title: The greatest allowed relative error in weights and threshold of strict separating systems.
abstract: An important consideration when applying neural networks is the sensitivity to weights and threshold in strict separating systems representing a linearly separable function. Perturbations may affect weights and threshold so that it is important to estimate the maximal percentage error in weights and threshold, which may be allowed without altering the linearly separable function. In this paper, we provide the greatest allowed bound which can be associated to every strict separating system representing a linearly separable function. The proposed bound improves the tolerance that Hu obtained. Furthermore, it is the greatest bound for any strict separating system. This is the reason why we call it the greatest tolerance.
authors.affiliation: Departament de Matemàtica Aplicada 3, Escola Politècnica Superior d'Enginyeria de Manresa, Manresa E-08242, Spain. josep.freixas@upc.edu
authors.forename: Josep
authors.initials: J
authors.lastname: Freixas
authors.forename: Xavier
authors.initials: X
authors.lastname: Molinero
mesh_terms: D000465:Algorithms; D016014:Linear Models; D016571:Neural Networks, Computer; D015203:Reproducibility of Results