that person's description is unnecessarily jargony. sparse tensor just means vector that's mostly zero and has some ones. take your corpus of concepts and number them 0 to n-1. then each word you want to turn into a vec turns into a vector that has ones for concepts it's associated with and 0 elsewhere. learning that association is what word2vec does.

Not specifically. You can look at the literature for ontology, relation networks, semantic databases, reasoning.

The video that made me clicked, was https://www.ted.com/talks/ajit_narayanan_a_word_game_to_comm... It depicts in a game to help autistic children better communicate, a simple order-independent language representation, which is isomorphic to graphs.

If you do the math, you see that some triplets query like (queen, subclass, ?) is just a point-wise multiplication with the knowledge database sparse tensor in this sparse boolean tensor representation (the ? is a column of 1). Then it's just chaining requests.

A graph of triplet is isomorphic to a boolean tensor of dimension (nbSubjects, nbRelations, nbObjects).