Computationally efficient softmax loss gradient backpropagation

Abstract

A computation unit comprises first, second, and third circuits. The first circuit traverses gradient loss elements gand normalized output elements pand produces an accumulation C. The accumulation C is produced by element-wise multiplying the gradient loss elements gwith the corresponding normalized output elements pand summing the results of the element-wise multiplication. The second circuit, operatively coupled to the first circuit, element-wise subtracts the accumulation C from each of the gradient loss elements gand produces modulated gradient loss elements g. The third circuit, operatively coupled to the second circuit, traverses the modulated gradient loss elements gand produces gradient loss elements gfor a function preceding the softmax function. The gradient loss elements gare produced by element-wise multiplying the modulated gradient loss elements gwith the corresponding normalized output elements p.