Title :
Algebraic analysis for neural network learning
Author_Institution :
Precision & Intelligence Lab., Tokyo Inst. of Technol., Yokohama, Japan
Abstract :
This paper clarifies the learning curve for a complex and non-regular neural network model whose true parameter set is an analytic set with singular points. Based on algebraic analysis we rigorously prove that the free energy or the Bayesian stochastic complexity is asymptotically equal to λ1 log n-(m1-1) log log n+constant, where λ1 is a rational number and m 1 is a natural number. We show that λ1 and m1 are determined by the zero point and its multiplicity of Sato-Bernstein´s polynomial for the average loss function
Keywords :
computational complexity; learning (artificial intelligence); neural nets; Bayesian stochastic complexity; Sato-Bernstein´s polynomial; algebraic analysis; average loss function; learning curve; neural network learning; neural network model; Bayesian methods; Electronic mail; Intelligent networks; Laboratories; Machine learning; Multi-layer neural network; Neural networks; Polynomials; Probability density function; Stochastic processes;
Conference_Titel :
Systems, Man, and Cybernetics, 1999. IEEE SMC '99 Conference Proceedings. 1999 IEEE International Conference on
Conference_Location :
Tokyo
Print_ISBN :
0-7803-5731-0
DOI :
10.1109/ICSMC.1999.814130
