  Conventional Neural Networks can approximate simple arithmetic operations,
but fail to generalize beyond the range of numbers that were seen during
training. Neural Arithmetic Units aim to overcome this difficulty, but current
arithmetic units are either limited to operate on positive numbers or can only
represent a subset of arithmetic operations. We introduce the Neural Power Unit
(NPU) that operates on the full domain of real numbers and is capable of
learning arbitrary power functions in a single layer. The NPU thus fixes the
shortcomings of existing arithmetic units and extends their expressivity. We
achieve this by using complex arithmetic without requiring a conversion of the
network to complex numbers. A simplification of the unit to the RealNPU yields
a highly transparent model. We show that the NPUs outperform their competitors
in terms of accuracy and sparsity on artificial arithmetic datasets, and that
the RealNPU can discover the governing equations of a dynamical system only
from data.
