Learning Explanatory Rules from Noisy Data

TL;DR

This paper introduces a Differentiable Inductive Logic framework that combines neural networks and logic programming to handle noisy data, enabling data-efficient reasoning in ambiguous and non-symbolic domains.

Contribution

It presents a novel differentiable logic system that is robust to noise and can be integrated with neural networks for improved reasoning on complex data.

Findings

Demonstrates robustness to noisy and mislabeled data.

Achieves better generalization than pure neural network models.

Enables reasoning in non-symbolic, ambiguous data domains.

Abstract

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.