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We onsider a fundamental problem in omputational learning theory: learning an arbitrary Boolean fun tion that depends on an unknown set of k out of n Boolean variables. We give an algorithm for learning su h fun tions from uniform random examples that runs in time roughly (n k ) ! !+1 ; where ! < 2:376 is the matrix multipli ation exponent. We thus obtain the rst polynomial fa tor improvement on the naive n k time bound whi h an be a hieved via exhaustive sear h. Our algorithm and analysis exploit new stru tural properties of Boolean fun tions.