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This Algorithm Can Tell Which Number Sequences a Human Will Find Interesting


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An interesting property of Pascal's Triangle is that its diagonals sum to the Fibonacci sequence (the list at right).

An IBM researcher constructed a machine learning algorithm that can spot specific patterns in mathematical structures and apply them to extract interesting sequences from randomly generated ones.

Credit: Maplesoft.com

Chai Wah Wu at IBM's T.J. Watson Research Center in New York has constructed a machine learning algorithm that can spot specific patterns in mathematical structures and apply them to extract interesting sequences from randomly generated ones.

The method employs the Online Encyclopedia of Integer Sequences (OEIS), which currently houses about 300,000 sequences.

The technique hinges on Wu's notion of finding empirical laws that function as measures of "interestingness" that could differentiate interesting sequences from uninteresting ones.

Wu says he quantified how well Benford's Law predicts the distribution of first digits in 40,000 sequences randomly selected from the OEIS, and the outcomes demonstrated "that many, but not all, sequences satisfy to some degree Benford's Law."

A second experiment involved producing 40,000 sequences of random integers and adding them to the 40,000 chosen from the OEIS, and then training the algorithm to spot OEIS sequences using Benford's Law and Taylor's Law, which it did with 0.999 accuracy and 0.9984 precision.

From Technology Review
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