In this paper, we extend the proof framework of direct product theorem based on samplers by [Impagliazzo, Jaiswal, Kabanets, Wigderson, SICOMP2010] to amplify the hardness of a wide variety of natural problems including planted clique, matrix multiplication, online matrix-vector multiplication, and triangle counting. This improves and significantly simplifies previous techniques of hardness self-amplification of [Asadi, Golovnev, Gur, Shinker, STOC22][Hirahara, Shimizu, FOCS22].

June 23, 2023