Scaling properties in neural network learning

Working definitions of learning and learners are examined from the scaling point of view. A back-error propagation neural network was trained to plot sin (x) given an input x (-π ⩾ x ⩾ π). The parameters for the simulation are the following: input-output (pattern) pairs=200; input units=1; hidden units=20; output units=1; learning rates=0.1; momentum term constant=0.2; weights and thresholds set to random values between [-1, 1]; number of trials where input samples were randomly selected=8585. The performance curve consists of the cumulated number of errors less than 0.1 in absolute value vs trial number. It is noted that the scaling exponent ranges from a value of 0.34 in the lower decade (10-100) to 0.66 in the upper decade (1000-10000), reflecting the heterogeneities in scaling along the training process