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The permutation symmetry of the hidden units in multilayer perceptrons causesthe saddle structure and plateaus of the learning dynamics in gradient learningmethods. The correlation of the weight vectors of hidden units in a teachernetwork is thought to affect this saddle structure, resulting in a prolongedlearning time, but this mechanism is still unclear. In this paper, we discussit with regard to soft committee machines and on-line learning usingstatistical mechanics. Conventional gradient descent needs more time to breakthe symmetry as the correlation of the teacher weight vectors rises. On theother hand, no plateaus occur with natural gradient descent regardless of thecorrelation for the limit of a low learning rate. Analytical results supportthese dynamics around the saddle point.Comment: 7 pages, 6 figure

On-Line Learning Theory of Soft Committee Machines with Correlated Hidden Units –Steepest Gradient Descent and Natural Gradient Descent–