Machine learning is enhanced by efficiently updating a weight that is represented as a conductivity of a resistive processing unit (RPU) that is connected between a row wire and a column wire. The weight is updated by the RPU interacting with bit streams carried on the row and column wires. Efficiency of the update is enhanced by calculating a bit length for the bit streams as a function of factors that include learning rate η, maximum activity xmax, maximum error differential δmax, and minimum weight update increment Δwmin.