Amplifying Local Efforts to Root out Terror Act of 2016 (H.R. 4401)This bill authorizes the Department of Homeland Security (DHS) to provide training at state and major urban area fusion centers for the purpose of administering community awareness briefings and related activities in furtherance of its efforts to counter violent extremism, identify and report suspicious activities, and increase awareness of and more quickly identify terrorism threats, including the travel or attempted travel of individuals from the United States to support a foreign terrorist organization abroad. (A "fusion center" serves as a focal point within the state and local environment for the receipt, analysis, gathering, and sharing of threat-related information between the federal government and state, local, tribal, territorial and private sector partners.)