Features are disclosed for reducing the dynamic range of an approximated trained artificial neural network weight matrix in an automatic speech recognition system. The weight matrix may be approximated as two low-rank matrices using a decomposition technique. This approximation technique may insert an additional layer between the two original layers connected by the weight matrix. The dynamic range of the low-rank decomposition may be reduced by applying the square root of singular values, combining them with both low-rank matrices, and utilizing a random rotation matrix to further compress the low-rank matrices. Reduction of dynamic range may make fixed point scoring more effective due to smaller quantization error, as well as make the neural network system more favorable for retraining after approximating a neural network weight matrix. Features are also disclosed for adjusting the learning rate during retraining to account for the low-rank approximations.