Advancing Development of AI Processes and Talent Act or the ADAPT Act This bill modifies the Department of Defense (DOD) public-private talent exchange program under which DOD and private sector employees exchange duties. It requires that an agreement under such program must specify that DOD employees may not improperly use information that relates to a DOD acquisition or procurement for the benefit or advantage of the private-sector organization. DOD must ensure that the authority for operating a public-private talent exchange program is used to exchange personnel working on artificial intelligence applications. DOD must brief the congressional armed services committees on efforts to expand existing DOD public-private exchange programs and to ensure that such programs seek opportunities for exchanges with private sector entities working on artificial intelligence applications.