  Artificial Neural Networks are powerful function approximators capable of
modelling solutions to a wide variety of problems, both supervised and
unsupervised. As their size and expressivity increases, so too does the
variance of the model, yielding a nearly ubiquitous overfitting problem.
Although mitigated by a variety of model regularisation methods, the common
cure is to seek large amounts of training data---which is not necessarily
easily obtained---that sufficiently approximates the data distribution of the
domain we wish to test on. In contrast, logic programming methods such as
Inductive Logic Programming offer an extremely data-efficient process by which
models can be trained to reason on symbolic domains. However, these methods are
unable to deal with the variety of domains neural networks can be applied to:
they are not robust to noise in or mislabelling of inputs, and perhaps more
importantly, cannot be applied to non-symbolic domains where the data is
ambiguous, such as operating on raw pixels. In this paper, we propose a
Differentiable Inductive Logic framework, which can not only solve tasks which
traditional ILP systems are suited for, but shows a robustness to noise and
error in the training data which ILP cannot cope with. Furthermore, as it is
trained by backpropagation against a likelihood objective, it can be hybridised
by connecting it with neural networks over ambiguous data in order to be
applied to domains which ILP cannot address, while providing data efficiency
and generalisation beyond what neural networks on their own can achieve.
