Suppose you are playing football. The ball arrives at your feet, and you decide to pass it to the unmarked striker. What seems like one simple action requires two different kinds of thought.

First, you recognise that there is a football at your feet. This recognition requires intuitive perceptual thinking - you cannot easily articulate how you come to know that there is a ball at your feet, you just see that it is there. Second, you decide to pass the ball to a particular striker. This decision requires conceptual thinking. Your decision is tied to a justification - the reason you passed the ball to the striker is because she was unmarked.

The distinction is interesting to us because these two types of thinking correspond to two different approaches to machine learning: deep learning and symbolic program synthesis. Deep learning concentrates on intuitive perceptual thinking whereas symbolic program synthesis focuses on conceptual, rule-based thinking. Each system has different merits - deep learning systems are robust to noisy data but are difficult to interpret and require large amounts of data to train, whereas symbolic systems are much easier to interpret and require less training data but struggle with noisy data. While human cognition seamlessly combines these two distinct ways of thinking, it is much less clear whether or how it is possible to replicate this in a single AI system.

Our new paper, recently published in JAIR, demonstrates it is possible for systems to combine intuitive perceptual with conceptual interpretable reasoning. The system we describe, ∂ILP, is robust to noise, data-efficient, and produces interpretable rules.