It's true that the number of topics is a free parameter of LDA. Yet, maybe unavoidable if we want to tweak between just looking at similar words vs at very coar

It's true that the number of topics is a free parameter of LDA. Yet, maybe unavoidable if we want to tweak between just looking at similar words vs at very coarse patterns. For document similariaty tools typically does not be that subtle as for analogy tasks. Thank you for pointing to your research/tools anyway. :) And well, word2vec/GloVe are by no means the end of story - just a simple baseline.