Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets

DOI10.1007/BF02124746zbMath0861.65133MaRDI QIDQ1923891

Eduardo D. Sontag

Publication date: 29 April 1997

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

zbMATH Keywords

neural networkscritical pointsdata fittingnonlinear least squares problemsregression datatheory of exponentials

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) General nonlinear regression (62J02) Probabilistic methods, stochastic differential equations (65C99)

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Cites Work

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• Semianalytic and subanalytic sets
• Feedforward nets for interpolation and classification
• Critical point theory and submanifold geometry
• On the real exponential field with restricted analytic functions
• The elementary theory of restricted analytic fields with exponentiation
• Projections of semi-analytic sets
• Real-Analytic Desingularization and Subanalytic Sets: An Elementary Approach
• A generalization of the Tarski-Seidenberg theorem, and some nondefinability results
• Definable Sets in Ordered Structures. II
• Finiteness results for sigmoidal “neural” networks