A method of increasing processing speed and decreasing digital storage consumption in performing neural network training utilizing one or more computing devices, the method comprising: performing, with the one or more computing devices, a forward propagation of the neural network training that receives, as input, a first set of weight values in a first reduced-precision format and a first set of activation values in the first reduced-precision format, and that outputs, into storage, a second set of activation values in the first reduced-precision format; performing, with the one or more computing devices, a backpropagation of the neural network training that receives, as input, a first set of weight values in the first reduced-precision format, a first set of error values in the first reduced-precision format and the first set of activation values in the first reduced-precision format, and that outputs, into storage, a first set of gradient values in the first reduced-precision format and a second set of error values in the first reduced-precision format; and performing, with the one or more computing devices, a weight update of the neural network training utilizing (1040, 1135) a first set of weight values in a full-precision format and a first set of gradient values in the full-precision format, the performing the weight update resulting in a storage (1060, 1160) of a second set of weight values in the reduced-precision format; wherein the forward propagation and the backpropagation comprise performing bounding box quantization on input values (1010, 1070), the bounding box quantization converting values expressed utilizing different exponents to values expressed utilizing a common exponent, the values expressed utilizing the common exponent comprising only an identification of the common exponent, instead of the common exponent itself, the identification of the common exponent consuming fewer bits than the common exponent itself. performing, with the one or more computing devices, a forward propagation of the neural network training that receives, as input, a first set of weight values in a first reduced-precision format and a first set of activation values in the first reduced-precision format, and that outputs, into storage, a second set of activation values in the first reduced-precision format; performing, with the one or more computing devices, a backpropagation of the neural network training that receives, as input, a first set of weight values in the first reduced-precision format, a first set of error values in the first reduced-precision format and the first set of activation values in the first reduced-precision format, and that outputs, into storage, a first set of gradient values in the first reduced-precision format and a second set of error values in the first reduced-precision format; and performing, with the one or more computing devices, a weight update of the neural network training utilizing (1040, 1135) a first set of weight values in a full-precision format and a first set of gradient values in the full-precision format, the performing the weight update resulting in a storage (1060, 1160) of a second set of weight values in the reduced-precision format; wherein the forward propagation and the backpropagation comprise performing bounding box quantization on input values (1010, 1070), the bounding box quantization converting values expressed utilizing different exponents to values expressed utilizing a common exponent, the values expressed utilizing the common exponent comprising only an identification of the common exponent, instead of the common exponent itself, the identification of the common exponent consuming fewer bits than the common exponent itself.