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’.