Various embodiments include methods and neural network computing devices implementing the methods, for generating an approximation neural network. Various embodiments may include performing approximation operations on a weights tensor associated with a layer of a neural network to generate an approximation weights tensor, determining an expected output error of the layer in the neural network due to the approximation weights tensor, subtracting the expected output error from a bias parameter of the layer to determine an adjusted bias parameter and substituting the adjusted bias parameter for the bias parameter in the layer. Such operations may be performed for one or more layers in a neural network to produce an approximation version of the neural network for execution on a resource limited processor.