Fig. 8. Discovering and using a cross-language metatheory.

a Re-solving the hardest textbook problems using the learned fragment grammar metatheory leads to an average of 31% more of the problem being solved. b illustrates a case where these discovered tendencies allow the model to find a set of six interacting rules solving the entirety of an unusually complex problem. c The metatheory comprises rule schemas that are human understandable and often correspond to motifs previously identified within linguistics. Left column shows four out of 21 induced rule schemas (Supplementary Fig. 6), which encode cross-language tendencies. These learned schemas include vowel harmony and spirantization (a process where stops become fricatives near vowels). The symbol FM means a slot that can hold any feature matrix, and trigger means a slot that can hold any rule triggering context. Middle column shows model output when solving each language in isolation: these solutions can be overly specific (Koasati, Bukusu), overly general (Kerewe, Turkish), or even essentially unrelated to the correct generalization (Tibetan). Right column shows model output when solving problems jointly with inferring a metatheory. Source data are provided as a Source Data file.