# Neural Status Registers

Neural networks excel at approximating functions and finding patterns in complex and challenging domains. Yet, they fail to learn simple but precise computation. Recent work addressed the ability to add, subtract, and multiply numbers but is lacking a component to drive control flow. True computer intelligence should also be able to decide when to perform what operation. In this paper, we introduce the Neural Status Register (NSR), inspired by physical Status Registers. At the heart of the NSR are arithmetic comparisons between inputs. With theoretically principled changes to physical Status Registers, the NSR allows end-to-end differentiation and learns such comparisons reliably. But the NSR also extrapolates: it generalizes to unseen data distributions. For example, the NSR trains on single digits and correctly predicts numbers that are up to 14 orders of magnitude larger. This suggests that the NSR captures the true underlying arithmetic. In follow-up experiments, we use the NSR to control the computation of a downstream arithmetic unit to learn piecewise functions. We can also learn more challenging tasks through redundancy. Finally, we use the NSR to learn an upstream convolutional neural network to compare images of MNIST digits to decide which image contains the larger digit.

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