Computationally Efficient Softmax Loss Gradient Backpropagation

A computation unit comprises first, second, and third circuits. The first circuit traverses gradient loss elements gpn and normalized output elements pn and produces an accumulation C. The accumulation C is produced by element-wise multiplying the gradient loss elements gpn with the corresponding normalized output elements pn and 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 gpn and produces modulated gradient loss elements gpn′. The third circuit, operatively coupled to the second circuit, traverses the modulated gradient loss elements gpn′ and produces gradient loss elements gxn for a function preceding the softmax function. The gradient loss elements gxn are produced by element-wise multiplying the modulated gradient loss elements gpn′ with the corresponding normalized output elements pn.