Improved hardness amplification in NP

We study the problem of hardness amplification in . We prove that if there is a balanced function in such that any circuit of size s(n)=2Ω(n) fails to compute it on a fraction of inputs, then there is a function in such that any circuit of size s′(n) fails to compute it on a 1/2−1/s′(n) fraction of inputs, with s′(n)=2Ω(n2/3). This improves the result of Healy et al. (STOC’04), which only achieves s′(n)=2Ω(n1/2) for the case with s(n)=2Ω(n).