High-Dimensional Computing

The difference between traditional computing and highdimensional computing is apparent in the elements that the computer computes with. In traditional computing the elements are Booleans, numbers, and memory pointers. In HD computing they are multicomponent vectors, or tuples, where neither individual component nor a subset thereof has a specific meaning: a component of a vector and the entire vector represent the same thing. Furthermore, the vectors are wide: the number of components is in the thousands.

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RAHIMI, Abbas, DATTA, Sohum, KLEYKO, Denis, FRADY, Edward Paxon, OLSHAUSEN, Bruno, KANERVA, Pentti and RABAEY, Jan M., 2017. High-Dimensional Computing as a nanoscalable paradigm. IEEE Transactions on Circuits and Systems I: Regular Papers. 2017. Vol. 64, no. 9, p. 2508–2521. ieee [Accessed 4 March 2024]. doi

We will demonstrate the idea with a simple example from language [4]. The task is to Identify the Language of a Sentence from its three-letter sequences called trigrams. We compare the trigram profile of the sentence to the trigram profiles of 21 languages and chose the language with the most similar profile. A Profile is essentially a histogram of trigram frequencies in the text in question.

[4] A. Joshi, J. T. Halseth, and P. Kanerva, “Language geometry using random indexing,” in Proc. 10th Int. Conf., Quant. Interact., San Francisco, CA, USA, Jul. 2016, pp. 265–274. doi pdf