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]
[2] The paper Geoff Hinton is reffering to : Sequence to Sequence Learning with Neural Networks by Ilya Sutskever, Oriol Vinyals, Quoc V. Le https://arxiv.org/abs/1409.3215
[3] Efficient Estimation of Word Representations in Vector Space by Tomas Mikolov, Kai Chen, Greg Corrado, Jeffrey Dean
https://arxiv.org/abs/1301.3781
[4] Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks
Alec Radford, Luke Metz, Soumith Chintala https://arxiv.org/abs/1511.06434
https://github.com/Newmu/dcgan_code/raw/master/images/faces_...