User:Jeblad/Minicolumns as a language


 * Subpages for Jeblad
 * My original note from nowiki.

Assume there is a language \mathcal{L}, organized as a 2-dimensional map, indexed by i and j, such that


 * $$\mathcal{L} = \left \{ f^{[i,j]}(\cdot), \mathbf{x}^{[i,j]}_{k}, \mathbf{y}^{[i,j]}_{k}, \right \}$$
 * [This has no natural zero-element]

where


 * is a function that takes an input and transforms it into an output, like $$f(x) \to y$$
 * and are high-dimensional vectors, organized as a sequence, indexed by k

The vectors \mathbf{x} and \mathbf{y} can also be viewed as the maps themselves, that is as 2-dimensional lists of values, but a vector notation is somewhat easier to explain and process as it is strickingly similar to the kind of vector produced by a word2vec or a rdf2vec. The vectors \mathbf{x} and \mathbf{y}, together with the function f(x) \to y, can be viewed as a subject – predicate – object triplet. Thus by processing the input vector with the function we relate the input to the output vector.