Before revision:  These match corresponding positive results using upper bounds on the threshold or approximate degree in the SQ model for PAC or agnostic learning , and in this sense our results show that the polynomial method is a universal, best-possible approach for distribution-free CSQ learning. Our results imply the first exponential (in the dimension) CSQ lower bounds for PAC learning intersections of two halfspaces and constant depth circuits as well as the first exponential lower bounds for agnostically learning conjunctions and halfspaces .
After revision:  These match corresponding positive results using upper bounds on the threshold or approximate degree in the SQ model for PAC or agnostic learning . Many of these results were implicit in earlier works of Feldman and Sherstov .