTU functions by any method, and is evidence that perceptron-like learning algorithms can learn arbitrary LTU functions in polynomial, ratherthan exponential time under normal training conditions.Similar modifications can be applied to theWinnow algorithm, achieving similar performance improvements anddemonstrating the generality of the approach.