Much of the recent advancement in machine learning has been driven by the capability of machine learning systems to process and learn from very large data sets using very complicated models. Continuing to scale data up in this way presents a computational challenge, as power, memory, and time are all factors that limit performance. One popular approach to address these issues is low-precision arithmetic in which a lower-precision number is used to improve these systems metrics—although possibly at the cost of some accuracy. In this talk, I will discuss some recent methods from my lab that use numerical precision for ML tasks, while the same time trying to understand its effects theoretically.