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U elx raw. ;c d) workingasacontinuous,differentiableapproximationtoargmaxis defined g j= log( loge ) wheree ˘U(0;1) c j = exp g jlogp(x) P d j=1 exp g. J x P c l=1 e >. SIMPLE = T / Java FITS Wed Mar 14 1349 EST 07 BITPIX = 16 / Bits per pixel NAXIS = 2 / number of axes NAXIS1 = 1072 / Axis length NAXIS2 = 1024.

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(5) where 1fg is an indicator function, whose value is 1 if the expression is true, otherwise 0 Once the model is trained, one can compute the probability of instance xbelonging to a label jusing Eq (4), and assign its class label as y= max j e >. L x i 1 A;. SIMPLE = T / Standard FITS file BITPIX = 16 / IEEE 2byte scaled integer NAXIS = 2 / Number of image dimensions NAXIS1 = 1600 / Size of 1st dimension in pixels NAXIS2 = 10.

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