Title: Bit-Regularized Optimization of Neural Nets. Abstract: We present a novel regularization strategy for training neural networks which we call ``BitNet''. The parameters of neural networks are usually unconstrained and have a dynamic range dispersed over a real valued range. Our key idea is to control the expressive power of the network by dynamically quantizing the range and set of values that the parameters can take. We formulate this idea using a novel end-to-end approach  that regularizes a typical classification loss function. Our regularizer is inspired by the Minimum Description Length (MDL) principle. For each layer of the network, our approach optimizes a translation and scaling factor along with integer-valued parameters. We empirically compare BitNet to an equivalent unregularized model on the MNIST and CIFAR-10 datasets. We show that BitNet converges faster to a superior quality solution. Additionally, the resulting model is significantly smaller in size due to the use of integer instead of floating-point parameters.