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Training feed-forward neural networks using conjugate gradients

Neural networks for optical character recognition are still being trained using back propagation, even though conjugate gradient methods have been shown to be much faster. Most multilayer perceptron network training results in the literature are obtained for small and unrealistic problems or from data sets that are proprietary and not available for comparison testing. We present results on a large realistic pattern set containing 2000 training and 1434 testing exemplars. Each pattern is composed of 32 Gabor coefficients obtained from a 32 by 32 pixel binary image of a handwritten digit segmented from the NIST Handwriting Image Data Base. These sets are believed to have approximately 1 segmentation errors. Comparative results for Moller''s scaled conjugate gradient method and for standard back propagation are presented for runs on a serial scientific workstation and a highly parallel computer. Typical training on a network with 32 inputs, 32 hidden nodes, and 10 output nodes gives a 98 recognition for the training set and 95 for the test set. Training with conjugate gradients requires fewer than 200 iterations; times are about 20 to 40 minutes on a scientific workstation and 6 minutes on the highly parallel computer. Testing (classification) is done at the rate of 600 to 1600 patterns per second on the scientific workstation and on the highly parallel computer respectively. These results suggest that commercial handwritten character recognition systems with great economic potential are feasible.