Normalized handwritten digits, automatically scanned from envelopes by the U.S. Postal Service. The original scanned digits are binary and of different sizes and orientations; the images here have been deslanted and size normalized, resulting in 16 x 16 grayscale images (Le Cun et al., 1990). The data are in two gzipped files, and each line consists of the digit id (0-9) followed by the 256 grayscale values (normalized between -1 and 1). There are 7291 training observations and 2007 test observations, distributed as follows: 0 1 2 3 4 5 6 7 8 9 Total Train 1194 1005 731 658 652 556 664 645 542 644 7291 Test 359 264 198 166 200 160 170 147 166 177 2007 or as proportions: 0 1 2 3 4 5 6 7 8 9 Train 0.16 0.14 0.1 0.09 0.09 0.08 0.09 0.09 0.07 0.09 Test 0.18 0.13 0.1 0.08 0.10 0.08 0.08 0.07 0.08 0.09 The test set is notoriously "difficult", and a 2.5% error rate is excellent. These data were kindly made available by the neural network group at AT&T research labs (thanks to Yann Le Cunn).