Very interesting.
Can a language define all it's concepts with language alone? I.e
Can a language map all it's concepts to words and other concepts defined by just words.
Is there some sort of Godel's incompleteness theorem for language?
Can a language map all it's concepts to words and other concepts defined by just words.
Is there some sort of Godel's incompleteness theorem for language?
I don't see why natural language would have this property. It is certainly possible to construct codes such that the distribution over codewords does not have this property.
I'm amazed that what the paper shows even works.
Can you think of one in english (or your native language)? You won't find it in any dictionary, since all those words have descriptions in terms of other words.
I would have thought that they needed to 'ground' (https://en.wikipedia.org/wiki/Symbol_grounding_problem) at least one shared reference word/concept so they could proceed to define everything relative to that and thereby communicate effectively and know how to map different languages to the same latent space. But I guess perhaps one can infer/approximate it statistically -- https://cis.upenn.edu/~ccb/publications/discriminative-bilin...