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Geoff Hinton refers to thought vectors performing reasoning by analogy using algebra [1] in his Royal Society Lecture.

The other widely reported vector algebras in a semantic space were discovered by Mikolov et al when producing ~300 dimensional vectors for a billion word Wikipedia corpus.

If one performs vector algebra and ~= is near by cosine distance then using Mikolov's Vectors[3].

King - Man + Woman ~= Queen

France - Paris + Gernmany ~= Berlin

Surprisingly this works for other modalities, Chintala, Radford & Metz found a latent semantic space in images, that adds vectors for glasses or smiles to peoples faces. [4] With a generative model new images can be created as outlined in this blog post by Soumith [5]

Karpathy shows trained nets can be assembled like lego across modalities, slice off the classifier to reveal the rich semantic 'thought vector' layer of an Imagenet trained Alexnet, plug in a RNN sentence generator using word2vec and ( some over simplification ... ) you get a convincing image captioner [6].

The thought vectors are akin to high level representations of the world and can cross modalities . Text to Images using thought Vectors ( from hnnews discussion [7] )

So the vectors of though are in some way a an AI mentalese or encoding of a symbolic representation of the world derived from the data and can ( again drastic over simplification ) transfer modalities and even between previously unlinked languages [8]

Also see Anything2Vec…