Past work probing compositionality in sentence embedding models faces issues determining the causal impact of implicit syntax representations. Given a sentence, we construct a neural module net based on its syntax parse and train it end-to-end to approximate the sentence's embedding generated by a transformer model. The distillability of a transformer to a Syntactic NeurAl Module Net (SynNaMoN) then captures whether syntax is a strong causal model of its compositional ability. Furthermore, we address questions about the geometry of semantic composition by specifying individual SynNaMoN modules' internal architecture & linearity. We find differences in the distillability of various sentence embedding models that broadly correlate with their performance, but observe that distillability doesn't considerably vary by model size. We also present preliminary evidence that much syntax-guided composition in sentence embedding models is linear, and that non-linearities may serve primarily to handle non-compositional phrases.
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