This paper presents evidence for the idea that much of artificial intelligence, human perception and cognition, mainstream computing, and mathematics, may be understood as compression of information via the matching and unification of patterns. This is the basis for the "SP theory of intelligence", outlined in the paper and fully described elsewhere. Relevant evidence may be seen: in empirical support for the SP theory; in some advantages of information compression (IC) in terms of biology and engineering; in our use of shorthands and ordinary words in language; in how we merge successive views of any one thing; in visual recognition; in binocular vision; in visual adaptation; in how we learn lexical and grammatical structures in language; and in perceptual constancies. IC via the matching and unification of patterns may be seen in both computing and mathematics: in IC via equations; in the matching and unification of names; in the reduction or removal of redundancy from unary numbers; in the workings of Post's Canonical System and the transition function in the Universal Turing Machine; in the way computers retrieve information from memory; in systems like Prolog; and in the query-by-example technique for information retrieval. The chunking-with-codes technique for IC may be seen in the use of named functions to avoid repetition of computer code. The schema-plus-correction technique may be seen in functions with parameters and in the use of classes in object-oriented programming. And the run-length coding technique may be seen in multiplication, in division, and in several other devices in mathematics and computing. The SP theory resolves the apparent paradox of "decompression by compression". And computing and cognition as IC is compatible with the uses of redundancy in such things as backup copies to safeguard data and understanding speech in a noisy environment.
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