State-Space Constraints Improve the Generalization of the Differentiable Neural Computer in some Algorithmic Tasks

Abstract: Memory-augmented neural networks (MANNs) can solve algorithmic tasks like sorting. However, they often do not generalize to lengths of input sequences not seen in the training phase. Therefore, we introduce two approaches constraining the state-space of the network controller to improve the generalization to out-of-distribution-sized input sequences: state compression and state regularization. We show that both approaches can improve the generalization capability of a particular type of MANN, the differentiable neural computer (DNC), and compare our approaches to a stateful and a stateless controller on a set of algorithmic tasks. Furthermore, we show that especially the combination of both approaches can enable a pre-trained DNC to be extended post hoc with a larger memory. Thus, our introduced approaches allow to train a DNC using shorter input sequences and thus save computational resources. Moreover, we observed that the capability for generalization is often accompanied by loop structures in the state-space, which could correspond to looping constructs in algorithms.