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> Why should it not be possible to solve this with statistical methods?

Doing just that for 10 years, beating hand-coded systems: https://www-nlp.stanford.edu/pubs/SocherLinNgManning_ICML201... [pdf]

> I would guess that most modern NNs from the NLP area (Transformer or LSTM) would be able to correctly differentiate the meaning.

Yes. See demos like: https://demo.allennlp.org/constituency-parsing/MTczNjYyNA== and https://demo.allennlp.org/dependency-parsing/MTczNjYyNg==

> I think there is no fancy NN (yet) behind Google search,

During the deep learning boom, Google made a huge push towards NN-based NLP. SEO's and their PR calls their efforts collectively RankBrain: https://en.wikipedia.org/wiki/RankBrain

I think we are on the cusp of combining symbolical/logical operations over the vectors produced by Neural Networks (or at least, major effort there). Could be by neatly tying up all these different NN-based NLP modules (parsing, semantic distance, knowledge bases, ...) with another set of decision layers stacked on top.



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