Inductive logic programming at 30

Hypothesizing an algorithm from one example: the role of specificity

Statistical machine learning usually achieves high-accuracy models by employing tens of thousands of examples. By contrast, both children and adult humans typically learn new concepts from either one or a small number of instances. The high data efficiency of human learning is not easily explained in terms of standard formal frameworks for machine learning, including Gold's learning-in-the-limit framework and Valiant's probably approximately correct (PAC) model. This paper explores ways in which this apparent disparity between human and machine learning can be reconciled by considering algorithms involving a preference for specificity combined with program minimality. It is shown how this can be efficiently enacted using hierarchical search based on identification of certificates and push-down automata to support hypothesizing compactly expressed maximal efficiency algorithms. Early results of a new system called DeepLog indicate that such approaches can support efficient top-down construction of relatively complex logic programs from a single example. This article is part of a discussion meeting issue 'Cognitive artificial intelligence'.

$$\alpha$$ILP: thinking visual scenes as differentiable logic programs

Deep neural learning has shown remarkable performance at learning representations for visual object categorization. However, deep neural networks such as CNNs do not explicitly encode objects and relations among them. This limits their success on tasks that require a deep logical understanding of visual scenes, such as Kandinsky patterns and Bongard problems. To overcome these limitations, we introduce $$\alpha {\textit{ILP}}$$ α ILP , a novel differentiable inductive logic programming framework that learns to represent scenes as logic programs—intuitively, logical atoms correspond to objects, attributes, and relations, and clauses encode high-level scene information. $$\alpha$$ α ILP has an end-to-end reasoning architecture from visual inputs. Using it, $$\alpha$$ α ILP performs differentiable inductive logic programming on complex visual scenes, i.e., the logical rules are learned by gradient descent. Our extensive experiments on Kandinsky patterns and CLEVR-Hans benchmarks demonstrate the accuracy and efficiency of $$\alpha {\textit{ILP}}$$ α ILP in learning complex visual-logical concepts.