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A longstanding debate in semiotics centers on the relationship between linguistic signs and their corresponding semantics: is there an arbitrary relationship between a word form and its meaning, or does some systematic phenomenon pervade? For instance, does the character bigram \textit{gl} have any systematic relationship to the meaning of words like \textit{glisten}, \textit{gleam} and \textit{glow}? In this work, we offer a holistic quantification of the systematicity of the sign using mutual information and recurrent neural networks. We employ these in a data-driven and massively multilingual approach to the question, examining 106 languages. We find a statistically significant reduction in entropy when modeling a word form conditioned on its semantic representation. Encouragingly, we also recover well-attested English examples of systematic affixes. We conclude with the meta-point: Our approximate effect size (measured in bits) is quite small---despite some amount of systematicity between form and meaning, an arbitrary relationship and its resulting benefits dominate human language.

Meaning to Form: Measuring Systematicity as Information