Deep Machine Learning (DML) algorithms have proven to be highly successful at challenging, high-dimensional learning problems, but their widespread deployment is limited by their heavy computational requirements and the associated power consumption. Analog computational circuits offer the potential for large improvements in power efficiency, but noise, mismatch, and other effects cause deviations from ideal computations. In this paper we describe circuits useful for DML algorithms, including a tunable-width bump circuit and a configurable distance calculator. We also discuss the impacts of computational errors on learning performance. Finally we will describe a complete deep learning engine implemented using current-mode analog circuits and compare its performance to digital equivalents.