I'm working on a computational text analysis project which uses ngram data from journal articles, and I'm trying to find a way to measure some aspect of the semantic "complexity" of the grammar in one subset of the data vs. another. I've mostly tried techniques from the NLP/CS/ML literature, so please let me know if this is not a subject of linguistics proper and is better suited to some other board.
So far, most of the techniques I've considered stem from word embedding models. I've tried measuring "complexity" by exposing the loss function of a word embedding model and seeing how big of an embedding size is needed to account for the majority of the loss. I've also looked into using a "semantic atoms" approach (https://arxiv.org/abs/1601.03764) and proxying "complexity" by the overall level of polysemy in a dataset. Lastly, I've looked into measuring the "intrinsic dimension" of a word embedding space (https://arxiv.org/abs/1804.08838) as a proxy for complexity, with smaller intrinsic dimensions corresponding to simpler grammars.
I'm not sure if any of these is the right way to go about it. Any other ideas for how to measure semantic complexity? I realize that I'm not being entirely clear about what I mean by this term, and that's because I don't really know. I'd know it if I saw it, but the best I can do right now is try to sketch the vague terrain of what I'm looking for. Thanks in advance for any advice.