  Human reasoning can distill principles from observed patterns and generalize
them to explain and solve novel problems. The most powerful artificial
intelligence systems lack explainability and symbolic reasoning ability, and
have therefore not achieved supremacy in domains requiring human understanding,
such as science or common sense reasoning. Here we introduce deep distilling, a
machine learning method that learns patterns from data using explainable deep
learning and then condenses it into concise, executable computer code. The
code, which can contain loops, nested logical statements, and useful
intermediate variables, is equivalent to the neural network but is generally
orders of magnitude more compact and human-comprehensible. On a diverse set of
problems involving arithmetic, computer vision, and optimization, we show that
deep distilling generates concise code that generalizes out-of-distribution to
solve problems orders-of-magnitude larger and more complex than the training
data. For problems with a known ground-truth rule set, deep distilling
discovers the rule set exactly with scalable guarantees. For problems that are
ambiguous or computationally intractable, the distilled rules are similar to
existing human-derived algorithms and perform at par or better. Our approach
demonstrates that unassisted machine intelligence can build generalizable and
intuitive rules explaining patterns in large datasets that would otherwise
overwhelm human reasoning.
