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Mikolov et al. [1] report that doubling the amount of training data results in an increase in computational complexity equivalent to doubling the number of vector dimensions. Altszyler and coauthors (2017) studied Word2vec performance in two semantic tests for different corpus size. [29]
In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144 ...
In formal language theory, weak equivalence of two grammars means they generate the same set of strings, i.e. that the formal language they generate is the same. In compiler theory the notion is distinguished from strong (or structural) equivalence, which additionally means that the two parse trees [clarification needed] are reasonably similar in that the same semantic interpretation can be ...
The columns of A span the column space, but they may not form a basis if the column vectors are not linearly independent. Fortunately, elementary row operations do not affect the dependence relations between the column vectors. This makes it possible to use row reduction to find a basis for the column space. For example, consider the matrix