TCB Publications - Abstract

K.-R. Müller, M. Finke, N. Murata, K. Schulten, and S. Amari. Large scale simulations for learning curves. In Jong-Hoon Oh, Chulan Kwon, and Sungzoon Cho, editors, Progress in neural Processing Vol. 1 / Neural Networks: The Statistical Mechanics Perspective, pp. 73-84. World Scientific, Singapore, 1995.

MULL95 The universal asymptotic scaling laws proposed by Amari et al. $\_{2, 11}$ are studied in large scale simulations using a CM5. Small stochastic feed-forward networks trained with back-propagation and conjugate gradient descent are investigated. In the range of a large number of training patterns t, the predicted asymptotic 1/t scaling is observed. For a medium range t a faster scaling in the number of training patterns t than 1/t is observed. This effect is explained by using higher order corrections of the likelihood expansion. For small t it is shown, that the scaling law changes drastically, when the network undergoes a transition from permutation symmetric to permutation symmetry broken phase. This effect is related to previous theoretical work $ \_{15, 3,17,16, 8}$.

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