Standard human IQ tests often require test-takers to interpret perceptually simple visual scenes by applying principles that they have learned through everyday experience. For example, human test-takers may have already learned about ‘progressions’ (the notion that some attribute can increase) by watching plants or buildings grow, by studying addition in a mathematics class, or by tracking a bank balance as interest accrues. They can then apply this notion in the puzzles to infer that the number of shapes, their sizes, or even the intensity of their colour will increase along a sequence.

We do not yet have the means to expose machine learning agents to a similar stream of ‘everyday experiences’, meaning we cannot easily measure their ability to transfer knowledge from the real world to visual reasoning tests. Nonetheless, we can create an experimental set-up that still puts human visual reasoning tests to good use. Rather than study knowledge transfer from everyday life to visual reasoning problems (as in human testing), we instead studied knowledge transfer from one controlled set of visual reasoning problems to another.

To achieve this, we built a generator for creating matrix problems, involving a set of abstract factors, including relations like ‘progression’ and attributes like ‘colour’ and ‘size’. While the question generator uses a small set of underlying factors, it can nonetheless create an enormous number of unique questions.

Next, we constrained the factors or combinations available to the generator to create different sets of problems for training and testing our models, to measure how well our models can generalise to held-out test sets. For instance, we created a training set of puzzles in which the progression relation is only encountered when applied to the colour of lines, and a test set when it is applied to the size of shapes. If a model performs well on this test set, it would provide evidence for an ability to infer and apply the abstract notion of progression, even in situations in which it had never previously seen a progression.