  Reduced numerical precision is a common technique to reduce computational
cost in many Deep Neural Networks (DNNs). While it has been observed that DNNs
are resilient to small errors and noise, no general result exists that is
capable of predicting a given DNN system architecture's sensitivity to reduced
precision. In this project, we emulate arbitrary bit-width using a specified
floating-point representation with a truncation method, which is applied to the
neural network after each batch. We explore the impact of several model
parameters on the network's training accuracy and show results on the MNIST
dataset. We then present a preliminary theoretical investigation of the error
scaling in both forward and backward propagations. We end with a discussion of
the implications of these results as well as the potential for generalization
to other network architectures.
