  Standard Neural Networks can learn mathematical operations, but they do not
extrapolate. Extrapolation means that the model can apply to larger numbers,
well beyond those observed during training. Recent architectures tackle
arithmetic operations and can extrapolate; however, the equally important
problem of quantitative reasoning remains unaddressed. In this work, we propose
a novel architectural element, the Neural Status Register (NSR), for
quantitative reasoning over numbers. Our NSR relaxes the discrete bit logic of
physical status registers to continuous numbers and allows end-to-end learning
with gradient descent. Experiments show that the NSR achieves solutions that
extrapolate to numbers many orders of magnitude larger than those in the
training set. We successfully train the NSR on number comparisons, piecewise
discontinuous functions, counting in sequences, recurrently finding minimums,
finding shortest paths in graphs, and comparing digits in images.
